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TableofContentsIntroduction

WhatisMusicTheory,WhyisItImportantandHowItCanHelpYouMusicReading—isItNecessarytoLearnMusicasaLanguage

Part1.MusicTheoryFundamentalsWhatisaSound,Pitch,Note,TimbreandTone?NotesinMusic

TheNoteCircleOctaveandRegistryRangesMiddleCandStandardPitchOctaveSubdivisionMasterTheIntervals

WhatIsanIntervalinMusic?MusicIntervalsSpelledOutInvertedIntervals(WithIntervalExercise)ChromaticandDiatonicIntervalsAugmentedandDiminishedIntervals

TheBuildingBlocksofMusic—Harmony,MelodyandRhythmWhatMakesaGreatMelody?

TheConceptofRootNote

Part2.MasteringScalesandModesWhatIsaScaleinMusic?TheMasterScaleTypesofScalesMinorPentatonicScale

MinorPentatonicStructureWhatIsaMode?

MajorPentatonicStructureModesoftheMinorPentatonicScale(WithAudioExamples)

MinorPentatonicMode1–MinorPentatonicScaleMinorPentatonicMode2–MajorPentatonicScaleMinorPentatonicMode3MinorPentatonicMode4MinorPentatonicMode5MinorPentatonicModeComparisonCharts

Term“Diatonic”,WhatDoesItMean?

7-NoteDiatonicScales—NaturalMajorandNaturalMinorScale

WhyIsMajorScaletheMostImportantScaletoLearn?UnderstandingMajorScaleStructureNaturalMinorScaleStructureMajorandMinorScale—UnderstandingtheDifferenceFiguringOuttheMajorScaleinAllKeys(MajorScaleExercise)DemystifyingDiatonicModes

ParallelandRelativeModes,ParentScalesandTonalCenter

DiatonicModesSpelledOut(withAudioExamples)IonianModeDorianModePhrygianModeLydianModeMixolydianModeAeolianModeLocrianmodeDiatonicModesComparisonCharts(PlusPMSExercise)

HowtoHearaMode(PracticalExercise)HarmonicMinorScale—HowandWhyWasItDerivedfromtheNaturalMinorScale

HarmonicMinorScaleStructureTheModesoftheHarmonicMinorScale(WithAudioExamples)

HarmonicMinorMode1–Aeolian#7HarmonicMinorMode2–Locrian#6HarmonicMinorMode3–Ionian#5HarmonicMinorMode4–Dorian#4HarmonicMinorMode5–Phrygian#3HarmonicMinorMode6–Lydian#2HarmonicMinorMode7–Mixolydian#1orSuperLocrianHarmonicMinorModesComparisonCharts

MelodicMinorScale—HowandWhyWasItDerivedfromtheHarmonicMinorScaleMelodicMinorScaleStructure

TheModesoftheMelodicMinorScale(WithAudioExamples)

MelodicMinorMode1–Dorian#7MelodicMinorMode2–Phrygian#6MelodicMinorMode3–Lydian#5MelodicMinorMode4–Mixolydian#4MelodicMinorMode5–Aeolian#3MelodicMinorMode6–Locrian#2MelodicMinorMode7–Ionian#1–TheAlteredScaleMelodicMinorScaleComparisonCharts

ScaleOverview—ScaleComparisonChartKeysandKeySignatures

HowtoUnderstandCircleofFifths(andCircleofFourths)

Part3.MastertheChordsWhatisaChord?HowChordsAreBuiltChordTypes(Dyads,Triads,Quadads)andChordQualities

UnderstandingChordQualitiesTriadChords

SuspendedChords7thChords(Quadads)3FundamentalChordQualitiesTheComplexityofExtendedchords(9’s,11’sand13’s)

RulesforLeavingOuttheNotesinExtendedChordsProblemwith11’sAddedToneChords–What’stheDifference

DemystifyingtheAlteredChordsMajorChordAlterationsMinorChordAlterationsDominantChordAlterationsAlterationPossibilitiesandtheUseofb5and#5BorrowedChordsvsAlteredChords–ClassicalvsJazzViewAlteredHarmony–HowAlteredChordsareUsedandWhereDoTheyComeFrom

ChordsBuiltin4thsHowChordsComefromScales

HowtoAnalyzeDiatonicChordsAssemblingDiatonicChords

TransposingfromOneKeytoAnotherChordInversionsandChordVoicings

MajorTriadInversionsMinorTriadInversionsInversionsofDiminishedandAugmentedChordsInversionsof7thsandExtendedChordsHowtoFindRootNotePositioninanInvertedChordSlashChordsVoiceLeadingPolychords

ChordProgressions(Part1)CommonChordProgressionsExtendingandSubstitutingChordProgressionsMovingTonalCenters(TonalCentersVsKeys)WhatIsModulationandHowIsItUsed

ChordArpeggios

Part4.AllAbouttheRhythmTheImportanceofHavingaGoodRhythm

UnderstandingTime,Beat,BarandTempoTimeDivisionsTimeSignaturesExplained

4/4Time6/8TimeHowtoCountin6/8Simple,CompoundandComplexTimeSignaturesTripletsandn-Tuplets

PolyrhythmsandPolymetersAccents,Syncopations,Dynamics,TempoChanges…BuildingBlocksofRhythm—CreateanyRhythmPatternEasily(WithAudioExamples)

4-BarRandomSequenceExercise1AddingSyncopation4-BarRandomSequenceExercise2

Part5.MoreWaysofCreatingMovementinMusicTimbre/ToneDynamicsConsonanceandDissonanceDramaExtendedTechniques

Part6.PuttingMusicalStructuresTogetherWhatisaComposition?ImprovisationasInstantaneousCompositionNoteRelativismHowChordsFunctioninaKey

HowNotesFunctioninaChordTypesofHarmony

TonalHarmonyModalvs.TonalHarmonyPolytonalityAtonalHarmony

QuestionstoPonder

Part7.GoingBeyondtheFoundationsChordProgressions(Part2)ChordSubstitutions

NotChangingtheRootChangingtheRoot

ChordProgressionSubstitutionsChordAdditionChordSubtractionSeriesSubstitutionModalReduction

ModalSubstitutionModalInterchangePolytonalSubstitutionsAWordonChromaticismMoreSubstitutionExamples

ImprovisingOverChordProgressionsChordTonesExtensionsUsingSubstitutionsinSingle-NoteLinesChord-Scales

ChromaticismPolytonalityModalHarmony(Miles,Debussy,Pre-Common-EraMusic)

ModalSubstitutionsModalInterchangeChromaticSlidingPolymodality

AtonalityChromaticPlayingOrnetteColeman–Harmelodics

FreeHarmonyBeyondHarmony,Melody,andRhythmSpiritualityandMusicTheory

ANotefromtheAuthor

OtherBooksbyNicolas

CheatSheet

Introduction

WhatisMusicTheory,WhyisItImportantandHowItCanHelpYouMostofushaveheardofmusictheory.Someofusareimmediatelyexcitedbythesensethatitisforeigntousandbytheideathatthereis,somewhere,abodyofknowledge thatwillmakeusbetterplayers, thatwillmakeusplay likeourheroes.Wemay even be excited by the idea of spending long hours studyingmusic,learningnamesandconcepts,workingtoapplythosethingstoourmusic.Becomingmasters,notjustofourinstrumentsbutofthefieldsofsoundthattheyproduce.

But we may also not be so excited. Music theory may seem miles away—difficult,burdensome,time-consuming.Wemayfeelasthoughwedon’twanttospendyearsofourlifelearningthingsthatmayormaynotturnusintothesortsofmusicianswewanttobe.Wemayhavethesensethatmusictheoryisforthescholars,forthestudentsatUniversities,forthejazzheads,andnotforus.Notfor plain musicians who just want to bleed ourselves a little from ourinstruments. It may even seem as though understanding theory will becounterproductive, since it seems like it will turn something expressive,something visceral, into something plainly understandable. Somethingwe cananalyzeandexplain.

Whateveryourattitudetowardtheoryisthisbookismeanttosaythatyouwillgreatlybenefitfromlearningthefundamentalconceptsofharmony,melody,andrhythm. Far from leeching your affective creativity, learning to think aboutmusicgivesyouaplace todepartfrom,aspaceinwhichtowork.Itamplifiesyour expressive potential in just the sameway that knowing something abouthowtomakefoodamplifiesagoodmeal—whenyouknowwhat to lookforandyouarefamiliaringeneralwiththeaestheticspacethatyou’reworkingin,thatspaceisricheranddeeper.Period.

Andthatiswhattheoryis.Aboveall,itisabodyofideasthathelpsfamiliarizeyouwith theaestheticspaceofmusic. Itdoesn’t tellyouwhatyoumustdo, itonly hones your ear andyour hands so that you can better discoverwhat youwant to do. Theory is harmony, melody and rhythm — the fundamentalstructures of sound that makes it possible for that sound to be organizedmusically.Anditwillmakeyouabetterplayer.

***Theaimofthisbookistohelpyoulearnmusictheoryinastructuredwaythatiseasy to follow and understand. Music theory is universal and applies to allinstruments. Since piano ismusic theory heavily oriented instrument (one canplay as much as 10 notes simultaneously) all key concepts are usually bestexplainedonapianokeyboard—whichIwilldowheneverthereissomethingimportanttodemonstratevisually.Sodon’tworryifyou’renotapianoplayer,you’llseejusthowapplicablemusictheoryisonanyinstrumentandwhyitisanessentialmeansofcommunicationbetweenallkindsofmusicians.

MusicReading—isItNecessarytoLearnMany people associatemusic theorywith readingmusic. And this is becausewhenpeopleteachtheory,mostnotablyinmusicschools,theyoftenteachitonthestaff(thesystemofmusicalsymbols),andusuallytheydothatwithrespecttothepiano.Readingmusiccanhelppeopletounderstandthefundamentalsofharmony,melodyandrhythm,sosomepeoplethink,becauseitgivesusawayofwritingitdown,visualizingit,andcommunicatingitclearly.

If you are interested in learning to read music, then there are many toolsavailableforyoutodoso,butitisworthsayingherethatitisn’tanecessarypartof learning theory.Theory isacollectionof ideas, ideas that interactwithoneanotherandguideourears.Putting that theorydownsymbolicallyon thestaff

canbeuseful,but itdoesn’tallby itselfmean thatwewillunderstand itorbeabletouseitanybetter.

Inshort,whenlearningmusictheoryit isnotnecessarytolearntoreadmusic.There are cases, however, when it is useful. If you are a band leader orcomposer, then it is essential to be able to communicate your vision to othermusicians.Whilethatdoesn’tnecessarilymeanwritingmusictraditionally,itisuseful to know how to. Likewise, if you are a session player or amember ofsomeone else’s band, it is highly likely that peoplewill be handing you sheetmusic to learn, or even to sightread (sightreading is the act of playing apiecewhileyoureadit,usuallyoneyouhaveneverreadbefore).

Inthosecases,itisusefultobeabletoreadmusic.Butingeneral,ifyouaren’tgoing to bemaking your living playing in other people’s bands and on otherpeople’s albums, and if you are happy to learn ways of communicating yourmusic tootherplayers that isnon-standardornon-traditional, thenyoumaybejustashappynotlearningmusicalnotation.Therearemanygreatmusicianswhodon’tknowhow to readmusic,however theydounderstandmusic theoryandhowmusicworks.

Readingtraditionalmusicalnotationispartofthebigworldofmusictheory;butrememberthatyoucanlearnandusemusictheorywithouthavingattainedthisskill, but you cannot learn and understand how to read music withoutunderstandingthebasicmusictheoryfirst.

Thechoiceofwhetherornottolearnhowtoreadmusicandwriteitdownonthestaff using traditionalmusical notation is entirely up to you— it depends onyourgoals as amusician.This is certainly auseful skill thatwill deepenyourunderstandingofhowwethinkaboutmusic,andIwoulddefinitelyrecommendyou to learn at least the basics of how we capture it on the staff. This bookexplainstheoryindetailbutitdoesn’tdealwithreadingorwritingdownmusicusingtraditionalnotation,becausethatisaseparatesubject—moresuitableforaseparatebook.Itisnotessentialinordertobenefitfromlearningmusictheory,plusitmakesitlesscomplicatedandeasiertolearn,especiallyforbeginnersornonprofessionalmusicians.

If you decide that you want to learn how to read music, write it down, andinterpretwrittennotation,andhowit’sallconnectedtothemusictheory,thenIhaveagreattoolforyoutoconsider:

Asiblingbook(2ndbookintheMusicTheoryMasteryseries)dedicatedsolelytolearning how to read music for beginners and attaining the basic level ofsightreading.Youcancheckitouthere:

www.amazon.com/dp/B071J4HNR5

Withthisbookyou’lleasily learn thefundamentalsof thenotationsystemandkeysignatures,clefs,staffelements,notes,howrhythmsarewritten,solfegeandmuchmore.Therearealsoprogressiveexercisesat theend inwhichyou’llberequiredtoapplyeverythingyou’velearnedinthebookandactuallysightreadamusicalpiece.Itwillalsobeveryexcitingtoseehowitallrelatestowhatyoulearnhereandhowmanyconceptscomplementeachother.

MusicasaLanguageIt is sometimes useful to think of music as a calculus, as a rigid system ofnumericalrelationships.Itseems,whenyouthinkaboutthefactthateverything

reduces to intervals and their relations, that fundamentally music theory ismathematical.Itissometimesuseful,butitisn’tentirelyaccuratetothinkaboutmusicthatway.

Music isn’t acalculus,music isn’t anabstract systemofnumbers,music is anexpression.Itiscreativeinthesamewaythatpaintingaportraitiscreative,andthe difference between creative musical meaning and representing musicmathematically is the difference between painting deeply and creatively andpaintingbynumbers.

Allofthisistosaythatmusicisn’tmath,musicisalanguage.Andjustlikeourordinary language, it is messy, subtle, complicated, expressive, nuanced andsometimesdifficult.Therearethingsyoucanlearn,rulesifyoulike,thatmakeup thegrammarofmusic.This is thesystemofnotes, intervals,scales,chords(whichwewill learn in thisbook),etc.But tomakeuseof theory it isalwaysimportanttorememberthewaylanguageworks—youcan’tlearnalanguagebylearning a set of rules, you have to learn it by immersing yourself in it andgettingasenseofitspractices.

Tounderstandmusic as a languagemeans to alwaysmake theory come alive,nevertoletitsitandbecomestale.Toliveitandpracticeitbylistening,playing,singing,expressing,writingandthinkingit.Intervalsareonlyasgoodastherealnotesthatcomposethem,andmusicisonlyasgoodasthelinguisticexpressionsthatitcomprises.

In Part 1 of this book we will setup the fundamental framework that constitutesmusiclanguage,namelynotesandintervals.In Parts 2 and 3 we’ll see how notes and intervals are used to create morecomplicatedstructures,suchasscalesandchords.Just likea languagemusicdoesn’thappenwithout time,which iswhyPart4 isallabouttimeandrhythm,andhowtounderstandthiscrucialcomponentofmusic.In Parts 5 and 6 you will learn about the types of harmony, how to approachcomposing and manipulating musical structures, and how to be more expressivemusically—whichgoesbeyondmerelyplayingthenotesorchords.Finally, in Part 7 we will dive deep into harmony and examine some advancedmusical concepts thatwill giveyouagranderperspective about thewide scopeofmusic,andthepossibilitiesyoumaynothaveevenconsideredorknewtheyexist.

Getready,andlet’sgetstarted.

Part1

MusicTheoryFundamentals

WhatisaSound,Pitch,Note,TimbreandTone?Thismayseemlikeasimplequestionbuttheanswermaybeascomplicatedasyouwant it tobe.Itcouldbesaidthateverythinginnatureisenergyvibratinganddifferentfrequencies;therearescientifictheoriesthateventherealityitselfon the tiniest layers is just that—a vibration in the quantum field. Whensomethingvibrates itproduceswaves.Waves, inphysics,aredisturbances thattransferenergyand thereare twomain typesweexperience inourperceivablesurroundings: mechanical and electromagnetic. The main difference is thatmechanical waves require the presence of physical matter, like air, throughwhichtheycantravel.Electromagneticwavesdonotrequirephysicalmedium—theycantravelthroughthevacuumofspace.

So what is a sound then? In the simplest terms, sound can be defined as:mechanical pressure waves that travel through a physical medium, like air orwater. Sound has its own unique properties, such as: frequency, speed,amplitude,duration,etc.Thepropertywhichconcernsusmostisthefrequency,whichwecandefineas:thenumberofpressurewavesthatrepeatoveraperiodoftime.Soundfrequencyismeasuredinhertz(Hz),where1hertzmeansthatapressurewave repeats once per second.Higher frequency simplymeansmorewavespersecondandviceversa.

This brings us to thepitch. Physically, it can be said that pitch is a specificfrequencyof soundproducedbyavibratingobject, suchasaguitar string.Ushumanshavetheabilitytohearawiderangeofsoundfrequenciesrangingfrom20Hzto20000Hz(or20kHz)onaverage,althoughthisrangereducesasweage(anditisnothingcomparedtosomeanimals).Musically,apitchislikethe

harmonicvalueofanote,anditissaidtobehigherorlowerthanotherpitches.Inasense,studyingharmonyandmelodyisstudyingpitchandtherelationshipsbetweenpitches.

Anote,bytheway,issimplyanamedspecificpitchwithaparticularduration,loudnessandquality.ThenotesarenamedwithanalphabetletterrangingfromA toG (we’ll get to them in a bit). Each of the notes has its own pitch, thatmakesitthenotethatitis(forexample,Anotefoundonthe5thguitarstringis110Hz,whentunedtothestandardpitch).

Twosoundscanhavedifferentrhythmicvaluesandcansounddifferentoverallbut if theyhave thesamepitch, theywillstillbe thesamenote. If twosoundsthatarethesamenotesounddifferent,thenitissaidthatthesetwosoundshavedifferent timbres.A timbre is like a sound color or sound quality that comesfromdifferentinstruments.Forinstance,aCnoteplayedonapianoisthesamenote as C played on a violin, but we perceive their sound quality differentlybecauseofthetimbre.

Finally,theterm‘tone’isoftenusedinterchangeablywithalotofthesetermsinmusic,which usually causes some confusion. Tone is often synonymouswithtimbre;whenwesaythatdifferentinstrumentshavedifferenttones,orthattheyhavegoodtones,weareactuallytalkingabouttheirtimbres.Furthermore,toneissynonymouswithanote,usuallywhenwetalkaboutplayingdifferenttones;and it is used as a name for a particular music interval.Musical tone is alsoconsideredasasteadysoundwithpropertieslikearegularnote,onlythatitisasingle(pure)frequencythatcanonlybeproduceddigitally.Ifyouwanttohearapure single frequency the best way to do that is in a soundproof room thateliminates any excess resonanceor vibration.On theother hand,musical noteproducedbyamusicalinstrumentiswaymorecomplexthanasinglefrequencyduetotheinstrument’snaturalresonanceandharmonics(aswellastheacousticsoftheenvironmentandthewaythatthenoteisplayed);whatwehearasasinglenoteisactuallyawholespectrumoffrequenciescomingfromtheinstrumentthatourearsperceive,moreorless,asasinglefrequency.

NotesinMusic

Whenweseemusicasalanguageitiseasytorealizethatthenotesinmusicarelikethealphabetofalanguage.Thenotesaresimplythefoundationofallmusic.

Thereareonly12notesinWesternmusic,whichishistoricallyderivedfromtheEuropean music and is by far the most common music system that we heartoday.Thereareothermusic“systems”outthere,likeIndian,African,Chineseandothertraditionalfolkmusic,whicharealldifferentandmakeuseofdifferentscales.

The12notesinWesternmusicareasfollows:

A,A#orBb,B,C,C#orDb,D,D#orEb,E,F,F#orGb,G,G#orAb

Herearethosenoteslaidoutonapianokeyboard:

Figure1:Notesinoneoctaveonpiano

Thereareacoupleofthingstonotehere.

1. Thenotesarenamedafterthefirst7lettersofthealphabet:A,B,C,D,E,F,G.2. Therearealso5notes lyingbetween those:A#/Bb,C#/Db,D#/Eb,F#/Gb,G#/Ab,

thatarenamedwithsharps(‘#’symbol),whichindicatethatanoteisraised,andflats(‘b’symbol)whichindicatethatanoteislowered.In this system, the sharp of one note is harmonically identical — also calledenharmonicallyequivalent—totheflatofthenoteaboveit.Inotherwords,A#isexactlythesametoneasBb,C#isthesametoneasDb,D#asEb,etc.

3. Therearenosharpsor flatsbetweenBandCorbetweenEandF.That’s justonefundamentalcharacteristicofthemusicsystemthatweusetoday.

4. Thenotesthatdon’thaveanysharpsorflats—allwhitekeysonpianokeyboard—arecalledNaturalnotes. The black keys on piano keyboard are always the noteswithsharpsorflats.

5. Thedistancebetweenanytwoofthese12notesthatarenexttoeachotheriscalledahalf-step (H), and each half-step is the same distance (for example the distancebetween Bb and B is the same as the distance between E and F). The distancecomprisingtwohalf-steps,whichis thedistancebetween,for instance,CandD, iscalledawholestep(W).

Inprevioussectionitwasmentionedthattheterm‘tone’issometimesusedasaname for a particular music interval. This is that case—oftentimes the termsemitone(S)isusedinsteadofthehalf-step,andtone(T)insteadofthewholestep.Thesearejustdifferentnamesforthesamething.Half-stepsorsemitonesareequaltothedistancefromonepianokeytothenext,oronefretonguitartothe next (which is why there are 12 keys or 12 frets per octave on thoseinstruments).

TheNoteCircleThenotecircleshowsall12notesthatexistinWesternmusic.

Figure2:Thefoundationofmusic

Whenever you’re moving clockwise on the note circle (from left to right onpianokeyboard),youareascendingandthenotesarebecominghigherinpitch.That’sthesituationinwhichwewoulduse‘#’symbol;forexample,wewoulduseC#insteadofDbtoindicatethatwe’reascending.

Ontheopposite,wheneveryou’removingcounter-clockwise(fromrighttolefton piano) the notes are becoming lower in pitch and hencewewould use ‘b’symbol—DbinsteadofC#,toindicatethatwe’redescending.

OctaveandRegistryRangesEach note has its own pitch, but aswe saw, there are only somany differentnotes(thereare12intheWesternmusicsystem).Thisdoesn’tcoverthewholerangethatourearscanhear.Thatmeansthatthosenoteshavetorepeatinhigherand lowerregisters.All registers contain the same 12 notes, repeated both inhigherandlowerpitches.

Whenanoterepeatsinahigherorlowerregister—whenithasadifferentpitchbutisthesamenote—wesaythatthedistancebetweenthosenotesismeasuredinoctaves.Anoctaveissimplythedistancebetweenonenoteandthatsamenoterepeatedin thenexthigheror lowerregisteronthefrequencyscale.Physicallyspeaking,anoctaveisthedistancebetweentwopitchesthatresultsinonepitchhaving exactly twice asmanywaves in the same amount of time (number ofoscillationspersecond).Inotherwords,thefrequencyofanotethatisanoctaveup fromanothernote is twice thatof the first,meaning that thereare twiceasmanywaves,andthepitchishigherdespitebeingthesamenote.

Betweenany twooctaves thereareallof thenotes, and theorderof thenotesstays the same.What that means is that if you understand something in oneoctave,youhaveunderstooditinallofthem.Ifyoulookbackatthenotecircle(Figure2)youcanseethatanoctaveisequaltogoingonefullwayaroundthenotecirclefromanystartingnote.Ifyougoclockwiseandenduponthesamenote you would get an octave higher note, and likewise if you go counter-clockwise you would get an octave lower note. After one octave, the notessimply repeat themselves in the same order in the next lower or higheroctave/register. Note that the terms ‘octave’ and ‘register’ are often usedinterchangeably.

Anoctavecanalsobeviewednotjustasthedistance(interval),butasasinglenote—the eight note—which has the same letter name as the first note, butdoublethefrequency.Thiswillbeimportantwhenwegettoscalesandchordslaterinthebook.

Limited bywhat our instruments can produce and the range that our ears canhear, there are only so many registers (or octaves) at our disposal. Differentinstruments vary a lot in their ranges; some instruments, such as pianos, havemanyoctaves,sothateventhoughthereareonly12notesthereare88keysonafull-sizekeyboard(88differentpitchesthatcanbeproduced,whichisasmanyas7octaves).

Here’s apictureof a full sizemasterpianokeyboardwithmarked allCnotesrepeatedineightdifferentoctaves/noteregistryranges.

Figure3:AnoctavewiththemiddleCiscalledtheMiddleoctave—it’sthe4thoctaveonafullsizepianokeyboard

Youmayhaveseenbeforeanotewithanumbernexttoitandwonderedwhatthatnumbermeans.Unlesswe’retalkingaboutaparticularchord, thatnumbertellsuswhatkindofregistryrangethenote is in.Lookingat thefigure4,youcan see that there are eight C notes on piano, and this number (1-8) tells usexactlywhichCtoplay(inwhatregistry/octaverange).Samegoesforanyothernote;forexample,D3meansthatthisDnoteisintheC3-C4range,orthethirdrange. This is especially important when writing down music using notationbecauseitdetermineswhatkindofclefswewillusetobestcovertherangeofapiece,andminimizetheuseofledgerlines(thisisexplainedthoroughlyinHowtoReadMusicforBeginnersbook).

MiddleCandStandardPitchOnFigure3youcanseeallregistryrangesonpiano.Onerangehasthelengthofone octave—so the distance between C3 and C4 is exactly one octave; same

with F2—F3, D6—D7, A4—A5, etc. The distance between C1 and C3wouldbe2octaves,G4andG73octaves,etc.It’simportanttorememberherethatCisthestartingnote/frequencyofeachrange,andthatC4noteiscalledthemiddleC.Onguitar (if tuned tostandard tuning), thisnote is foundon the5thfretofthe3rd(G)string.

Weusepitch todeterminehowhighorhow lowsomething sounds.But therewasaproblembackinhistory(beforeXIXcentury)whennoteswerenotfixedto certain pitches (pitchwas not standardized), andmusicianswould just pickcertain frequencies according to their subjective hearing and assign notes tothem.Forthis,andmanyotherreasons,itwasobviousthatpitchstandardizationwasneeded.Throughouthistory therehavebeenmanyattempts to standardizethemusicalpitch.Themost commonmodernmusic standard today sets theAabovemiddleC to vibrate at exactly 440Hz.ThisA4 serves as the referencenote, with other notes being set relative to it. This is called the “Standardpitch”,or“Concertpitch”.Mostinstrumentstodayaretunedaccordingtothis“default”tuning.Onstandardlytunedguitarforexample,AabovemiddleCisfoundonthe5thfretofthe1st(thinnesthighe)string.

SinceA4hasthefrequencyof440Hz,whatfrequencywouldanoctavelower—A3have?

Theansweris:220Hz,andA5wouldbe880Hz.

This tuning standard is widely recognized and used, but there are also othertuning choices used by different orchestras around the world, most of whichrevolvearoundA4beingsettodifferentfrequencies,suchas:441Hz,442Hz,436Hz,etc.Thereisanothertypeofpitchstandard,calledScientificpitch (orPhilosophicalpitch),wherethefocusisputontheoctavesofCratherthanonA.InStandard pitch,A4 is 440Hz, andC4 (ormiddleC) is 261.625Hz, but inScientificpitchC4 is adjusted so that it is equal toawholenumber—256Hz,and A4 is 430.54 Hz. This pitch standard is sometimes favored in scientificwritings because 256 is a power of 2, which is very useful in the computerbinarysystemandservesdifferentpurposes.

OctaveSubdivision

Oneoctaveconsistsof6wholesteps,onestepconsistsof2half-steps,andonehalf-stepconsistsofupto100cents.Whatthatmeansis that,forexample,DandD#areonehalf-stepapartbutbetweenthemthereareupto100cents.Centsin music are typically used to express microtones, which are very smallintervals—smallerthanahalf-step(whichyoucanalsocallasemitone).

Figure4:Mostsoftwareprogramsthatworkwithsoundfilesallowyoutochangethepitchinoctaves,semitonesandevencents

Beyond one semitone, rather than using hertz as a frequency measure unit(whichifyouremembershowstheamountofairpressurewavesproducedinagivenamountoftime),wemoreoftenusecentswhicharealogarithmicmeasureused for musical intervals. It is enough to say that they are simply moreconvenientandeasiertouseformusicians.Humanearisverysensitiveasitcanrecognize up to only a few cent difference between two successive notes(pitches), but the interval of one cent is too small to be heard between twosuccessivenotes.

Yourinstrumentcanbeintuneandstillsoundalittlebitoff,andthat’sthecasewhen there’s a small pitch difference that can only be measured in cents.

Correctingthesesmalldifferencesissometimescalledfine-tuningandthetunersthatyoucanfindtodayallowfor thiskindofsuper-accurate tuning(withevenlessthanonecentaccuracy).Themore“exactly”intuneyourinstrumentis,thebetter itwill sound, especially on the recording.That’swhy it is important tokeepitintune.

We’venowcoveredthenotesandthenotecircle.Beforewediveanyfurther,itisessentialthatyouunderstandandlearntheintervalsinmusic.

MasterTheIntervals

WhatIsanIntervalinMusic?An interval is a relationship between two notes. It describes the harmonicdistancebetweennoteswithauniquesound.

Eachintervalhasauniquesoundandauniquename.Thenamesoftheintervalscome from their position in diatonic scales (more on diatonic scales soon). Inthatsense,intervalscanbeeither:

1. Major2. minor3. Perfect

Major and minor intervals are used a lot in Western music, while Perfectintervalsaregenerallyusedmoreinethnicmusicallaroundtheworld.

MusicIntervalsSpelledOutTakealookatthenotecircleagain.There’sanintervalbetweenanyofthenotesfrom the note circle – you can start on any note and play any other note(includingitself),andyouwillplayanintervalofsomekind.

In order to show you all the intervals,we need to first choose theRoot note,which can be any note. TheRoot note is the starting note, it is the harmoniccenterofwhateverchordorscaleyouareusing.InthisexamplethenoteCwillbeusedastheRoot.

1. FirstwehaveCtoC.Yes,there’sanintervalbetweentheRootandtheRoot(theexactsamenoteplayedtwotimes),andit’scalledPerfectUnison.

2. Thenextnote,C#/Db,isaminor2ndaboveC(andalsoamajor7thbelowit).Thisisalsotheequivalentofonesemitone(S).

3. DisaMajor2ndaboveC(andaminor7thbelow).Alsotheequivalentofonetone(T).

4. D#/Ebisaminor3rdaboveC(andamajor6thbelow).

5. EisaMajor3rdaboveC(andaminor6thbelow).

6. FisaPerfect4thaboveC(andaPerfect5thbelow).Fourthsandfifthsaresaid tobe“perfect” rather thanmajororminorbecause theyare the same in themajor andminor scales, aswell asmost other diatonic scales(don’tworryifyoudon’tunderstandthisrightnow).

7. F#/GbisAugmented4th—alsocalledaTritone—aboveC(andaTritonebelowit).This is a strange interval. It is highly dissonant and often avoided. It sometimesfunctionsasasharp4th,andother times it isa flat5th.The tritone isalso theonlyinterval that is the inversionof itself—ifanote isa tritoneupfromanothernote,thenitisatritonedownfromitaswell.

8. GisaPerfect5thaboveC(andaperfect4thbelowit).

9. G#/Abisaminor6thaboveC(andamajor3rdbelow).

10. AisaMajor6thaboveC(andaminor3rdbelow).

11. A#/Bbisaminor7thaboveC(andamajor2ndbelow).

12. BisaMajor7thaboveC(andaminor2ndbelow).13. Andlastly,wehaveCwhichisaPerfectOctaveintervalaboverootC.

Wehavenowgonethroughthefullnotecircle.

There are 4 Major intervals, 4 minor intervals, 4 Perfect intervals, and that“strange”interval—theTritone(Augmented4thorflat5th).

Intermsofsemitones:

PerfectUnison(CtoC)is0semitonesapart

minor2nd(CtoC#)is1semitone

Major2nd(CtoD)is2semitones

minor3rd(CtoD#)is3semitones

Major3rd(CtoE)is4semitones

Perfect4th(CtoF)is5semitonesTritone(CtoF#)is6semitones

Perfect5th(CtoG)is7semitones

minor6th(CtoG#)is8semitones

Major6th(CtoA)is9semitones

minor7th(CtoA#)is10semitones

Major7th(CtoB)is11semitonesPerfectOctave(CtoC)is12semitones.

Sometimes,wedefineintervalsaboveanoctave.Thesearenamedbyadding7towhateverthenamewasinthefirstoctave.Forexample,amajor2nd intervalanoctavehigherbecomesamajor9th,aminor6thbecomesaminor13th,andsoon.

Note that in music theory the terms: “Major” and “Perfect” are usuallycapitalized,while“minor”isn’t.

Intervals are used to define both chords and scales because a particular set ofintervalsdefinesauniquesound,auniqueharmonicspace.Ifyouhavelistedallof the intervals that are inagiven scaleor chord, thenyouhave fullydefinedthatscaleorchord.Inlatersectionsyou’llseehowintervalsareusedtodefinechordsandscalesandhowimportanttheyareinmusictheory.

InvertedIntervals(WithIntervalExercise)Beyond the interval quality (major,minor, perfect) and its name, there is onemorepropertyofintervalswhichisimportanttounderstand.

Takealookatthenotecircleagain.Noticethatintervalsbetweenanynotecangouportheycangodown.Theycanbeeither:

1. Ascending(lowernoteinpitchgoingtoahighernote,forexampleCtoD#)

2. Descending(highernoteinpitchgoingtoalowernote;forexample,BtoAb)3. Harmonic(whentwoormorenotesareplayedsimultaneously)4. PlayedinUnison(thesamenoteplayedtwice)

YoucansaythatBisaMajor3rdintervalupfromG,butthatEbisaMajorthirddownfromG.Sothatmeansthatintervalscanbeinverted—ifBisaMajor3rdupfromG,thenitisalsoadifferentinterval—inthiscase,aminor6th—downfromtheGofthenextoctave.

Inthisway,intervalscomeinpairs.Everyrelationshipcanbedefinedbytwodifferent intervals, one up and one down.That should explain the intervals inparenthesisfromtheintervalslist.

To explain it further, interval is a relative property of notes. For example,wewanttofigureoutwhatintervalitisfromAtoC.Wehave2possiblesolutions.

CnoteisaparticularintervalawayfromA.IftheCnoteishigherinpitchthanA,thenthisintervalisascending.SowecansaythatCisaminor3rdupfromA,andthatCisA’sminor3rdinterval.

A->C=minor3rd(ascendinginterval)

ButifthenoteCislowerinpitchthanA,thenthisisadescendinginterval.WecannowsaythatCismajor6thdownfromA.

A->C=major6th(descendinginterval)

Whenfiguringoutintervals,unlesswedon’thaveanyinformationonwhatkindofintervalitis(ascending,descendingorharmonic),wealwaystreatthelowernoteastherootnote,andwecountintervalsclockwiseonthenotecirclefromthelowestnote.

Trytodothisyourselfandseehoweasyitis.Herearesomeintervalstofigureout.

E->C(ascending)—?E->C(descending)—?D->A#(ascending—thesharpsymboltellsyouthatthisisanascendinginterval)—?D ->Bb (descending— again, the flat symbol indicates that this is a descendinginterval)—?Gb->Ab—?

Itisimportanttorememberthatwhenanintervalisascendingyouwillsee/usesharp(#)symbol,andwhenitisdescendingyouwilluseflat(b)symbol.

Like I said before, there is a different interval pair for every note of the notecircle.Youcanusethenotecircleandcounttheintervalsthere.Theanswerswillbeprovidedattheendofthisbook.

ChromaticandDiatonicIntervalsAll of the intervals shown so far fall under one large group of Chromaticintervals. The termChromatic tells us that this is a set ofALL intervals thatexistbetweenthenotesthatareusedintheconventionaltonalmusictoday,sameashowthechromaticscaleisthesetofall12notesthatexistintoday’s12-tonemusicsystem.

Within those Chromatic intervals there is a specific group of intervals, calledDiatonic intervals which are quite important. Diatonic intervals are thoseintervals that theMajor scale iscomprisedof.Major scale is themostpopularscaleinmusicandallotherscalesaremeasuredagainstitinonewayoranother.

Majorscale,themostimportantscaletolearn,isaDiatonicscale(youwillsoonfindoutwhatthismeans,justbearwithmeforabit),andthat’swhyallintervalsthatmakeuptheMajorscalearecalledDiatonicintervals.

Inthatsense,Diatonicintervalsare:PerfectUnison (CtoC),Major2nd (C toD),Major3rd(CtoE),Perfect4th(CtoF),Perfect5th(CtoG),Major6th(CtoA),Major7th(CtoB).

These Diatonic intervals fall under Chromatic intervals as a special group ofintervalswhichmakeup theMajorscale. Inotherwords,allof these intervalsappearintheMajorscale.

AugmentedandDiminishedIntervalsBeyond Major, minor and Perfect intervals, there are also Diminished andAugmentedintervals.Theseintervalsareinawayhiddenbecausetheyareusedintheoryforshowingtheintervalstructureofonlythosescalesandchordsthatrequiretheuseofthem.WhatdoImeanbythis?

All scales and chords are made up of individual notes and intervals betweenthosenotes.Weuse this intervalstructure towriteout thenotesandnameanyscale or chord.However, at certain times, dependingon the scale,wehave toabidebycertainrulesinmusictheorywhenitcomestowritingoutthenotesandintervals.That’susuallywhenthesetheoreticalintervalscomeintoplay.

Wewillget to theserulessoon, fornowunderstand thatdiminished intervalslower or narrow the minor and Perfect intervals by one semitone.Augmented intervals expandorwiden theMajorandPerfect intervalsbyonesemitone.

Table1:CompletelistofChromaticintervals

Acoupleofthingstonotehere:

1. Diminished and Augmented intervals are equivalent to their Major, minor andPerfect intervalcounterparts– theyare thesamedistance,buthavedifferentname.

For example,diminished4th andMajor3rd arephysically (distance-wise) the sameintervals.Thenamewhichwillbeusedfor intervals isusually in theMajor,minorandPerfect column,but in some instances, dependingon the scaleor a chord thatinterval is a part of, we will have to use its alternative— diminished/augmentedname.

2. NoticethatMajor,minorandPerfectintervalslackoneintervalwiththedistanceof6semitones. 2 semitones are equal to1 tone, so this interval has3 tones, and that’swhyit’scommonlycalled“Tritone”.Thisisadiminished5th/Augmented4thinterval(canbeeither),anditistheonlyintervalfromthiscolumnwhichappears,notintheMajorscale itself,but in themodesof theMajorscale,alsocalledDiatonicmodes(whichwe’llgettoinPart2ofthisbook).

3. Diminished intervals are usually shown with a lower case first letter, whileAugmentedintervalsusuallyhaveanuppercasefirstletter.

Understandingintervals—trulyunderstandingthemandhowtheyrelatetooneanotherandlearningtohearandusethem—takesalifetime.Inasense,alloftheotherlearningaboutscalesandkeysandchordsisawaytomakesenseofthewide-openspaceofthenetworkofintervalsinthe12-tonesystem.Itisverywellworthalwayskeepinganeyeonyourcomfort levelwith this ideaand trainingyoureartorecognizethem.

TheBuildingBlocksofMusic—Harmony,MelodyandRhythmWesaythatmusicconsistsofthreethings:

1. Harmony,2. Melodyand3. Rhythm.

Harmonyandmelodybothdescribe the relationshipbetweenpitches (althoughdifferently) without respect to their duration, whereas rhythm describes therelationshipbetweensoundsandtheirdurationswithoutrespecttotheirpitches.

Harmonyiswhathappenswhenwecombinenotesinmusic.Ifyouaddoneormorenotestoanothernote,andyouplaythematthesametimeorinasequence,

thenyou’veaddedharmonytotheoriginalnote.Thisisonewaytothinkabouttheharmony.

Harmony is the vertical relationship between pitches. It is a structure, like alattice;anetwork.Whenyouunderstand therelationshipbetween twoormorenotesharmonically,youaretreatingthemasthoughtheywerehappeningatthesame time (even if theyarehappeningoneafter another). It ispossible in thiswaytothinkaboutthewaytheoverallharmonicstructureofapiecemovesandchanges. Harmony is the thing that most people mean when they talk abouttheory.

Melodyislikeharmonyinthatitdescribestherelationshipbetweenpitches,butit is a horizontal rather than vertical understanding. While still a matter ofrelativestructure,melodyisallaboutthewaythatnotesactinsequence,sothatthesame4notesplayedindifferentordershavedifferentmelodicvalues,evenifthose4notestakentogethermighthavethesameharmonicstructure.

Melody could be considered simply as part of the harmonywhich focuses onhownotessoundtogetherinasequence.Usuallyweaddharmonytoamelodyline(whichputs themelodyinacertaincontextandmakesitsoundricher),orwemayaddmelodytotheexistingharmony.

Rhythm is the relationship, in time, between notes (or sounds in general)regardless of pitch relationships. Rhythm describes the way sounds pulse (ordon’tpulse),theirspeedandregularity.Rhythmicstructuresdescribethewayapiecemoves according to a particular kind of time-based division.While notgenerally the focus of as much theoretical attention, rhythm is equally asimportant. An understanding of the role of time and duration in music isessential sincemusic is, after all, a time-basedart form.That’swhy there is awholesectiondedicatedtorhythminthisbook.

WhatMakesaGreatMelody?Astrongmelodyisessentialtogoodmusic.Itisthedifferencebetweenbringingsomeone’s ear on a ride and driving right past it. Good melody is all abouttelling a story. Itmoves and unfolds, builds and releases. It plays against andwith the chord structure of a song (the harmony) in away thatmakes peoplewanttohearit.

Goodmelodyishardtounderstand,andevenhardertoprescriberulesfor(read:impossible),butingeneralwesaythatamelodyconsistsoftensionandrelease.Thatmeans that a goodmelodymoves away from the harmonic center of themusic,buildingtension,andthenmovesbackinsomeinterestingway,releasingthattension.

To tell a story is to create an arc.To rise and to fall.And that’swhat a goodmelodydoes:itbeginssomewhere,andwhileitusuallyfollowsthestructureofthechords,itdoessoinawaythatcreatesmovementanddrama,thatmakesalittle friction between the single notes in the melody and the structure of thechords(itsharmonicstructure).Inmostmusic,thisisfollowedbysomekindofrelease, in which the relationship between the single notes and the chords isagaineasy,consonantandstable.

TheConceptofRootNoteThisconceptisquiteimportantinmusictheoryandwe’regoingtouseitalotinthefollowingpages,soitisworthexplainingnow.

Therootnoteofascaleorachordisthenote—usuallythelowestnoteinthescaleorchord,or the“bass”note(but itdoesn’thave tobe)—that isused todefine the intervallic relationships in the rest of the scale or chord. In otherwords,alloftheothernotesaredefinedasintervalsrelatingbacktothatonerootnote.

Therootnoteisthefirstthingthatthenameofachordorascalelists,sothatifsomeoneis talkingaboutaDminor6thchord, thenyouknowthat theDis therootofthatchordandtherestofthechordisdefinedrelativetothatDnote.IfsomeoneistalkingaboutaG#majorscale,thenyouknowthattheG#istherootnote of that scale and then the rest of scale notes are defined relative to thatstartingG#note.

Part2

MasteringScalesandModes

WhatIsaScaleinMusic?Scales are someof themost important things inmusic. In a certain sense, theentireharmonicandmelodicstructureofapieceofmusiccanbedescribedwithrespect toscales.Theycanbeused togeneratechordsandchordprogressions,andcandefine andproducemelodic ideas tobeusedover those chords.Theycanbeused to compose complicatedworksbut also to improvisemusic, evenadvancedmusic,withlittleeffort.

Put as simply as possible, a scale is an abstract collection of notes and therelationshipsbetweenthosenotesorpitches.

It isacollectionandnotasequencebecause itdoesn’texist time—itdoesn’thaveanorder,anditdoesn’timplyanyparticularmelodicarrangement.Itisjustasetofrelationshipsbetweennotesthatdefinesaharmonicspace.

Itisabstractbecauseitisnottiedtoanyparticularactualarrangementofnotes—itdoesn’ttellyoutoplaythe6thnoteinascaleorthe3rdnoteinascale,allitdoesisgiveyouasetoftonesthatdefineaspaceinwhichyoucanplay.

It isn’tnecessarytoplayallof thenotesinwhateverscaleyou’reusing,anditisn’tnecessarytoplayonlythosenotes,justtousethescaleasasortofgeneralcategory. Scales are loose characterizations of harmonicmaterial,more like atendencyandlesslikearule.

Becausescalesareabstract, theydon’tdependonanyparticularexpression. Inotherwords, they are in the background, at a higher,more general, levelthantheactualnotesofthemusic.

YoucanplayaLedZeppelinsolooryoucanplayaStevieRayVaughansolo,and they will be completely different things, but they will both be using theminorpentatonicscale.Becauseofthis,scalesareusefultoolsforunderstandingwhat someone is doing musically and for knowing what you want to domusically, since they allow you to know, in general, what is going on in themusicandwhatwillhappenifyou,forinstance,playaparticularseriesofnotesoveraparticularchord.

Scalescomeinmanyforms:somehave5notes,somehave7,somehavemore,butallofthemdefinearoot,whichisthecenterofharmonyandmelody,andasetofrelationshipsbetweentherestofthenotesinthescaleandthatroot.

Also,all scaleshave theirownscale formulaconsistingof tones (wholesteps)andsemitones(half-steps).Simplybyknowingthescaleformulaitisveryeasyto figureout thenotesofanyscaleandplay themonany instrument (aswe’llsoonsee).

Scalesareusedtodefinechords,whichformtheharmonicstructureofasong,and also to compose melodies, which consist of (usually) single-note linesplayed over top of that harmonic structure. They are also used to createharmonies,whichoccurwhenmorethanonesingle-notelineisplayedtogether.Thebestwaytostartunderstandingscalesistostartwiththechromaticscale.

TheMasterScaleThemostfundamentalscaleinWesternmusicistheChromaticscale.It isthemasterscale.Thechromaticscalecontainsall12tonesineveryoctave,andsoinasenseitisthesetofallotherscales.Everychordandeveryscaleiscontainedinthechromaticscale.

Becausethechromaticscaleissolarge,itisaveryusefulwayofthinkingabouttheoverallharmoniclandscape.Everythingthatyoucanplay(aslongasyouareintune)hassomekindofrelationshiptoeverythingelse,andthechromaticscaleisthesetofallofthoserelationships.Thechromaticscaledoesnothaveakeyitself,itisthesetofallkeys(moreonkeyslater).

But because it is so democratic and decentralized, the chromatic scale isn’talwaysuseful.Itisveryabstractandit’snotmusical.

Sometimes—mostofthetime—youdon’twanttoplayjustanynote,inanykey,atanytime.Sometimes—again,mostofthetime—youwanttocutthechromatic scale up, define a slightly (or radically)more limited harmonic andmelodicspace.That’swhenalloftheotherscalesbecomeuseful.

Consistingof12notesperoctave,thechromaticscaleisbrokenevenlyinto12half-steps(H)or6wholesteps.Thenotesofthechromaticscalearesimplyall12notesfromthenotecircleinthesameorder.

It is very easy to play a chromatic scale and it’s particularly good to use as atechnical exercise (especially for beginners who are getting used to theirinstrument).Just takea lookatFig1againandyou’llseehowit’s laidoutonpiano.Toplayityoucanstartonanynote(itdoesn’thavetobeA),andjustplayallofthenotesinorderascendingordescendinguntilyougettotheoctave.

Justasunderstandingintervalsisalifelongproject,makingsenseoutofthewidearrayof possible scales and their interactions is aswell. It is useful, however,whenundertakingthatproject,toremembertheplaceofthechromaticscale.Itcontainsallof them, itdemocratizes, it spreads theharmonyandmelodywideopen,anditallowsyoutodovirtuallyanythingyouwantto.Learningtousethatfreedom responsibly is oneof the things that sets great players apart from themean.

TypesofScalesTherearebasicallyonlyafewtypesofscales.Oneofthemwehavejustcovered—thechromaticscale.Thechromaticscaleisthesetofallotherscales.Itisthemasterscale.Butitdoesn’tdefineadistinctharmonicspacebeyondthedivisionof harmony into 12 equal parts. For that, you need scaleswith fewer than 12notesinthem.

Commonly,thereare2otherscaletypesthatmakethefoundationofharmony,andthose2typesbreakupintoafewothers.

1. First,thereare5-notescales.Thesearecalled“pentatonic”scales,meaning“5-per-octave.”Thevariationsofthosesimplescalesareenoughtoproducearichlandscapeallbythemselves.Whilethereareavarietyofdifferentnotepatternsthatcanmakeuppentatonicscales, there isone inparticular,whichdefine theminorpentatonicscaleaswellasthemajorpentatonicscale,thatismostoftenused.Thesescalesarefoundinbluesandrockmusic,andvariationsofthosesimplescalesare enough to produce a rich landscape all by themselves. There’s a reason whythey’recalled“minor”and“major”and it’sbecause theyoriginatefromthe7-notescalesthatbearthesamename.There are also other pentatonic scales, especially in non-westernmusic,which arerarer but still sometimes useful. For example, Chinese scale used to composetraditionalChinesefolkmusicisapentatonic(5-note)scale.

2. Thenthereare7-notescales.7-notescaleshavemanyforms,themostbasicofwhichare called“diatonic scales” (more on this later). Themost commonMajor scale(do-re-me…)andNaturalminorscaleareboth7-notediatonicscales.Thewords“minor”and“major”refertosomethinglikethemoodofthescale,withminor scales in general sounding sad, dark and thoughtful and major scales ingeneralsoundinghappy,bright,andlively(likeminorandmajorchords).Mostblues,forinstance,isplayedinaminorkey,whichmeansthatitmakesuseofaminorscalequiteoften,whereasmostpopisplayedinamajorkey,whichmeansitmakesuseofamajorscale.

There are twoother varieties of 7-note scales that areused in classicalmusic,neo-classical,advancedrock,andjazz,andtheyaretheharmonicminorscaleandthemelodicminorscale(andtheirvariations).

Beyond5-noteand7-notescales, thereareafewspecialized8-notejazzscales(calledbebopscales).Otherwise,itisalwayspossibletoproducenewscalesbyadding notes from the chromatic scale to an existing scale, resulting in scaleswithasmanyas11notes(thisismostoftendoneinjazz).

It is also possible to create new scales by altering an existing scalechromatically.Ingeneral,creatingnewscalesbythischromaticalterationand/oradditionresultsinwhatwecall“synthetic”scalesormodes.

Keepinmindthatthereare12notesinmusic,sothereare12harmoniccenters(orrootnotes)thatascalecanstarton.Thisgoesforanykindofscalenomatterthenumberofnotesitcontains.

MinorPentatonicScaleWhiletherearemanydifferentkindsofpentatonicscalesthatcanbeassembled,there is really onlyonepentatonic structure that is used commonly inwesternmusic.Thisstructurehas2variationsinparticular thatareubiquitousinblues,rock,pop,country,jazzandbluegrass.Thosetwoscalesaretheminorpentatonic(whichisthemostfamiliar)andthemajorpentatonic.

Theminorpentatonicscaleisthefoundationofmostofthebluesandrockthatmostofushaveheard.Itisasimple,easytorememberscalewithaverydistinctsound. It connotes a soulful, deep affect and can bemade to sound quite sad.Thisscaleconsistsofnotesthatareallfoundinthenaturalminorscale,andsoitisofuseanytimetheminorscaleiscalledfor.

It is possible tomake an entire career out of this one harmonic collection, asmany blues, folk, bluegrass, funk and rock musicians have. Outside of theWestern world, this and similar scales are common in traditional Asian andAfricanmusic(thelatterbeingthehistoricalsourceoftheminorpentatonicscaleintheAmericanFolktradition).

MinorPentatonicStructureRememberwhenIsaidthatweuseintervalstodefinechordsandscales?Here’showwedothat.

Wesaythattheminorpentatonicscaleconsistsof5notes:

ARoot,aminor3rd,aPerfect4th,Perfect5th,andaminor7th

or(whenabbreviated)

R,m3,P4,P5,m7

Thesenumbersrefertothenotes’relativepositionwithinadiatonicscale(inthiscase,thenaturalminorscale),buttheintervalsthemselvesexistinmanyscales,includingtheminorpentatonicscale.

Ifthescaleisplayedinorder,thereis:

1. ARoot,abbreviatedto‘R’.

2. Arootisfollowedbyanoteastepandahalf(3halfsteps)abovetheroot—thisistheminor3rd,orsimply‘m3’.

3. Thenanoteafull(whole)stepabovethat—thisisthePerfect4th,or‘P4’.

4. Anoteafullstepabovethat—thisisthePerfect5th,or‘P5’.

5. Andanoteastepandahalfabovethat—thisistheminor7th,orm7.*

*NOTE:Thesearethe5notesoftheminorpentatonicscales.Thedistancebetweenthelastnote(theminor7th)andthefirstnoteinthenextoctaveisonefullstep.

Nowcheckwhatisunderlinedabove.Thesedistances(intervals)canbeusedtodescribethescaleinanother,simpler,way:

WHWWWHW

or(samething)

TSTTTST

This is called a scale formula. In this case it’s the minor pentatonic scaleformula. A scale formula simply represents a unique set of intervals foundwithineachscale.Itiswrittenbyusingtonesandsemitones(andacombinationofthetwo—TS).

Just by knowing a scale formula you can start on any of the 12 notes on anyinstrument,applytheformula,andeasilyfigureouthowtoplayanyscale.

Whenputincontext:

R—TS—minor3rd—T—Perfect4th—T—Perfect5th——TS—minor7th—T—R

Forexample,ifwestartfromanAnotewecanthenapplytheformula:TS—T—T—TS—T, and easily figure out the rest of the notes of the Aminorpentatonicscale.Thenoteswouldbe:

A—TS—C—T—D—T—E—TS—G—T—A

AistheRootCistheminor3rd(aboveA)DisthePerfect4th(aboveA)EisthePerfect5th(aboveA)Gistheminor7th(aboveA)andlastlyAisthePerfect8th—Octave(O)

When applying a scale formula you can follow the note circle to find out thenoteseasier.

Figure5:MinorpentatonicstructureonapianoinA

Thiscanbedoneonanynote/key.

This is one of the first, if not the first, scale that many people (particularlyguitarists)learn,andoncelearneditcanbeusedveryquickly.

Ifyouplacetherootofthisscaleontherootofvirtuallyanychord(especiallyminoranddominantchords)thentheothernotesinthescalewillalmostalwayssoundgood.Ifyou’replayingtheblues,thenallyouneedtodoismakesuretherootofthisscaleisthesamenoteasthekeythatthesongisin.

WhatIsaMode?Itisworthusingtheminorpentatonicscaletodemonstrateanimportantconcept.Wesawthatthisscaleconsistsofacollectionof5notes,andthatwhentheyareorientedaroundtheroot,thereisaparticularsetofintervalsthatdefinethescale.

But what if we take those same exact 5 notes — for instance, the A minorpentatonic scale (A, C,D, E andG)— and re-orient them. In other words,

whatifratherthancallingAtheroot,wetreatthissamecollectionofnotesasaCscale,treatingCastheroot.

Nowthenoteshavedifferentnames:

Cisnolongertheminor3rd(ofA),itisnowtheRoot.

DisnolongerthePerfect4th(ofA),itisnowtheMajor2nd(ofC),

EisnowtheMajor3rd,

GisnowthePerfect5th,and

AisnowtheMajor6th.

Sothenewsetofnotesis:

Root,Major2nd,Major3rd,Perfect5th,Major6th;

or:

R,M2,M3,P5,M6

This is a completely different abstract collection of notes than the A minorpentatonicscale—eventhoughitconsistsofthesame5tones—becauseitisnowacompletelydifferentsetofintervals.

MajorPentatonicStructureByusingthesamepattern,butbeginningatadifferentnote,wehavecreatedadifferentscale.ThescalethatwehavecreatediscalledtheCmajorpentatonicscale,andit’salsoanimportantandverycommonscaleinblues,country,rock,pop,etc.

Figure6:MajorpentatonicstructureonpianoinC

Whatwehavecreatedbyre-orientingthescaleiscalleda“mode”.Wecansaythat themajorpentatonicscaleisamodeoftheminorpentatonicscale,or thattheminorpentatonicscale isamodeof themajorpentatonicscale(weusuallysaythemajorpentatonic isderivedfromtheminorpentatonicbecauseit is themostusedoneinvirtuallyallbluesandrock).

Somajorpentatonicscaleisderivedfromtheminorpentatonicstructure,onlyitbeginsonwhatwasthe2ndnoteoftheminorpentatonic.

Like the minor pentatonic scale, the major pentatonic scale is simple andrecognizable, and most of us know it without realizing it. Because of thedifferentsetofintervals,thisscalesoundsdifferent—ithasabrighter,happiersoundthanitsminorcousin,whichisaresultofthefactitbeinga“major”scale.Thenotesofthemajorpentatonicscaleareallcontainedinthemajorscale,andsoitisusefulwheneverthatscalecanbeused.

Because there are 5 notes in theminor pentatonic scale, there are 5 differentnotesthatcanactastherootofdifferentmodes.Foreachnoteinthecollection,thereisadifferentmode,inwhichthatnoteistherootandthe4othernotesaredefinedwithrespecttoit,resultingin5differentsetsofintervalswitheachnote.

This is a very basic understanding of modes. As your understanding andapplicationinplayingdeepens,youwillstartseeingthemascompletelyseparatescalesratherthansimplenotere-orientationsoftheparentscales(that’swhyyoucansometimesusetheterms‘scale’and‘mode’interchangeably).

Onadeeperlevel,modesshowtherelationshipsbetweenchordsandscales,andtheyarecompletelyrelativetothechordsthatareplayingunderneathinthebackground, or on the backing track. This concept will be extremelyimportant when it comes to 7-note scales, But first, let’s tackle the minorpentatonicscalemodes.

ModesoftheMinorPentatonicScale(WithAudioExamples)Fromwhatwe’velearnedsofar,wecaneasilylistallofthemodesoftheminorpentatonicscale.Sinceitcontains5notestherewillbefiveofthem.

I’ve included audio examples for each mode to help you hear how thatmode/scalesounds.Eachaudiotrackconsistsofthefollowing(inorder):

1. Scaletonesplayedupanddown(startingandendingontheRootnote)—thiswillhelptoestablishthescale’stonalcenterinourears.

2. Aseriesofchordsthatbelongtothatscale.Sinceatthispointinthebookyoumaynotbefamiliarwithhowchordsarebuiltandgeneratedbyscales,justfocusonthesound of the chords, and notice how everything relates to the first chord that isplayed.Afteryougothroughthechordsectionlaterinthebookyoucancomebacktothesescaleaudiosagainanditwillbeclearwhythosechordsareplayed.

3. Animprovisationexcerptoveradronenote(anote,usuallyalowbassnote,thatissustainedor isconstantlysounding throughout theexcerpt in thebackground).Thefollowing examplewill be inA, sowe’ll be usingA note as the drone note overwhich we’ll be playing scale tones for each mode separately, in a musical way(improvisebasically).

Hearing,distinguishingandusingmodes isaprocess thatwill takesometime,butonceyoudo it,mostof the things in theorywill start tomakemuchmoresense,thedotswillbeconnected,anditwillmakeyouamuchbettermusician.Sobepatientandtakeyourtimewiththis.Let’sgettothemodes.

MinorPentatonicMode1–MinorPentatonicScaleThefirstmodeoftheminorpentatonicscaleisjusttheminorpentatonicscale.Itconsistsofa:

Root,minor3rd,Perfect4th,Perfect5th,minor7th

InA,thescaleis:A,C,D,E,G.Here’showthisscale,ormode1,sounds:

MinorPentatonicScaleMode1audioexampleinA->http://goo.gl/ixb9BQ

Pay close attention how each of the notes played sound against the backingdronenote.Somewilladdtension,somewillfeelmorepleasantandsomewillprovideresolution.

MinorPentatonicMode2–MajorPentatonicScaleThe secondmode of theminor pentatonic scale has a special name. It is theMajorpentatonicscale,aswe’veseenintheprevioussection.

Itconsistsofthefollowingintervals:

Root,Major2nd,Major3rd,Perfect5th,Major6th

Withabbreviations:R,M2,M3,P5,M6

InC,thenotesare:C,D,E,G,A;

CistherelativemajorkeyofAminorpentatonic,whichisconsidereditsparentscale. You don’t need to understand this for now, just have the idea in yourmind.

Here is thekeything—in the improvisationexcerptfor thismodewewillbeplayingover theAdronenoteagain so the tonal centerwillbeA. Inorder tohear how thismode soundswewill playMajorpentatonic scale, ormode2minor pentatonic scale, in A rather than C, over this backing note. Hopeyou’restillwithme.

Inordertodothat,weneedthenotesoftheAMajorpentatonicscale,sowejustapply theMajor pentatonic formula starting from theA note. This formula isshownonFigure6,buthereitisagain:

R–T–M2–T–M3–TS–P5–T–M6–TS–R

AndthenotesoftheAMajorpentatonicscaleare:

A–T–B–T–C#–TS–E–T–F#–TS–A(Octave)

Now all we have to do is simply play these notes, improvise a melody withthem,and listen to their individual(aswellasoverall)effectover theAdronenote.Thiswill give us the soundof themode 2 ofminor pentatonic scale, orsimply:Majorpentatonicscale.

MinorPentatonicMode2audioexampleinA->http://goo.gl/x6ExEb

Again, pay close attention to each of the notes and how it sounds against thebackingAdronenote.Noticehow theMajor3rd,C# in this case, gives it thatmajorupbeatfeel.Bepatientwiththis.

MinorPentatonicMode3Hopeyourheaddoesn’thurtmuchafterallthisaswewillnowexamineanothermode.:)Luckily,it’sthesameconceptforothermodes,andifyougetitonce,yougetitforallmodes.Fromthenit’sjustcontinuouspracticeandpatience.

ThethirdmodeinourAminorpentatonicexamplebeginsonDandconsistsofa:

Root,Major2nd,Perfect4th,Perfect5th,minor7th

Orsimply:R,M2,P4,P5,m7

Let’squicklyrecaphowwegottothis(it’sthesameprocessaswiththeMajorpentatonicmode).

InMode1 of theAminor pentatonic the noteswere:A,C,D,E,G.Mode3beginsonthe3rdnote,whichisD,andcontinuesfromthere.

Sothenotes,nowinD,are:D,E,G,A,C.

DisnolongerPerfect4thofA,itisnowtheRoot.

EisnolongerthePerfect5thofA,itisnowtheMajor2ndrelativetoD.

Gisnolongertheminor7thofA,itisnowthePerfect4threlativetoD.

AisnolongertheRoot,itisnowthePerfect5threlativetoD

Cisnolongertheminor3rdofA,itisnowtheminor7threlativetoD.

Trytodothisformodes4and5byyourselfwhenwegettothem,itwillbeanicelittlementalworkout.

Now again, D minor pentatonic mode 3 is relative mode to the A minorpentatonic because they share the same notes, and A minor pentatonic is itsparentscale.ButsinceourbackingdronenoteisstillA(intheaudioexample),in order to hear the characteristic sound of this mode we need to useminorpentatonicmode3inA.

Sowejusttakethemode3’sintervalstructurewiththescaleformulaandapplyitstartingfromtheAnoteagain.Thiswillgiveusthefollowingnotes:

A(R)–T–B(M2)–TS–D(P4)–T–E(P5)–TS–G(m7)–T–A(O)

PlayingthissetofnotesandintervalsinA,overtheAbackingdronenotewillgiveusthesoundofthemode3oftheminorpentatonicscale.

MinorPentatonicMode3audioexampleinA->http://goo.gl/1aQJcV

MinorPentatonicMode4ThefourthmodebeginsonEandconsistsofa:

Root,minor3rd,Perfect4th,minor6th,minor7th

Itsnotesare:E,G,A,C,D.

NowEistheRootandwehaveanewsetofintervals.Butagain,sincewewillbeplayingoverAdronenotewe’llneedtouseminorpentatonicmode4inAtogetitssound.Sowetakeitsintervalstructurealongwiththescaleformula(T’sandTS’s),andapplythemstartingfromAnote.Thiswillgiveusthefollowingnotes:

A(R)–TS–C(m3)–T–D(P4)–TS–F(m6)–T–G(m7)–T–A(O)

It is worth nothing again: the intervals in parenthesis explain the note’srelationship to theRoot.Likewithanymode, those intervalsdefineamode

andareresponsibleforitscharacteristicsound.

MinorPentatonicMode4audioexampleinA->http://goo.gl/e8BXnq

MinorPentatonicMode5Finally, the fifth mode begins on the 5th note of the minor pentatonic scale,whichinourAminorpentatonicexampleisG.Ithasa:

Root,aMajor2nd,aPerfect4th,aPerfect5thandaMajor6th

Itsnotes,inG,are:G,A,C,D,E.

Togetthismode’ssoundovertheAdronenoteusedintheaudioexamplewewillhavetouseminorpentatonicmode5inA.

Withoutrepeatingthewholeprocessagain,thenotesofthe5thminorpentatonicmodeinA,are:

A(R)–T–B(M2)–TS–D(P4)–T–E(P5)–T–F#(M6)–TS–A(O)MinorPentatonicMode5audioexampleinA->http://goo.gl/ngqWWY

We’veseenthatmode5ofAminorpentatonicisinG,withthenotes:G,A,C,D,E.As ithasbeen stated several times, thebackingdronenote inouraudioimprovisation excerpts isA, so to get themode’s soundwe had to useminorpentatonicmode5inAinstead(itcangetconfusingsincemodesoftheminorpentatonicdon’thavespecialnames like thediatonicmodes).Thepoint is,wecould’ve used the 5thmode ofAminor pentatonic,which starts onG, for theimprovisationexcerpts,butinthatcasewewouldhavetoplayovertheGdronenotetohearthecharacteristicsoftheAminorpentatonic5thmodesound.Sincewe played the 5th mode of the minor pentatonic in A, can you figure out itsparentminorpentatonicscale?It’sBminorpentatonic.

Don’tworryifyoudon’tgetthisnow,itwillbeclearerwhenwegettodiatonicmodes, just remember,modes are completely relative towhat’s playing in thebackground–playingthesamethingoveradifferentbackingwillhavedifferenteffects.

On another note, the soundof amodebecomes a bitmore apparentwhen it’splayedoverafullchord,orachordprogressioninthebackingtrack.Thoughit’s

important(andeasiertolearnmodes)tojuststartwithadronenoteandkeepitsimpleatthebeginning.Wehaveyettogooverthechordslaterinthebook.

MinorPentatonicModeComparisonChartsTo sum up, here’s a table showing minor pentatonic modes in A with theirintervalfunctions:

Table2:MinorpentatonicmodesinA

Ifyouwantagoodworkoutyoucantrytofilloutthistableinadifferentkey,forexampleC(youwouldstartwithCastheRootnoteinthetopleftcorner).

Table3:MinorPentatonicIntervalComparison

NoticeonTable3hownotesand their functionschangewithdifferentmodes.Noticeforexamplehowmodes2and5aresimilar—Mode2hasaMajor3rd(3)andMode5hasPerfect4th(4).Lookforpatternsandnoticethedifferences.

Wewillnowmoveonto7-notescales,butfirst...

Term“Diatonic”,WhatDoesItMean?A scale is diatonic when it is a mode, or variation, of the major scale. Thisincludes thenaturalminor scaleandall7of thediatonicmodes (ofwhich themajorandminorscalesaretwo).

Theword“diatonic”isGreek,anditmeans“acrosstheoctave.”Thenamerefersto the fact that the structure of diatonic scales is such that there is an evendistribution of 7 notes across the 12-note octave. There is never, in anydiatonicscale,morethanafull(whole)stepbetweentwonotes,andthehalf-stepsarespreadoutbyatleasttwofullsteps.

While thereare7diatonicscales—called thediatonicmodes,which includesthemajorscaleandtheminorscale—thereisonlyonediatonicstructure.

Thisisbecauseall7ofthosescalesaredefinedintermsofoneanother.Infact,theyaregenerated fromoneanother (though inmostcases theyare said tobegeneratedfromthemajorscalebecauseitisthemostfundamentalscale).

They share a structure because they are effectively the same 7-note patternbeginningatdifferentnotes/points(ifyoutreatthefirstnoteofthemajorscaleasthefirstnoteofthediatonicstructure,thenyoucandefineacompletelydifferentscalemoving up that structure but beginning on the second note, or the fifthnote,oranyothernote—justliketheminorpentatonicmodes).

Sincethereisonlyinfactonediatonicstructure,itispossibletotalkbothaboutdiatonic scales (meaning the modes of the major scale) and also about THEdiatonicscale(asintheunderlyingstructureofthosemodes).

Thisisanexclusiveusageandunderstandingoftheterm“diatonicscale”,whichis not entirely consistent, but is by far the most common and recommended.Sometheoristsalsoincludeharmonicandmelodicminormodesasdiatonicforspecificreasons,butthisismuchrarerandcancausesomeconfusion.

7-NoteDiatonicScales—NaturalMajorandNaturalMinorScaleAsweknownow, themostbasic, fundamental typeof7-notescale iscalleda“diatonic scale”, and this category includes what are probably the two mosteasily recognizable scales by name: the natural major scale (usually simply“the major scale”) and the natural minor scale (usually simply “the minorscale”).

These two scales form the harmonic andmelodic bedrock thatWesternmusiclays on and has laid on for a very long time, and similar scales are foundthroughoutthehistoryofworldmusic(intraditionalIndianmusic,forinstance).

It is worth noting now that just like with the minor pentatonic and majorpentatonic,naturalmajorandnaturalminorscalesaresimplythemodesofeach

other, butwithmajor scalebeing thoughtof as themost fundamental diatonicscale.

Alsoworthnotingisthatthe5-notemajorpentatonicscaleisjustlikethe7-notenaturalmajorscale,exceptthattwonotesareomitted.Samegoesfortheminorpentatonicandthenaturalminorscale.

Thesepentatonicscalescamefromthedesiretoremovetheintervalsthatareasemitone apart in the diatonic structure. Because of that, minor and majorpentatonicscalesareessentiallysimplifiedandsafersoundingminorandmajorscales.Seescalecomparisonchartlaterinthebookandthiswillbecrystalclear.

WhyIsMajorScaletheMostImportantScaletoLearn?Beyond the pentatonic scale, the first scalemostmusicians learn is themajorscale.Itisalsothefirstscalemostofus,evenatayoungage,canrecognize.ItisthefoundationinWesternmusic,andvirtuallyall7-notescalesarederivedfromitinonewayoranother—itistheyardstickagainstwhichtheyaredefined.Forallofthesereasons,itisoftenthefirstpieceofrealmusictheorythatinstructorsintroducetobeginningmusicians.

Themajorscaleisthescalethatresultswhenyousingthatfamiliar“do,re,me,fa, sol, la, ti, do” (singing notes in this way is referred to as solfege). It isgenerallydescribedasahappy,upliftingscale,anditiseasytoproducehighlyconsonantmelodiesusingit.Forthisreason,manypopsongsarewrittenusingthemajorscale.

The intervals that define any given scale are described according to theirrelationshiptotheintervalsthatmakeupamajorscale.Inotherwords,allscalesareinsomewaymeasuredagainstthemajorscale.

This7-notescaleisthefoundationforalldiatonicharmony;allofthevariationsofthemajorandnaturalminorscalescanbegeneratedbythemajorscale,andsinceallnon-diatonicharmonycanbe seenasdiatonicharmony thathasbeenaltered (chromatically) in some way, there are virtually no scales that aren’tsomehowderivablefromthemajorscaleanditsvariations.

In most types ofWestern music, from classical to celtic to pop, major scaleforms the foundation of the harmony.Minor pentatonicmight be regarded as‘the king’ in all blues music, but even that scale is derived from the naturalminorscale,whichisagainderivedfromthemajorscale.

InWesternmusiceverythingrelatesbacktomajorscaleinonewayoranotherandthat’swhyitisthemostimportantscaletolearn.

UnderstandingMajorScaleStructureThemajorscaleisa7-notescalesoitconsistsofsevennotes.Thestructureofamajor scale is relatively even (the consequence of being a diatonic scale); itconsistsof:

1. ARootnote(R)

2. Thenanoteawholestepabovethat,calledtheMajor2nd(M2)

3. Anoteawholestepabovethat—theMajor3rd(M3)

4. Anoteahalfstepabovethat—thePerfect4th(P4)

5. Anoteawholestepabovethat—thePerfect5th(P5)

6. Anoteawholestepabovethat—theMajor6th(M6)

7. Andalastnoteawholestepabovethe6th,whichistheMajor7th(M7);

Thedistancebetweenthe7thnoteandthefirstnoteofthenextoctaveisahalf-step,andtheoverallstructureofthescale(youcanalsosay‘scaleformula’)is:

whole,whole,half,whole,whole,whole,halfWWHWWWH

or:

Tone,Tone,Semitone,Tone,Tone,Tone,SemitoneTTSTTTS

Figure7:Majorscalestructure

Andhere’showitlooksonaguitarfretboard:

Figure8:Majorscaleonasingle(thickestlowE)string

Sowehave:

R—T—M2—T—M3—S—P4—T—P5——T—M6—T—M7—S—R(Octave)

This is the formofalldiatonic scales (only since they’remodesof eachothertheybeginatdifferentpointsinthestructure).

Eachscalehasastartingnote—calledtheRootnote(R),whichgivesthescaleitsname.Rootnotecanbeanyofthe12notesfromthenotecircle.

Ifwesay:“In thekeyofAmajor” (oryoucan justsay“inA”, if it’samajorkey),itmeansweuseAnoteastherootnoteandthenapplyfromitthemajor

scalestructure(TTSTTTS).

So“inA”thenoteswouldbe:

A—T—B—T—C#—S—D—T—E—T—F#—T—G#—S—A

Figure9:MajorscaleinA

InthekeyofC,thenotesare:

C—T—D—T—E—S—F—T—G—T—A—T—B—S—C

IfyoustartontheDnoteyouwouldgettheDmajorscale,ifyoustartontheG,thatwouldbetheGmajorscale,BbwouldbeBbmajorscale,andsoon.

Outofall12keys,Cmajorkeyisspecificbecauseitcontainsallofthenotesofthe chromatic scaleminus the sharps and flats:C,D,E,F,G,A,B—whichmeansthatonapianotheCmajorscaleisjustthewhitekeys.Everyotherkeyhasoneormoreblackkeys(sharps/flats).

It isworth repeating that knowing the scale formula of a scale is very usefulbecause you can start on any note, apply the formula, and youwould get allnotes of that scale. You don’t have to remember all the note positions of aparticular scale on your instrument— if you just know the scale formula andunderstand its interval structure it isveryeasy to remember,playanduse thatscale.

Inthecaseofthemajorscalethisisparticularlyimportantbecause,ifyourecall,allotherscalesarederivable fromthemajorscale,and ifyouknowtheMajor

scalestructure it ismucheasier tounderstand, learnanduseotherscales,eventhenon-diatonicones.

NaturalMinorScaleStructureSecondonly to themajorscale is thenaturalminorscale,orsimply theminorscaleforshort.Nolessfoundational,itisremarkablydifferent.Theminorscaleislesscommoninpopmusicthanthemajorscale,sinceitisfarhardertocreateamelody that will stick in someone’s ear with theminor scale thanwith themajorscale.

Thisscale isuseful inverymanysituations,and it ismarkedbyapronouncedtension that creates musical friction while at the same time sounding ratherconsonant.

Thenaturalminorscaleis,accordingtomanypeople,asad,deep,darksoundingscale.Itisthedarkcousinofthemajorscale.Thoughitcanbeplayedinwaysthatmakethemusicmovequicklyandevenbrightly,thenaturaltendencyofthisscaleisinthedirectionofdarkness.

Theminor scale is dark, deep, and heavy sounding, and is often described as“sad.” Though themajor scale ismore common in some forms ofmusic, theminor scale is far from rare, occupying a central place in classical and jazz,amongotherstyles.

Theminorscaleisamodeofthemajorscale(the6thmode).SotheminorscalethatisthemodeoftheCmajorscale:

—istheAminorscale,consistingofthenotesA,B,C,D,E,FandG.

Thestructureofthisscaleisthesameasthatofthemajorscale:whole,whole,half,whole,whole,whole,half,onlyit isre-orientedsothatthe6thnoteofthemajorscale is theRootof thecorrespondingminorscale(InC, thatmeansthe

rootoftheminorscaleisA;inAmajortherelativeminorscaleisF#minor,andsoon).

Sothestructureoftheminorscaleisthesameasthemajor,onlyshiftedsothatitnowstartsfromthe6thnote.It’sthesameconceptaswiththepentatonicsbutisworthgoingthroughagain.

Nowitis:

tone,semitone,tone,tone,semitone,tone,tone.

or

TSTTSTT

Theminorscaleconsistsofthefollowingnotes:

Root,Major2nd,minor3rd,Perfect4th,Perfect5th,minor6th,minor7th

Sowehave:

R—T—M2—S—m3—T—P4—T—P5—S—m6—T—m7—T—R

Hereitisonaguitarfretboard:

Figure10:Naturalminorscaleonthethickestguitarstring

ThenotesinAminornoware:

A—T—B—S—C—T—D—T—E—S—F—T—G—T—A

Figure11:MinorscalestructureinA

Notice the similarities between thisAminor scale and its relativemajor—Cmajorscale(It’sthesamestructureonlythenotesarere-orientedsothatnowAis thestartingnote).Becauseof this,keyofAminor isalsowithout sharpsorflats.ThisgoesforanymodeoftheCmajorkey.

Alsonotice thesimilaritiesbetween thisminorscaleandminorpentatonicandmajorandmajorpentatonicscale.Canyoufigureoutwhichnotesareleftout?Refertothescalecomparisonchartshouldyouhaveanytroublewiththis.

Asanexerciseyoucantrytofigureouttherelativeminorscalesofthefollowingmajorkeys:G,D,A,E,B,F.

MajorandMinorScale—UnderstandingtheDifferenceWehavealreadysaidthatthemajorandminorscalesaremodesofoneanother.They are each diatonic modes and so they are each variations on the samefundamentalharmonicstructure.

Butthatdoesn’tmeantheyarethesamescale.Whiletheyshareastructure,theybegin at different parts of that structure,whichmeans that the set of intervalsthatdefinethosescalesisradicallydifferent.Musicisallabouttheintervals,and

ifthesetofintervalswithinascaleisdifferent—eventhoughthescalessharethesameharmonicstructure—thenthesoundofthatscalewillbedifferentaswell.

Whatwasthedistancebetweenthe1stand3rdnotesofthemajorscaleisnowthedistancebetweenthe3rdand5thnotesoftheminorscale.Thatmeansthat,ifyouplayamajorscaleandaminorscalethatarerelativetoeachother(thatcontainallofthesamenotes),thenthenotethatwasthemajor3rdofthemajorscaleisnowtheperfect5thoftheminorscale.Thenotethatwastheperfectfourthofthemajorscaleisnowtheminor6thoftheminorscale.

The major scale consists of intervals (with respect to its root) that define ahappy,bright, typicallymajor-soundingscale,while theminorscale’s intervals(withrespecttoitsroot)defineasad,dark,typicallyminor-soundingscale.

In general, the difference between these scales is quite stark, and it is thedifferencebetweendarknessandlight,betweenhappy,easyplayandsad,darkdepth. It is easy to hear the difference, and once you do, it will be easy toidentifythegeneraldifferencebetweenmajorandminortonalitiesinthefuture.

Awordonthatlastthought—Thereisthedifferencebetweenthemajorscaleandthenaturalminorscale,butthenthereisalsothedifferencebetweenmajorandminor tonalities ingeneralbetweenanychordsor scalesof themajor andminor families. There aremanymajor chords andmanymajor scales, just astherearemanyminorchordsandmanyminorscales.Eachofthemisdifferentfromtheothers,sometimesradically.

The thing that allmajor scales and chords have in common, however, is theirbeingmajorscalesandchords.Whilethemajorscaleisthetypical,iconicmajorscale and the natural minor scale is the typical, iconic minor scale, there areothermajorscales(suchastheLydianmode)andotherminorscales(suchasthePhrygianmode)thatshareenoughincommonwiththoseiconicscalestobeinthe same major or minor family, both of which belong to one big diatonicfamily.

Once you have learned to distinguish between the major and minor scales,distinguishingbetweenmajorandminortonalitiesingeneralisonlyastepaway,andgenerallycomeseasily.

FiguringOuttheMajorScaleinAllKeys(MajorScaleExercise)Agreatexerciseforyounow(andacoollearningexperience)istofigureoutthemajorscaletonesforeachofthenotes/keys.

Takealookatthetableonthenextpage,copyitifnecessaryandfillitoutwiththeappropriatenotes.Youcanusethenotecircleonlyifyou’restuck,andalsotocheckafterwardsifyougotitright.

Figure12:Majorscaleinallkeys

Thereare12notesinmusic,sotheremustbe12Majorscales—eachstartingfromadifferentnote,right?Well,yes,butinmusictheoryit’snotthatsimple.Wehavetodealwithboth#’sandb’s.

Inordertofillouttheentiretablecorrectlyyouhavetofollowasimpleruleinmusic theorywhichsays that therecan’tbe two sideby sidenoteswith thesamename. Inotherwords, youneed tohave each letter of the alphabet in ascalekeyonlyonce,andyoujustadd#’sorb’sasnecessary.Agoodpractice

whenfiguringoutthenotesofascalethenistofirstjustwriteoutthealphabetlettersfromthestartingnote.

Let’s checkout thekeyofA#as an example– apurely theoreticalkeyandahardone to figureout.One toneafterA# isC,one toneafterC isD,andonesemitoneafterD isD#,etc.Butwecan’thaveA#–C–D–D#because thisbreakstherule:BletterismissingandtwoD’saresidebyside.That’swhyweusedoublesharps(orflatsforflatkeys)andwewritethiskeyinthefollowingway:

A#—T—B#—T—C##—S—D#—T—E#—T—F##—T—G##—S—A#

On the table the first7-8keysareverycommonlyused inmusic. I’ve left thetheoreticalkeyslikeA#foryouasachallengeandpractice.Trytofigurethemoutandyou’llgainamuchbetterunderstandingofmajorscalekeys.

Notethatforthekeysstartingonanotewithsharp(#)youwoulduse#’s,andifthe key starts on a note with flat (b), you need to use b’s. I’ve provided acomplete list of all notes in all keys at the end of this book so that you candoublecheckyourwork.

DemystifyingDiatonicModesIf there is one thing that scares musicians, in particular guitarists, it is thediatonicmodes.Widely known but rarely understood, “themodes” are nearlymythicformanyplayersatmanylevels.

Mostofusknowthatthemodesareimportant,thatgreatplayersknowallaboutthem,but it feels like theyaremiles away—part ofwhatpeople call “musictheory”andnotatallthesortofthingthatwecanunderstand,muchlessmakeuseof.

Maybewehaveheardofmodaljazzandbelievethatthemodesareofinteresttoadvancedjazzplayerswithyearsofformal trainingbut that theyareotherwiseunnecessaryorbeyondourreach.

But themodesarenotmonstrous.Theyarenot amyth.Theyarenotonly forpeoplewhospendtheir20sinmusicschool.Theyaren’tjustforjazzmusicians,

andtheyaren’t,onceyouhavelearnedthem,anymoredifficulttousethananyotherscales.Whattheyare,however,isimportant.

The modes give us a way to understand the interconnectedness of differentscales,offerusavarietyofscalestochoosefrominmanysituationsandgiveusthetoolstocomposeorimproviseinanynumberofwaysoverandinvirtuallyanyharmonicframework.

We have seen that a mode is simply a re-orientation of a scale, treating adifferentnoteastherootandre-definingtheothernotesinthescale.Thenotesstaythesame,butsincetheharmoniccenterisdifferent,thesetofintervalshaschanged(whatwasaperfect5thintheAminorscalebecomesamajor3rdintheCmajor scale).And that is the essenceofmodality— the fact of the relativeharmonicvalueofnotes.

Anoteisnotastatic,unchangingthing;anotedoesdifferentthingsindifferentcontexts (depending on the harmony that is playing underneath or in thebackground).Itisrelative.Thatisthefactthatconfusesmanyplayers,anditisthereasonthatthemodesareoftenavoided.

Beforegoinganyfurther,itisimportanttounderstandafewterms.

ParallelandRelativeModes,ParentScalesandTonalCenterWhenwe talk aboutmodes and scales, we talk about twoways for scales torelatetooneanotherconsonantly.Oneisbeinginparallel,andtheotherisbeingrelative.

RelativeModesRelative modes are what most of us think about when we think about “themodes”, and it is the way the modes have been presented thus far. Relativemodes are scales that contain all of the same notes but begin at differentplaces.CmajorandAminorarerelativescales,sameasGmajorandEminor.

Comingbacktotheminorpentatonicmodes,itwassaidthatallofthemodesoftheminor pentatonic are relative to one another because they share the samenotes,aswe’veseen:forexample,AminorpentatonicandCmajorpentatonic

arerelativescales,sameasthemode3ofAminorpentatonicinDandAminorpentatonic,andsoon.

Relativemodesareusefulwhenextendingtherangeofapieceupordowntheharmonic space, on a guitar fretboard for instance.They are also usefulwhenfiguringoutwhichchordswillsubstitutebestforotherchords,butwe’llget tothatlaterinthebook.

ParentscalesThis is the scale that othermodes are derived from.Aswe’ve seen, for all 5modes of the minor pentatonic, the first mode — the minor pentatonic, isconsideredtheParentminorscale,sinceothermodesarederivedfromit.

It is important tobeable to tellquicklywhat is theparentscaleofeachmodethatyouencounter.Forexample,canyoufigureoutwhatistheparentscaleofminorpentatonicmode4inC#?

Youwouldneedtolistoutthenotesfirstbyapplyingtheminorpentatonicmode4formulastartingfromC#:

C#(R)–TS–E(m3)–T–F#(P4)–TS–A(m6)–T–B(m7)

Weknowthatrelativemodesarejustre-orientationsoftheparentscale,soafterwhichnoteC#comesasthe4th?

It’s F# (F#, A, B,C#, E). So the parentminor scale of theminor pentatonicmode4inC#,isF#minorpentatonic.

Therearequickermethodstofigureouttheparentscaleswhichusuallyinvolveusingyourinstrument,althoughthisissomethingthatwillcomenaturallywithtime as you continue to use modes in your playing. On guitar fretboard forinstance, there are physical shapes you can derive from the notes and theirpositionsrelativetooneanother,andyoucanvisualize thisshapeanytimeyouwanttorecalltheParentscaleandotherrelativemodesofamode,quickly.

TonalcenterTonalcenterislikethecenterofgravity–itisusuallythechordoranote(asinour casewith audio examples) that themode is played over.Whenwe use amode, there are some notes thatwill help define the tonal center in our solo.Theseare thegoodnotes, oryoucould also call them thehomenotes. Thesenotesareusuallythenotesofthechordthatisplayinginthebackgroundatthe

moment,andthestrongestofthemistheRootnote(itisusuallythesafestonetolandonduringplaying).

Then, therearesomenotes thatpullawayfromthe tonalcenter,establishingamovement, and there are some thatwill add lots of tensionwhich tends to beresolvedtoahomenote.Therearealsobadnotes,whichcanreallyclashwiththetonalcenterorothernotesplayinginthebackground,andtheyusuallywon’tsoundgoodatall.

ParallelModesAparallelmodeorscale issimplyascale thatshares its rootwith theoriginalscaleinquestion.Inotherwords,themodesthatsharethesametonalcenterareparallelmodes.For instance,AmajorandAminorareparallelmodes,BminorpentatonicandBmajorpentatonicareparallelmodes,sameasELocrianand E Lydian (don’t worry about the fancy names for now), or any othermode/scale with the same starting note. In audio examples for the minorpentatonicmodesweplayedparallelmodesagainsttheAdronenote.

Relativemodessharethesameparentscale—theyhavethesamenotes,ordereddifferently,buttheyhavedifferentRoots,whichmeanstheyhavedifferenttonalcenters.Parallelmodesontheotherhandsharethesameroot—thesametonalcenter, but they have different Parent scale. This distinction is important tounderstandandremember.

Parallelmodesarequiteusefulinmodalharmony,whenitisnotuncommontoaltertheharmonyofapiecebysubstitutingoneparallelmodeforanother.Thisiscalledmodalinterchange.Moreonthismuchlaterinthebook.

DiatonicModesSpelledOut(withAudioExamples)We’veseenthatthemajorscaleisamodeoftheminorscaleandthattheminorscale is amode of themajor scale. In general, themajor scale is taken to beprimarywhen talking about the diatonicmodes, andwhenwe talk about “the

modes,”wearealmostalwaystalkingaboutthesescales—diatonicscales:themajorscaleanditsmodes,whichincludethenaturalminorscale.

Thereare7notesinthediatonicscaleandsothereare7diatonicmodes.Unlikethe pentatonic scalemodes, diatonicmodes each have their ownGreek name,and thosenamesareusuallyhowwe refer to themodeswhenweare thinkingmodally.

Again,wewillhaveaudioexamplesforeachmodeinthesameformat:

1. Ascale/modeplayedupanddown2. Chordsfromthatscaleplayedinorder(intriadform)3. Animprovisationexcerpt,thistimeovertheCdronenote.

Thekeywe’llbeusingisCMajorandalloftheimprovisationexcerptswillbeplayedoverCdronenote.

IonianModeThefirstmodeisthenormalMajorscale.ThisiscalledtheIonianmode.InC,itsnotesare:C,D,E,F,G,A,B.

Itconsistsofa:

Root,Major2nd,Major3rd,Perfect4th,Perfect5th,Major6th,Major7th

Thismodehasahappy,melodic,consonantsound.Wehavealreadyexaminedthis scale/mode in the previous sections. In the improvisation excerptwewillplaythismodeoverCdronenotesowewilluseCIonianmode,youcouldjustsayregularCmajorscale.

IonianmodeaudioexampleinC->http://goo.gl/szNpFJ

DorianModeThe2ndmodeoftheMajorscaleistheDorianmode.Itstartsonthe2ndnoteoftheMajorscale.TheDorianmodeisaminormode(thoughitisnot“theminorscale”) since its 3rd is minor and not major (this is how scales are dividedbetweenmajorandminoringeneral).

InD,itsnotesare:D,E,F,G,A,B,C.

Ithasa:

Root,Major2nd,minor3rd,Perfect4th,Perfect5th,Major6th,minor7th

Howdidwegetthisintervals?Easy,justforthismodelet’sdoaquickrecap.

DDorianisrelativetoCMajorscalebecause,aswecansee,theysharethesamenotesbuthavedifferenttonalcenters.SinceweknowthenotesinCMajor,weknow them inDDorian aswell, and it’s easy to figure out the intervals fromthere:

DistheRoot

EistheMajor2ndupfromD

Fistheminor3rdupfromD

GisthePerfect4thupfromD

AisthePerfect5thupfromD

BistheMajor6thupfromD

Cistheminor7thupfromD

Anotherwaytogettothisintervalstructurewithoutthetonalcenter, is totakethemajorscaleformula:

TTSTTTS

—andre-orientit likewedidwiththenotes.Sincethismodestartsonthe2ndnoteoftheMajorscale,westarton2nd‘T’(bolded).

SothescaleformulaforDorianmodeis:

TSTTTST

Nowwejuststart fromtheRoot(whichcouldbeanynote)andcontinuefromthere:

R–T–M2–S–m3–T–P4–T–P5–T–M6–S–m7–T–R(O)

TheDorianmodeisdarkerthantheIonianmodebecauseoftheminor3rd,butitsounds a little brighter than the minor scale because of theMajor 6th. It is acommon scale in jazz and especially blues. Make sure to consult the ScaleComparisonChartsafterwardstolookforthesedifferences.

Nowlikewiththepentatonicmodes,wewillplaythismodeinparallelsinceourdrone note isC.Thatmeans thatwewill playCDorianmode overC in theimprovisationexcerpt.

Firstweneedtofigureout thenotes inCDorian,whichissupereasybecausewecanjustapplyitsDorianscaleformulaoritsintervalstructure,bothofwhichwe’refamiliarwith:

C–T–D–S–Eb–T–F–T–G–T–A–S–Bb–T–C(O)

Canyouexplainwhyweusedb’stowriteoutthesenotesandnot#’s?

DorianmodeaudioexampleinC->http://goo.gl/EiwnD7

Again,listentotheeffectofeachnoteoverthedronenote.Noticewhichnotesare stable and safe sounding and which ones are more dissonant providingtension,andhowthattensionisreleasedtoastablenote.

PhrygianModeThe thirdmode is thePhrygianmode. It starts on the 3rd note of theMajorscale. It isaminormode (becauseof theminor3rd), thoughagain it isnot thenaturalminorscale.InE,itsnotesare:E,F,G,A,B,C,D.

Ithasa:

Root,minor2nd,minor3rd,Perfect4th,Perfect5th,minor6th,minor7th.

The Phrygianmode is dark sounding and due to itsminor 2nd, is very exoticsounding.Theminor2ndnoteisjustahalf-stepabovetheRoot,sothisnoteaddsalotofdissonancebecauseitnaturallywantstoresolvetothenearesttonic(theRoot). This mode is used in some jazz, metal, as well as Latin and Indian-influencedmusic.

IntheaudioexampleweuseCPhrygianovertheCdronenote.ThenotesinCPhrygianare:

C(R)–Db(m2)–Eb(m3)–F(P4)–G(P5)–Ab(m6)–Bb(m7)PhrygianmodeaudioexampleinC->http://goo.gl/dvr2ke

LydianModeThefourthmodeistheLydianmode.Itstartsonthe4thnoteoftheMajorscale.Thisisamajorscalebecauseit’s3rdismajor,anditsnotesinFare:F,G,A,B,C,D,E.

Ithasa:

Root,Major2nd,Major3rd,Augmented4th(Tritone),Perfect5th,Major6th,Major7th

TheLydianmodeisaverypleasantsoundingmode—similartothemajorscale(itdiffersfromitonlybyonenote:theTritone),onlyslightlymoreexotic.Thereisasubtledissonanceinthismode,thoughitisamajormode,andsoittendstosoundrathercomplex,evensophisticated.Itiswidelyusedinjazzinplaceofamajorscaleandovercertainjazzchords.

Sincewe’llbeusingCLydianmodetoplayovertheCdronenote,we’llneedthenotesoftheCLydianscale:

C(R)–D(M2)–E(M3)–F#(Aug4)–G(P5)–A(M6)–B(M7)LydianmodeaudioexampleinC->http://goo.gl/YtV1MW

MixolydianModeThe fifthmode is theMixolydianmode. It starts on the 5th note of theMajorscale.ItisamajormodeanditsnotesinGare:G,A,B,C,D,E,F.

Itconsistsofa:

Root,Major2nd,Major3rd,Perfect4th,Perfect5th,Major6th,minor7th

TheMixolydianmodeisagreatbluesscaleandhasaround,stablesound.LikewiththeLydianmode,theonlydifferencetotheMajorscaleisonenote—theminor7th.

In theaudioexamplewewilluseCMixolydian toplayoverCnote. Itsnotesare:

C(R)–D(M2)–E(M3)–F(P4)–G(P5)–A(M6)–Bb(m7)MixolydianmodeaudioexampleinC->http://goo.gl/nKAPRv

AeolianModeThesixthmodeistheAeolianmode.ThisistheNaturalminorscale.InA,itsnotesare:A,B,C,D,E,F,G.

Ithasa:

Root,Major2nd,minor3rd,Perfect4th,Perfect5th,minor6th,minor7th

TheAeolianmodeisquitedark,evensadsounding, thoughit isnotaltogetherdissonant, and it is widely used in virtually all types of music. We haveexaminedthisscaleintheminorscalesection.

In the improvisationexcerptwewilluseCAeolianmode,orCNaturalminorscale.Itsnotesare:

C(R)–D(M2)–Eb(m3)–F(P4)–G(P5)–Ab(m6)–Bb(m7)AeolianmodeaudioexampleinC->http://goo.gl/kkGZLh

LocrianmodeTheseventhandthefinalmodeistheLocrianmode.Itstartsonthe7thnoteoftheMajorscale.InthecaseofCMajor,itstartsonB;soinB,itsnotesare:B,C,D,E,F,G,A.

Itcontainsa:

Root,minor2nd,minor3rd,Perfect4th,diminished5th(Tritone),minor6th,minor7th

Thismodeisstrange,andrarelyused.Itisaminorscale,butbothits2ndand5thnotes are flat. It is the only diatonic mode without a Perfect 5th, the Locrianmodethusishighlyunstable.Historically,thisscalewasavoidedaltogether.Itssoundisheavy,dissonantandunstable.

We’ll be usingCLocrian in the improvisation excerpt over theCdronenote.ThenotesinCLocrianare:

C(R)–Db(m2)–Eb(m3)–F(P4)–Gb(dim5)–Ab(m6)–Bb(m7)LocrianmodeaudioexampleinC->http://goo.gl/i6DVRG

DiatonicModesComparisonCharts(PlusPMSExercise)Ihopethatyoucanseebynowhowmodesareeasyonceyouunderstandthemfundamentally.

Tosumup,here’satableshowingthediatonicmodes:

Table4:DiatonicmodesinC.AllthesemodesarerelativetoCMajorscale.

Andhere’satableshowingallmodeswiththeirrespectiveintervalsandnotes.

Table5:Diatonicmodeswiththeirintervalsandnotes.

Studythischart. It isveryimportantchartfor thediatonicmodesandyouwillneedtomemorizeitifyouwanttousemodesinyourplayingefficiently.Also,takesometimetoanswerthefollowingquestions:

Howb’sappearafter theIonianmode?NoticethatDorianaddsb’sonthe3rd andthe7th,andPhrygianaddsflatsjustbehindthose—onthe2ndandthe6th.Whatistheonlymodewitha‘#’andwhere?Whatisthemodewithonlyone‘b’andwhere?Whatisthemodewiththemostflatsandwherearetheylocated?WhatistheonebigdifferencebetweenAeolianandPhrygianmodesandwhy?WhydoesLocrianmodesoundobscureandwhyisitdifficulttouse?Whyhavewewrittenb5fortheLocrianmodeinsteadof#4?

ParentMajorScale(Exercise)Whenusingmodes,youshouldthinkabouttheminparallel,thatis,treatthemasseparatescales,butatthesametimeitisimportanttoknowtheirrelativescalesandwhatistheParentMajorscaleofeachmodeinanykey.

Forexample,parentmajorscaleofELocrianis…

…Fmajor,andparentmajorscaleofFLydianis…

…Cmajor.

Let’sexplainthesetwo.First,ELocrian–weknowthatLocrianisthe7thmodeofitsParentMajorScale(PMS).WealsoknowthatinaMajorscale,the7thnoteisjustahalfstepbehindtheRootnote.Inthiscase,anotethatisahalf-stepupfrom E is F, so PMS of E Lociran is FMajor or F Ionian (both are correct,althoughit’smorecorrecttosayFMajorinthiscase).FiguringoutthePMSfortheLocrianmodeisveryeasyinanykey.

Youcanapplythisprocessforallmodessimplybycountingthestepsandhalf-steps.

DorianisjustonewholestepupfromitsrelativePMSRoot,or10half-stepsdownfrom the root octave. So in any Dorian key you can just count two half-steps orsemitonesbackinyourhead.Forexample,PMSofD#DorianisC#Majorscale.Phrygian istwowholestepsupfromthePMSrootor4half-steps.Intheoppositedirection,itis8half-stepsdownfromtherootoctave.Lydianis5half-stepsupfromtheroot,or7half-stepsdownfromtherootoctave.Mixolydian is 7 half-steps up from the root, or 5 half-steps down from the rootoctave.Aeolianis9half-stepsupfromtheroot,or3half-stepsdownfromtherootoctave.Locrianis11half-stepsupfromtheroot,or1half-stepdownfromtheoctave.Ionianiszerohalf-stepsupordownfromtheroot.

ButwhatifwehaveamodethatisinthemiddleofthePMS,namely:Phrygian,Lydian,MixolydianorAeolian,andwedon’twanttobotherwithcountingthehalf-steps?

Forthat,let’sdeterminethePMSofFLydian.Theprocesswhichcanbedoneforanymode, isasfollows(itwasdescribedbrieflyearlier in theParentscalesection):

First,welistoutthenotesofFLydian(youcanuseTable4–Diatonicmodeswiththeirintervals,forthis):

F(R)–G(M2)–A(M3)–B(#4)–C(P5)–D(M6)–E(M7)–F(O)

SinceweknowthatLydianisthe4thmodeofitsPMS,welookatthenotesandseetowhichnotetheFcomesasthe4th?

It’sC.

C(1),D(2),E(3),F(4),G(5),A(6),B(7).

SoPMSofFLydianisCMajorscale.

AsanexercisetrytofigureouttheParentMajorscaleofthefollowingmodes:

1. GDorian?2. F#Mixolydian?3. EPhrygian?4. A#Aeolian?5. GLydian?6. DLocrian?7. BIonian?8. DbMixolydian?

TherewillbeanswersprovidedattheendofthebookintheCheatSheetsection.

HowtoHearaMode(PracticalExercise)It is one thing to know what the modes are, to know what modality is inabstractionand tobeable toname themodes,even tospell their intervalsandrelationship.Itisonethingtoknowascale,butitisquiteanothertounderstanditpractically. It isone thing tohave it inyourmind; it isanother tohave it inyourears.Thepointoflearningscalesandtheirmodesistobeabletomakeuseofthem,andthatmeansbeingabletoreallyhearthemandtoknow,fromtheirname,whattheywillsoundlikeandhowtheywillfeel.

Insomemusiccourses, there isa lotof focuson formalear trainingandsightsinging, in which students are asked to recognize, name and notate scales(amongotherthings)bytheirsoundandsingthemaccuratelyafteronlyseeingthemwrittendownorbeingtoldtheirname.

Itisnot,foreverymusician,necessarytobetrainedinthatway.Theabilitytoattachaparticularnameandaparticularsetofwrittensymbolstoasound(andtobeable tosing,frommemorythosemusicalstructures) isfarremovedfromtheactofactuallyplayingorwritingwiththosestructures.

But some form of ear training, in which there is a general, emotional,unconscious sense of what different scales do and how they will impact themusic is very important to being a goodmusician.Evenmusicianswhodon’tknow anything about theory, if they are good, have this sort of internal,unconsciousconnectiontodifferentsetsofintervals.

Itishowyouknowwhatwillworkandwhatwillnotwork,andhowyouknowwhatyoulikeandwhatyoudon’tlike.Inshort,itishowyouknowwhattoplayandhowtosoundlikeyou,howtohaveastyleofyourown.

So how can you develop that sort of familiaritywith scales and theirmodes?There is no shortcut really, you simply have to learn to hear them and usethem… a lot. But there are some exercises (beside the regular ear trainingexercises)thatcanhelp.

Theexerciseissimple:

1. Playadronenote(onguitar,theEstringwouldbemostnatural),whichwillestablishyourkey,yourtonalcenter.Thenyoucanplayvariousscalesandmodesinthatkey.SoplayanEnoteforexampleandletitdrone(sustain),andthenplayanEIonian,andthenanEDorian,andthenanEPhrygian,andsoon.Playallofthemodesthatshare the same tonal center. This is what we have done for the Pentatonic andDiatonicmodes’audioexamples,butyoushouldbeabletodoitonyourownnow.Try it. Listen for differences in harmonic effect and feel for differences in overallaffect.

2. Onceyouhavedone this, it isuseful tomoveon toplayingoverasinglechordorentirechordprogressions.Makeorfindabackingtrackforeachmodeandplayoverthoseprogressionsusingthosemodes.Youwilldevelopasenseforthedifferencesbetweenscales.However,ifyou’renotfamiliarwithchordsandchordprogressionsyet,youwillbeable todo thisafteryougo through theChordsection later in thebook.

3. Finally,beginsubstitutingscalesandmodes foreachotherover thesamechordorprogression. If you areplayingover aminorprogression, for instance inAminor,you can perhaps begin by playing inAAeolian (naturalminor scale) and end byplayinginAPhrygian.Thistakestimetotrulyunderstandandbeabletodo,butitiswell worth the effort! By the end of this book you will have a much betterunderstandingofhowtogoaboutthis.

Youmightalsochooseasinglechord:aMajor7thchordfor instance,andplaybycyclingthroughallofthevariousmodesofthepentatonic,diatonic,harmonicminorandmelodicminorscales.Youcanevenusescales thatdon’tmakeanynatural sense— like aDorian over aMajor 7th chord— just to hear what itsoundslike.Doingthissortofsubstitutionwillhelpyoureallylearntofeelthedifferences between scales and will encourage you to remember certainharmonictechniquesandexoticsoundsthatyouenjoyandwanttoincorporateinyourstyle.

HarmonicMinorScale—HowandWhyWasItDerivedfromtheNaturalMinorScaleThediatonicmodesareuseful, and theyofferahostofharmonicpossibilities.They are not, however, exhaustive.There are 12 tones in the chromatic scale,andevenifyoulimityourselftocombiningthose12tonesinto7-notemajororminorscales,therearemorethan7possibilities.

The diatonic scale is one, very stable, cutting of the chromatic scale and itorganizes anoctave in a particularly usefulway formost playersmuchof thetime,but ithasaveryparticular sound.Sometimesmusicianswantadifferentsound,andwhentheydo,theyreachforotherorganizationsoftones.Generally,theseneworganizationsarederivedfromthediatonicscaleinsomeway,andsoonce you know the diatonicmodes, learning other sets of scales is often lessdifficult.

Historically, the most important 7-note scale to be derived from the diatonicscalewaswhatiscalledtheHarmonicminorscale.Theharmonicminorscalewastheresultofthedesiretomaketheminorscaleresolveinaparticularwaywhenplayedascending.

Themajor scale has amajor 7th, and sowhen it is played from start to finishgoingup,thereisastrongresolutionattheend—thelastnoteisonlyahalf-stepbelowtherootinthenextoctave(themoreanoteisclosertotherootthemoreit

wantstoresolvetoit),andsowhenourearsgettothe7thnoteofthescaletheyverynaturallyfeeltheRootcomingnext(whichislikethecenterofgravityinmusic).This is particularly useful for composing and improvisingmelodies inmajorkeysbecauseitmakesiteasytoresolvetension,whichisultimatelywhatmelodiesareallabout.

But in aminorkey, it isn’t so easy.The7th note of theminor (Aeolian) scale(andalsotheDorian,Phrygian,andLocrianmodes)isafullstepawayfromtheRootinthenextoctave.ThismeansthattheRootdoesn’tpullonthe7thnoteinthesamewaythat itdoes in themajorscale,whichin turnmeans that there islessofasenseofmagnetismbetweenthe7thnoteandtheRoot.

Theresult,practically,isthatresolutionsinaminorkey,whetherinthechordsor in themelody, feel less stable than resolutions in amajor key.This canbesolved,however,byalteringtheminorscaleslightly.

Sometimeago,composersrealizedthat if theyraisedthe7thnoteintheminorscalebyahalfstepandlefttherestofthescaleuntouched,theycouldcreateanewscalethathadmostofthepropertiesoftheminorscale—agenerallydeep,darkfeeling—butthatalsohadthepossibilityofstableresolutions,sincenowtherewasonlyahalf-stepbetweenthe7thnoteofthescaleandtheroot(justlikethemajorscale).

ThisnewscalewascalledtheHarmonicminorscale,anditsstructureisderivedfromtheNaturalminorscale.

HarmonicMinorScaleStructureTheharmonicminorscalederivesitsstructurefromtheminorscale,whichisaversion of that diatonic structure, only reordered: whole, half, whole, whole,half,whole,whole.Onlynow,thefinalnoteisraised,whichmeansthatthelastintervalisahalf-step,andthesecond-to-lastintervalhasbeenincreasedtoastepandahalf.

InA,wesaidthatthenotesoftheminorscaleare:A,B,C,D,E,F,G.ThenotesoftheAharmonicminorscalethenare:A,B,C,D,E,F,G#

Sotheharmonicminorstructureisthis:

whole,half,whole,whole,half,whole+half,half

or:TSTTSTSS

Intermsofintervals:

R—T—M2—S—m3—T—P4—T—P5—S—m6—TS—M7—S–R

InA:

A—T—B—S—C—T—D—T—E—S—F—TS—G#—S—A

Figure13:HarmonicminorscalestructureinA

Because of the structure like this (step and a half between 6th and 7th note)harmonicminorscaleisnotadiatonicscale.

TheModesoftheHarmonicMinorScale(WithAudioExamples)Nowwe’regettingintosomeexoticstuff thatmanypeopleconsideradvanced.Butitreallyisn’tsinceyounowunderstandmodes.Likethemajorscale,thereare7notesintheharmonicminorscale.Alsolikethediatonicscale,thereare7modes of the harmonicminor scale. The same conceptwe had before applieshereaswell,soitshouldbereallysimple.

Harmonicminormodesdohave theirownnames,whicharenotvery intuitiveand may seem confusing. In essence, they are just variations of the diatonicmodes’ names because they show their relation to the minor scale and otherdiatonicmodesthey’rederivedfrom.

Herearetheharmonicminormodes(HMMforshort)listedinAalongwiththeaudioexamplesfollowingthesameformatwehadsofar.

HarmonicMinorMode1–Aeolian#7Thefirstmodeof theharmonicminorscale is just thenormalharmonicminorscale.Itconsistsofa:

Root,Major2nd,minor3rd,Perfect4th,Perfect5th,minor6th,Major7th.

WhyisthismodecalledAeolian#7?Well,ifyoucomparethisintervalstructure(whichwealreadyexamined),tothatoftheregulardiatonicAeolianmode,youwill see that it is thesamestructure,butwithone importantdifference: the7thnote.

IndiatonicAeolianwehadminor7th,butherewehaveMajor7th.The7thnoteissharpened,hencewhymode1oftheHarmonicminoriscalledAeolian#7.

InAithasthefollowingnotes:A,B,C,D,E,F,G#,andthosearethenoteswewillusetoplayovertheAdronenoteintheimprovisationexcerpt.

Harmonicminormode1–Aeolian#7audioexampleinA->http://goo.gl/f62mgA

HarmonicMinorMode2–Locrian#6Thesecondmodeoftheharmonicminorscalehasa:

Root,minor2nd,minor3rd,Perfect4th,diminished5th,Major6th,minor7th.

IfyoucomparethestructureofthismodetothediatonicLocrianmodeyouwillsee that it is the same interval structure but with one significant difference:diatonic Locrian hasminor 6th, and this one hasMajor 6th, so that’s why it’ssimplycalled:Lociran#6.

DiatonicLocrian:1–b2–b3–4–b5–b6–b7

Locrian#6:1–b2–b3–4–b5–6–b7

ThismodeissometimesalsocalledLocriannaturalbecausethe6thisnolongerflattened.

InB,HMM2orLocrian#6notesare:B,C,D,E,F,G#,A.

IntheimprovisationexcerptthismodewillbeplayedoverAnote,soinordertohearitscharacteristicsoundweneedtouseALocrian#6.

InALocrian#6thenotesare:A,Bb,C,D,Eb,F#,G,andthosearethenoteswe’llbeusingtoimproviseoverAdronenote.Notethatthisisarareinstancewherewehavetousebothsharpsandflatsbecauseoftheruleinmusictheorywe talked about — the rule which says that alphabet letters should not beskippedwhenwritingoutthenotesofakey.

Harmonicminormode2–Locrian#6audioexampleinA->http://goo.gl/LY6Vav

HarmonicMinorMode3–Ionian#5ThethirdHMMhasa:

Root,Major2nd,Major3rd,Perfect4th,Augmented5th(whichisenharmonicallyequivalenttoaminor6th),Major6th,Major7th.

ThismodeiscalledIonian#5andit’seasytotellwhy–again,justcompareitsstructure to the regular Ionian structure, the difference is shown in the nameitself.

InC,itsnotesare:C,D,E,F,G#,A,B.

Butasalways,sincewe’replayingovertheAnoteintheimprovisationexcerptwewillusetheAIonian#5.

ThenotesforthismodeinAare:A,B,C#,D,E#(enharmonicallyequivalenttoF),F#,G#.

Harmonicminormode3–Ionian#5audioexampleinA->http://goo.gl/UeyjgR

HarmonicMinorMode4–Dorian#4ThefourthHMMhasa:

Root,Major2nd,minor3rd,Augmented4th,Perfect5th,Major6th,minor7th.

ItsnotesinD,are:D,E,F,G#,A,B,C.

CanyouexplainwhyisitcalledDorian#4?

InADorian#4 thenotesare:A,B,C,D#,E,F#,G, and these are the noteswe’llbeusingtoplayoverAnote.

Harmonicminormode4–Dorian#4audioexampleinA->http://goo.gl/3YbEBr

HarmonicMinorMode5–Phrygian#3ThefifthHMMhasa:

Root,minor2nd,Major3rd,Perfect4th,Perfect5th,minor6th,minor7th.

InE,itsnotesare:E,F,G#,A,B,C.

CanyouexplainwhyisitcalledPhrygian#3?

InAPhrygian#3,thenotesare:A,Bb,C#,D,E,F,G,andthesearethenoteswe’llbeusingtoplayoverAnote.

Harmonicminormode5–Phrygian#3audioexampleinA->http://goo.gl/zaHsHv

HarmonicMinorMode6–Lydian#2ThesixthHMmodehasa:

Root,Augmented2nd(enharmonicallyequivalenttoaminor3rd),Major3rd,Augmented4th,Perfect5th,Major6th,Major7th.

InF,itsnotesare:F,G#,A,B,C,D,E.

CanyouexplainwhyisitcalledLydian#2?

InALydian#2,thenotesare:A,B#(enharmonicallyequivalenttoC),C#,D#,E, F#, G#, and these are the notes we’ll be using to play over A note toshowcasethismode.

Harmonicminormode6–Lydian#2audioexampleinA->http://goo.gl/qiJKtq

HarmonicMinorMode7–Mixolydian#1orSuperLocrianFinally,theseventhHMmodehasa:

Root,minor2nd,minor3rd,diminished4th(enharmonicallyequivalenttoaMajor3rd),diminished5th,minor6th,diminished7th(enharmonicallyequivalenttoMajor6th).

ItsnotesinG#are:G#,A,B,C,D,E,F.

G#(R)–S–A(m2)–T–B(m3)–S–C(dim4)–T–D(dim5)–T–E(m6)–S–F(dim7)–TS–G#(O)

Thisscaleistheoddestsofarandhasdifferentnames.

1. ItissometimescalledanAlteredscale,sinceitistheMajorscalewitheachofthescaledegreesflatted(altered).ThoughthisisnottherealAlteredscalesincewehavebb7.TheAlteredscaleisactuallythe7thmodeoftheMelodicminorscaleandwe’llgettothatsoon.RegularMajorscale:1–2–3–4–5–6–7.Harmonicminormode7:1–b2–b3–b4–b5–b6–bb7.

2. ItisalsosometimescalledSuperLocrianwhichisafancynamebutthat’sbecauseitisthesameasdiatonicLocrian,butitgoesonestepfurther.LocrianhasthePerfect4th,while in SuperLocrian that note is flatted (diminished 4th) and the b7 note isflattedonceagain.DiatonicLocrian:1–b2–b3–4–b5–b6–b7.SuperLocrian:1–b2–b3–b4–b5–b6–bb7.

3. ItisalsosometimescalledMixolydian#1,butwhy?Let’stakeourGMajorscaleandGMixolydianscale(whoseParentMajorscaleisC),andlistouttheirnotes.GMajorhas:G(1)–A(2)–B(3)–C(4)–D(5)–E(6)–F#(7)GMixolydianhas:G(1)–A(2)–B(3)–C(4)–D(5)–E(6)–F(b7)

Now the 7th mode of the harmonic minor scale in this context (when comparedagainstGMixolydian)lookslikethis:

GMixolydian#1:G#(1)–A(2)–B(3)–C(4)–D(5)–E(6)–F(bb7)

Theproblemhereisthatthereisoneextraflatonthe7th,makingitfunctionastheMajor6thinthiscontext.

Sowehavethreedifferentnamesforthesamething.It’simportanttounderstandeachnameanditscontext(whatisittellingyou?),becauseaswesaid,thenamesdescribe amode’s relationship to other scales.Knowing these relationships iswhatwill helpyouwithunderstanding andusingmodes in your playing.Youcanuseanynamethatyoulikejustaslongasyouknowhowit’srelatedtootherscales and modes. In my opinion the best name to use here would be SuperLocrian.

InA,thenotesofthismodeare:A,Bb,C,Db,Eb,F,Gb,andthesearethenoteswe’llbeusingtoplayoverAdronenoteinthebackingtrack.

Harmonicminormode7–SuperLocrianaudioexampleinA->http://goo.gl/3u9yuv

NotethatHMmodescanhavedifferentnamesdependingontheircontext,thisissomething that is open to interpretation.What I’mpresentinghere is themostlogicalwaythatthesemodesare(usually)namedby.

HarmonicMinorModesComparisonCharts

Table6:HarmonicminormodesinA.

And here’s a table showing all harmonic minor modes with their respectiveintervalsandnotes.

Table7:Harmonicminormodesintervalstructure.

MelodicMinorScale—HowandWhyWasItDerivedfromtheHarmonicMinorScaleTheHarmonicminor scale and itsmodesopenup theharmonic spacebeyondthediatonicscale.Knowingthose7scalesisanimportantstepinbeingabletoimproviseorcomposechordsormelodiesinanysituation,andtheygiveyouabroader, more delicate palette from which to paint. But they are still notexhaustive.

TheMelodic minor scale is to the Harmonicminor scale what the HarmonicminorscaleistotheNaturalminorscale.Itgoesonestepfurther.TheHarmonicminorscalecameoutofthedesiretohaveacertainkindofresolutionbetweenthe7th and theRoot, and so one of the tones (the 7th of theminor scale)wasraisedtomakeitmorelikethemajorscale.

TheMelodicminorscalecomesoutofasimilarconcern—theHarmonicminorscale does a good job of giving the root a kind ofmagnetism, and there is astrong resolution from the 7th to the next root, but that has what is for somepeopleanunwantedeffect.

The diatonic structure was such that there was never more than a full stepbetweenanytwonotesofanyofthemodes,butintheHarmonicminormodesthereisastepandahalfbetweentwoofthenotes(theminor6thandtheMajor7th).Thisiswhythescalessoundsoexotic—ourearshearanunevenspacinginthestructureofthescaleitself.

This is sometimes a good thing, as in when you want to sound exotic, butsometimes you don’t want to sound that way and you still want to play in aminor key, while having the resolution that theMajor 7th note gives you. Ormaybeyoujustwantasoundthatisnon-diatonicbutthatisn’texoticinthesameway that themodesof theHarmonicminor scaleare.Orperhapsyouare inasituationwherenoneofthemodesoftheharmonicminorordiatonicscaleswillfit.Inallofthesecases,youareprobablyreachingfortheMelodicminorscale.

TheMelodicminorscale isproducedby taking theHarmonicminorscaleandcorrecting the minor 6th note so that there is no longer a step and half gapbetween the minor 6th and the Major 7th. Since there is only a half-step gapbetween the 5th and the 6th, this is possible in a way that results in, like thediatonicmodes, there being never anymore than a full step between any twonotes.

The6thnoteoftheHarmonicminorscaleisraisedbyahalfstep,andanewscaleisborn:TheMelodicminorscale.

MelodicMinorScaleStructureThenotesoftheMelodicminorscaleare:

Root,aMajor2nd,aminor3rd,aPerfect4th,aPerfect5th,aMajor6thandaMajor7th.

Andthestructurelookslikethis:

R–T–M2–S–m3–T–P4–T–P5–T–M6–T–M7–S–R

Figure14:MelodicminorscalestructureinA

Aswiththediatonicandharmonicminormodesthisstructuredefinesaseriesofscales (modes), each with one of the seven notes as the root. Some of thesescales are used widely in jazz, and their sound is, while not as exotic as theharmonicminormodes,stillquitepronounced.

TheModesoftheMelodicMinorScale(WithAudioExamples)There are 7 modes of the melodic minor scale. They are quite similar to theharmonicminormodes.Thesemodesalsocanhavedifferentnames(theydon’thave a standardized nomenclature), but they’re presented herewith the namesfromtheDiatonicmodesthey’reessentiallyderivedfrom.

For diatonic modes we used CMajor as the Parent Major scale, the relativeminorofthatscale(Aeolianmode)istheAnaturalminorscale.BothHarmonicandMelodicminorscalesarederived fromtheNaturalminorscale,and that’swhyallaudioexamplesforthesescalesandtheirmodesareinA.

MelodicMinorMode1–Dorian#7

Thefirstmode(theregularmelodicminorscale)hasa:

Root,Major2nd,minor3rd,Perfect4th,Perfect5th,Major6th,Major7th.

InA,ithasthefollowingnotes:A,B,C,D,E,F#,G#.

Why is it called Dorian #7? When you compare its interval structure to thediatonic modes you can see that diatonic Dorian mode has the most similarstructure.

DiatonicDorian:1–2–b3–4–5–6–b7.

Melodicminormode1:1–2–b3–4–5–6–7.

Soallnotesarethesame(havethesameintervalfunctions)exceptthatmelodicminormode1hasMajor7th,anddiatonicdorianhasaminor7th.That’swhythismodeiscalled:Dorian#7–the7thnoteissharpened.Sincethisscaleormodeisusedquitealotinjazz,itisalsosometimesreferredtoastheJazzminorscale,orjustsimplyMelodicminorscale.

Wewillplaythismode/scaleinA,andjustlikewiththeHarmonicminormodeswewill useA drone note to play over in the improvisation part of the audioexample.WealreadyhavethenotesoftheMelodicminormode1inAshownabove.

Melodicminormode1–Dorian#7audioexampleinA->http://goo.gl/NRFEp7

MelodicMinorMode2–Phrygian#6Thesecondmodehasa:

Root,minor2nd,minor3rd,Perfect4th,Perfect5th,Major6th,minor7th.

InB,itsnotesare:B,C,D,E,F#,G#,A.

Thestructureforthismodeis:1–b2–b3–4–5–6–b7.

When you compare this structure to theDiatonicmodes you can see that themostsimilarstructureisthatofthePhrygianmode:1–b2–b3–4–5–b6–b7.

Sothe2ndmodeoftheMelodicminorscaleislikethePhrygiandiatonicmode,theonlydifferencebeing that it has aMajor6th instead of aminor 6th.That’swhythismodeiscalled:Phrygian#6.

Todemonstrate thesoundof thismode,sincewe’reusingAdronenote,we’lluseMelodicminormode2inA.

APhrygian#6notesare:A,Bb,C,D,E,F#,G.

Melodicminormode2–Phrygian#6audioexampleinA->http://goo.gl/367PSE

MelodicMinorMode3–Lydian#5Thethirdmodecomprisesa:

Root,Major2nd,Major3rd,Augmented4th,Augmented5th(whichisenharmonicallyequivalenttoaminor6th),Major6th,Major7th.

InC,itsnotesare:C,D,E,F#,G#,A,B.

Ithas:1–2–3–#4–#5(sameasb6)–6–7.

DiatonicLydianhasthemostsimilarstructuretothis,butinthiscasethe5thissharpened;that’swhythismodeiscalled:Lydian#5.Inthissamemannertrytofigureoutthenamesfortherestofthemelodicminormodes.

InA,thenotesofthismodeare:A,B,C#,D#,E#(sameasF),F#,G#.

Thesearethenoteswe’llbeusinginouraudioexample.

Melodicminormode3–Lydian#5audioexampleinA->http://goo.gl/iL4SYR

MelodicMinorMode4–Mixolydian#4Thefourthmodehasa:

Root,Major2nd,Major3rd,Augmented4th,Perfect5th,Major6th,minor7th.

ItsnotesinD,are:D,E,F#,G#,A,B,C.

InA,Mixolydian#4containsthenotes:A,B,C#,D#,E,F#,G.

Melodicminormode4–Mixolydian#4audioexampleinA->http://goo.gl/xkHiZ8

MelodicMinorMode5–Aeolian#3Thefifthmodeconsistsofa:

Root,Major2nd,Major3rd,Perfect4th,Perfect5th,minor6th,minor7th.

InE,itsnotesare:E,F#,G#,A,B,C.

InA,thenotesoftheofthismodeare:A,B,C#,D,E,F,G.

Melodicminormode5–Aeolian#3audioexampleinA->http://goo.gl/6NoSa6

MelodicMinorMode6–Locrian#2Thesixthmodehasa:

Root,Major2nd,minor3rd,Perfect4th,diminished5th),minor6thandaminor7th.

InF#,itsnotesareF#,G#,A,B,C,D,E.

InA,thenotesofthismodeare:A,B,C,D,Eb,F,G.

Melodicminormode6–Locrian#2audioexampleinA->http://goo.gl/khYa9U

MelodicMinorMode7–Ionian#1–TheAlteredScaleFinally,theseventhmode,asusualthemostcomplicatedone,hasa:

Root,minor2nd,minor3rd,diminished4th(enharmonicallyequivalenttoaMajor3rd),diminished5th(orTritone),minor6th,minor7th.

InG#,itsnotesare:G#,A,B,C,D,E,F#.

Firstofall,thestructureofthismodeis:1–b2–b3–b4(sameas3)–b5–b6–b7.When you compare this structure against the diatonicmodes, you can seethatitismostsimilartotheLocrianmode,whichhasthePerfect4th:1–b2–b3–4–b5–b6–b7.Wecantechnicallycallthismode‘Locrianb4’,buttherearesome other options; as with the 7th mode of the Harmonic minor there are acoupleofwaystonamethismode.

First,thismodecanbecalledSuperLocrian,butitisalittlebitambiguousnameespeciallybecausewe’vealreadyused it toname theHMM7,whichhasbb7,andMMM7hasab7.Thatistheonlydifference—onenoteasemitoneapart,but still a significantdifference.SoSuperLocrian isnot agoodname for thismode,butthereisonenamebywhichitiswellknown:TheAlteredScale.

TheAlteredscale,asthenamesuggests,isascalewhichhasallofthenotesoftheregularMajorscalebutalteredbyonesemitone.

Majorscale:1–2–3–4–5–6–7

Alteredscale(MMM7):1–b2–b3–b4–b5–b6–b7

SuperLocrian(HMM7):1–b2–b3–b4–b5–b6–bb7

SousuallywhensomeonetalksabouttheAlteredscale,theyarereferringtothe7thmodeoftheMelodicminorscale.Havethatinmind.

ThisscalecanalsobecalledIonian#1,and thereason is thesameaswhy theHMM7canbecalledMixolydian#1.

Ionianmodestructure(sameasMajorscale)is:1–2–3–4–5–6–7.

Melodicminorscalestructureis:1–b2–b3–b4–b5–b6–b7.

But sincewe’re not talking about specific noteswe can also show the Ionianmodestructurelikethis:b1–b2–b3–b4–b5–b6–b7.ThisisstilltheIonianmode because the intervallic relationships between these notes remained thesame—we’veputa‘b’nexttoallofthenotes.AndsincetheMMM7structurehas‘1’insteadof‘b1’,orinotherwords,the1stnoteissharpened,wecancallthismodeIonian#1.

Thisscale,likethe7thmodeofharmonicminor,isusefulinsituationsthatcallforanalteredscale.Inmostothersituations,however,itisnotused.

InA,thenotesofthisscaleare:A,Bb,C,Db,Eb,F,G.

Melodicminormode7–TheAlteredScaleaudioexampleinA->http://goo.gl/qfqcju

MelodicMinorScaleComparisonCharts

Table8:MelodicminormodesinA

Table9:Melodicminormodesintervalstructure

ScaleOverview—ScaleComparisonChartHerearethescalesthatwe’velookedthusfar.Thesechartswillmakeiteasiertosee the similarities between scales, and how everything is derived from theMajorscale,whichagain,isjustone7-notecuttingoftheChromaticscale.

Table10:Scalecomparisonchart1

Table11:Scalecomparisonchart2

Table11isquiteimportanttabletorememberbecauseitsummarizesthescaleswe’velearnedaboutsofarandshowshowtheyarerelatedtooneanother;theyaredifferent,yetquitesimilar.

Noticehowbothminorandmajorpentatonicarejustthecut-outsofthenaturalminor and major scale. But even so, they still sound different, because theintervals are different (especially because of that larger TS interval), andintervalsarewhatmusicismadeupfrom.

Studythischart,noticethedifferences,analyzeit,andtrytomemorizeit,itwillserveyoualot.

KeysandKeySignaturesSofarinthisbookwe’vementionedkeysinseveralinstances,butlet’sexplainmorecloselywhatitmeanswhenwesaythatsomethingisinsomekey.

In virtually all cases, nearlywithout exception, a piece ofmusic is organizedaccordingtosomescale—usuallythemajororminorscale—witharootnoteasitscenter,or“tonic.”Thisiscalledthekeyofthepiece,andittakestheformmostoftenofanotefollowedbytheword“major”or“minor”,forinstance,“Dmajor” or “Bb minor.” Since there are 12 notes, that mean that we have 12possiblekeysatourdisposal.

Akeyislikeaharmoniccenterofamusicalpiece.Knowingthekeyofasonggivesamusiciana lotof information, since it tellsyouwhat scale the song isorganized around. In the case of most rock, pop, blues and country music,knowing the key of the song is enough to tell an improvisor what notes willsoundgoodoverthechordchangesofthatsong.

Inthecaseofjazz,itisoftenmorecomplicatedthanthat,sinceasonginonekeymaymove through various tonal or harmonic centers as the song progresses,thus requiring different scales to be played. In general, however, the key of asong gives a musician the most basic and important information about itsharmonicframework.

Whenwewritethekeyofasong,weindicatethescalethatthesongisorganizedaround.Akeyalsotellsushowmanysharpedorflattednotesarecontainedinthatscale(forexample,Cmajorcontainsnosharpsorflats,butDmajorcontainstwosharps:F#andC#).Thisiscalledakeysignature.

Keysignatureissimplyameasureofsharpsorflatsinakey.Eachdistinctscalehasitsownkeysignature,andeachkeysignaturecaneitherindicateamajorkey(suchasCmajor)oraminorkeythatsharesthesamescale(asweshouldknowby now this is called a relativeminor key). The key signature is used in themusic notation system at the beginning of the staff to indicate the key of thepiece,andthat’swhyitisveryusefulconceptformusicianswhousetraditionalmusicalnotation.

HowtoUnderstandCircleofFifths(andCircleofFourths)Whenyoutakeamusictheorycourseoryoubegintakingprivatelessons,oneoftheveryfirst thingsyouwillreceiveisadiagramofacirclewithlotsofnotesaround it. It is formostpeopleconfusingand forvirtuallyallpeopleunusableuntiltheylearnwhatitreallyisandwhatitmeans.

Thatcircleisthecircleoffifths.Thereisalottosayaboutthecircleoffifths,but ingeneral it is a visual tool—awayofarrangingnotes in intervalsofperfectfifths.

Thisisusefulformanyreasons.Itdescribestherelationshipsbetweenallofthepossible notes you can play in a very particular way. It allows us to betterunderstand chord progressions (more on this later) as well as the distancebetweenanygivenkeys. Italso lists somefeaturesofeachkey thatareusefulwhenunderstandingtheinternalstructureofthosekeys.

The most important of all is that circle of fifths gives us an easy way torememberhowmanysharpsorflatsareineachdiatonickey(andremember:indiatonickeys,thereareeithersharpsorflats,butneverboth).

Beginning with Cmajor (relative Aminor), which has no sharps or flats (or“accidentals” as they are called), it is possible to move up or down by aninterval of fifth to determinewhat other keyswill look like andwhat its keysignaturewillbe.

SoacircleoffifthssimplyshowsallkeysarrangedinfifthsstartingfromCatthetopbecausethekeyofC(major)hasnoaccidentalsinit.

AfifthupfromCisG,andthecirclecontinues:G—upafifth—D—upafifth—A—upafifth—E—upafifth—B—upafifth—F#.

Movingupthecircleinthiswayaddsonenotewitha‘#’inthekeyofG,twosharpsinthekeyofD,threesharpsinthekeyofA,etc.

F#sharpsitsonthebottomofthecircle(6’oclock).WecouldgoonascendingfromF#toC#,G#,D#,A#,F,Candclosethecircle,butweusuallystartfromCatthetopandtheneithergoleft(descending)orright(ascending).

StartingfromCagain,wecandescendthecirclebymovingcounter-clockwiseinfifths,thistimeusingflats:

C—downafifth—F—downafifth—Bb—downafifth—Eb—downafifth—Ab—downafifth—Db—downafifth—Gb(sameasF#)

—downafifth—Cb(orB)—Fb(orE)—downafifth—A,andsoonallthewaydowntoC.*

*NOTE:Itisimportanttoclarifyheresomethingthatconfusesalotofpeople.Sincewe’redescendingon thecircleof fifths, thenotesarebecoming lower inpitchbyaperfect fifthinterval.Thismeans that ifyoumovecounter-clockwise,and thenotesaredescending inpitch, you’re stillmoving by an interval of perfect fifth. However, if youmove counter-clockwiseonthecircleoffifthsandthenotesareascendinginpitch,thenthatisconsideredas the circle of fourths— amirror reflection of the circle of fifths. Some musiciansprefer to think in terms of the circle of fourths because chord progressions tend tomovemoreofteninthisway.Inanycase,hereisthecircleoffourthssequence:

C—upafourth—F—upafourth—Bb—upafourth—Eb—upafourth—Ab,etc.

Soadescendingfifthislikeanascendingfourth,onlyoneoctaveapart.Youcaneasily verify this by looking at the note circle shown on Figure 2. If youremember, the perfect fifth interval is 7 semitones and the perfect fourth is 5semitones,upordownfromthestartingnote.Allyouhavetodoistocountthesemitonesupordownfromanystartingnote.Iencourageyoutocheckthisforyourself.

Coming back to the circle of fifths, moving counter-clockwise adds one notewithabinthekeyofF,twoflatnotesinthekeyofBb,threeflatsinthekeyofEb,andsoon.

Figure15:Circleoffifthsatitsbasicform.Sometimestherelativeminorkeysareaddedbeneatheachmajorkey(AminorforC,Eminor

forG,BminorforD,F#minorforA,andsoon)

This special relationship between notes, by an interval of “fifth”, is in manywaysthefoundationofharmonicmovement.Bylistingthenotesinascendingordescendingfifths,acycleisproducedinwhichallofthenotesarerepresented.

Thatcycle,depictedasacircle,helpstotellusthingsabouteachofthosenoteswhen they areused to createkeys, such as, for instance,what the structureofthosekeysis.Usually,thisisunderstoodintermsofmajorandminorscales,andarelationshipisestablishedbetweenrelativemajorandminorkeys.

What’smost important is thatarranging thekeys in fifthsmakes iteasy toseehowkeysrelatetooneanother.

Whenitcomestoreadingandperforming(sightreading)writtenmusicitisveryimportant to understand how these concepts (such as key signatures and thecircleoffifths)workintheoryandinpractice.Foranin-depthlookatthischeckoutmyHowtoReadMusicforBeginnersbook.

Part3

MastertheChords

WhatisaChord?Someinstrumentsaresingle-noteinstruments,capableofonlyplayingonenoteat a time.Other instruments, however, like guitars and pianos, are capable ofplayingchords.

Achord, at itsmostbasic, is simplyamusicunit consistingofmore thanonenotebeingplayedatthesametime.Inotherwords,itisthesoundwegetwhenwecombineanytwo(ormore)notesandplaythematthesametime.

Chordscomefromscales.Infact,theyaremadeupfromnotesinascale.Eachscaleimpliesacertainlistofchords;onceyouhaveascaleinmind,itiseasytoproducechordsthatarecontainedinthatscale.We’llgettothissoon.

Chordsare,likescales,definedbyasetofintervalsrelativetotherootnote.Thisishowchordsarenamed—thenameofachord tellsuswhatkindofnotes itcontains;ittellsuswhatistherootnote(couldbeanyofthe12notes),andfromwhichintervalsthatchordismadeof.Theintervallicstructureofachord—thewaythenotesinthechordrelatebacktoitsrootnote—iscalledthe“spelling”ofthatchord,andifyouknowthenameofthechordthenyouknow,becauseofitsspelling,thenotesthatarecontainedinit.

IfwehaveaMajor7thchord, for instance, thenby theendof thischapteryouwilllearnhowitconsistsofsomeRoot,aMajor3rd,aPerfect5thandaMajor7thnote (all relative to the root). This is the spelling of aMajor 7th chord. Ifweassignthischordaspecificrootnote,forexampleGnote,thenthenameofthischordwouldbe:GMajor7th;andifwethenlookattheGmajorscale,wewouldknowthattheothernotesinthechord,becauseofitsspelling,are:G(R)B(M3)D(P5)F#(M7).

It ispossible, simplybynaming the intervalscontained in thechord, tocreatehighlycomplexchords(suchasaMajor13flat9chord).Thesechordsaremostoften used in jazz and they create sophisticated harmonic spaces. Their use ishighly specialized, with certain chords only being played in very specificsituations.

HowChordsAreBuiltTraditionally, chords are built from intervals of thirds. In other words, theyconsist of a root note and another note, or series of notes above that root thatascendinthirds.Toachievesuchastructureallthatisrequiredistotakeascaleandcountup froma rootnotebya third (whichmeansup twodegrees in thescale)togetachordnote,andthenforeachnewnoteinthechordcountupbyanotherthird(tothefifth,theseventh,andsoon).

Similarly to scales, chords can be described by their chord formulas. Sincechordsaremadeupfromnotesofthescaletheycomefrom,theirformulasimplyshowsthescaledegreesthatthatchordusesfromitsscale.Ifwehavea“1357”chordformulaforexample(whichistheformulaforaMajor7thchord),itsimplymeans that this chord consists of theRoot (first scale degree), 3rd, 5th and 7thscaledegree.IfwetakeaMajorscale,andassignitakey,let’ssaykeyofC,wecansimplyapplythisformulatogetthenotesoftheCMajor7thchord.

ThisiswhyCmajor7thchordconsistsofthenotes:C(Root—givesthechorditsname),E(Major3rd),G(Perfect5th)andB(Major7th).Chordformulasandchord spelling are very similar and useful concepts that give us a way ofanalyzingthechords.We’llexplorethisalotmoreinfurthersections.

Itispossible,andnotuncommon,toalterchordsthathavebeenbuiltbystackingthirds— by moving one or more of the notes up or down, by inverting thechords(rearrangingtheirnotes)sothatanewchordisproduced,orbyaddinganote from the scale you’re working with to a pre-existing chord. It is alsopossibletocreatechordsbystackingintervalsotherthanthirds—forinstance,

fourthsorfifths,althoughthisisfarlesscommon.Generallyspeaking,however,chordsaregeneratedinthewaywehavedescribed—bystackingthirdsabovearootnoteaccordingtoaparticularscale.

ChordTypes(Dyads,Triads,Quadads)andChordQualitiesAchordisanysoundproducedbymorethanonenote.Thatmeansthatanytimetwo or more notes are produced at the same time, a chord is formed. Wecategorize chords according to how many notes are contained in them, andthough it is possible to talk about chords containing very many notes (up totwelve), the usual formulations contain two, three, or four notes. In jazz andsomeclassical,chordswithmorethanfournotesoccurwithsomefrequency,butingeneraltheyareconsideredextensionsofthreeorfournotechords.

Mostoften,chordsconsistof3or4distinctnotes,althoughmanytimeswhenweplay a chord some of these notes are repeated in various octaves resulting inmorethan3or4tonescomposingthechord.Thisisobvious,forexample,ifyouplayabasicchordonguitarmostbeginnersfirstlearn,suchasEminor,andthenanalyzewhichnotesyoujustplayed—eventhoughyouplayedallsixstrings,whichmeans six notes, there are only 3 distinct notes in this chord, some ofwhicharerepeatedoncertainstringstogetafullersoundingchord.

Themostcommonchordsconsistofsimple3-notechords,calledtriads.Inmorecomplex harmoniesmost chords contain at least 4 notes (in general these arecalledthe7thchordsorquadads).

Mostcommonchordtypesarecategorizedasfollows:

1. Dyads—thesearechordscontaininganytwonotes.2. Triads—thesearechordscontainingthreedistinctnotes.3. Quadads—thesearechordscontainingfourdistinctnotes.

In the case of triads (which aremost used chord-types in rock, pop and othergenres) andquadads, it is usually the case that the chords are built of stackedthirds(aspreviouslydiscussed).

Inthecaseofdyads,however,anyintervalcanbeused.Infact,anyChromaticinterval (seeTable1) isalsoadyadchord;so theycanbeanykindof:major,minor, perfect, augmented or diminished dyads. The most common dyads inrock, are dyads produced by playing two notes a 5th apart — Root and thePerfect5th (sometimes followedbyanotherRoot—anOctave,on top).Theseareusuallycalled“Powerchords”,andarecommonlyusedbyguitaristsinrockandmetalgenres.

It is possible to play a chord consisting of only 2 notes (and even of only 2tones)andalsoofmorethan4notes.Itisnotuncommonforajazzmusiciantoplay chords consisting of 5 or 6 different notes, and piano players have theability to play asmany as 10 distinct notes at one time. Inmost cases this isavoidedbecausethemoredistinctnotesareaddedtoachordthemoretheywillclashwitheachother,andthechordwillsoundmoreandmoredissonant.Mostpopsongshaveverysimpleharmonyconsistingofsimplechordswithveryfewnotes, whereas jazz on the other spectrum is usually very advanced harmonywithmorecomplexchords.

UnderstandingChordQualitiesIngeneral,andparticularlywhentalkingabouttriadsandquadads,chordshavedifferent flavors thatcharacterize them.These flavorsareusuallycalledchordqualities, and they make the chords sound different, not in the terms of thehigherorlowerpitch,butintermsofthemoodortheeffecttheyproduce.

For example, themost common chord qualities aremajor andminor, and thedifference between them is easy to notice: major chords are happy sounding,while minor chords are sad sounding. EMajor sounds quite different than Eminor, not in the sameway asEMajorwould sound different fromFMajor,where chord quality is the same but pitch of the root note is different by onesemitone.

The ‘quality’ that a chordwill have entirely depends on the interval structure(spelling)ofthatchord,andeachchord,aswesaid,hasauniquesetofintervalsandaformulathatdescribeshowitrelatestoitsscale.Inthenextfewsectionswe’llgoovereachchordqualityfortriadsandquadads.Notethatwhenwesay‘chordquality’weoftenexclude‘quality’andsimplyrefertoitasa‘chord’—thisjustmeansthatwehaven’tassignedanyofthe12notestothechordyet.

Bytheendofthischapteryouwillhaveahugelibraryofchordsatyourdisposalandmorethansolidchordfoundation;anditwillbeeasytorememberthemallwiththetricksI’llshowyou.

TriadChordsWe’llstartwith3-notechordsfirstbecausetheyarethesimplestandeasiesttounderstand.They’re themost commonchords today. It isworth repeating thatgenerally,whenwe talkabout triads,weare talkingabout those triads thatarecomposedoftwo3rds(usuallyeithermajor3rdorminor3rd interval)stackedontopofoneanother,orthataresimplemodificationsofthosestacked-3rdtriads.

Triadchordsareasfollows:

Majortriads—thesechordsconsistofa:Root,aMajor3rdandaPerfect5th.Thismeansthattheyarecomposedofaroot,amajor3rdabovethatrootandaminor3rdabovethatsecondnote.NoticeherethatthedistancefromaMajor3rdtoaPerfect5this3semitones—whichisaminor3rdinterval.

Thechordformulaforamajortriadis:135.

InC,theCmajortriadwouldbe:CEG.

Minor triads— these are composed of a minor 3rd interval and a major 3rdintervalstackedontopofthat(theinverseofthecompositionofmajortriads).

ThatmeansthattheyconsistofaRoot,aminor3rdandaPerfect5th.

Asfortheminortriadchordformula—firstwehavearoot—1,thenwehaveminor3rd insteadofamajor3rd.Thesetwointervalsareonesemitoneapart,sothatmeansinordertogettheminor3rdwejusthavetoflattenthemajor3rdnotebyasemitone,sowesimplywrite:b3.Andthenwehaveaperfect5thasusual.Also,notethatthedistancebetweentheminor3rdandperfect5this4semitones,whichisamajor3rdinterval.

Soaminortriadchordformulaissimply:1b35,andfromourCmajorchordconsistingofnotes:CEG,wewouldgetCminorwiththenotes:CEbG.

Youcan seeherehowonlyonenotedifferenceas little asone semitoneapartchanges the mood of the chord dramatically. It goes from happy sounding(major) tosadsounding(minor).Wecanconcludethat3rd inachordisaveryimportantnotethatmakesahugedifferencetoitssound.

Whenitcomestotriads,therearealso:

Augmentedtriads—thesearemajor triadswithasharp5th.Thatmeans theyarebuilt from twomajor thirds stackedon topofone another and contain thenotes:Root,Major3rd,Augmented5th(sameasminor6th).Theirsoundisjarring(sometimesagoodthing)andthesearerarelyplayed.

Theaugmentedtriadchordformulais:13#5.

#5tellsthatwesimplyhavetoraisetheperfect5thnotebyonesemitone.

Asforthenotes,CAugmented,orjustCaug,wouldbe:CEG#.

Diminishedtriads—theseareminor triadswitha flat5th (Tritone).Theyarecomposedoftwominorthirdsstackedononeanother,whichmeanstheyconsistofaRoot,aminor3rdandadiminished5th.

The diminished chord formula is: 1 b3 b5,which tells thatwe have to flattenboth3rdand5thnoteoftheparentscale.

TheCdiminishedchord,orjustCdim,wouldthenbe:CEbGb.

Allof these fourbasic triadsarecomposedof two intervals—majorandminor3rds—stackedontopofoneanotherinvariouspermutations.

SuspendedChordsItiscommon,however,toalterthosetriadsslightlyandarriveatchordsthatarederivedfromstacked3rdsbutthatcontainotherintervals.Thisisdonebyalteringthesecondnoteinthosetriads—the3rd,whetheritisamajor3rdoraminor3rd.

ThesenewchordsarecalledSuspensions,andtherearetwotypesofthem.First,therearesuspendedchordsinwhichthe3rdisloweredtoa2nd.ThesearecalledSuspended2ndchords,orjustsus2.

Suspended2ndtriads—Ifyoubeginwithamajororminortriadandlowerthe3rdtoamajor2nd,thenyouwillhaveasus2triad.ItconsistsofaRoot,aMajor2ndandaPerfect5th,anditisbuiltfromaperfect4thstackedontopofamajor2ndinterval.

Thechordformulaforasus2chordis:125.

ThismeansthatthenotesofCsus2chordwouldbe:CDG(wejusttakethe2ndnoteinsteadofthe3rdfromtheCmajorscale).

Suspended4thtriads—Thesecondkindofsuspendedtriadisoneinwhichthe3rdisraisedtoa4th(ratherthanloweredtoa2nd).Thesearecalled:Suspended4thchords,andarecommonlyusedinjazzaswellasinrockandpoptoaddspecificcolortomajorandminortriadprogressions,thatisneithermajornorminor.

Beginningwithamajororminortriad,Sus4’sarederivedbyraisingthesecondnoteinthechord(majororminor3rd)uptoaperfect4th.Itisbuiltfromamajor2nd interval stacked on top of a perfect 4th (the opposite of sus2), and it iscomposedofaRoot,aPerfect4thandaPerfect5th.

Thechordformulaforasus4chordis:145.

ThenotesofCsus4chordwouldbe:CFG.

Thisconcludesallformsoftriadchords...Almost.

It is also possible to talk about suspensions of diminished and augmentedchords— although these are very rarely used. In these cases, the suspendedchordshave the samequalities asbefore,only the fifth is either flatted (in thecase of a suspension of a diminished chord) or sharped (in the case of asuspensionofanaugmentedchord).

Thesechordsareshowninthefollowingway:

dimsus4(14b5),

dimsus2(12b5),

augsus4(14#5),

augsus2(12#5).

Outofthesechordsthedimsus4isextremelydissonantbecausethereisonlyahalf-stepdifferencebetweenthePerfect4thanddiminished5th.

Takealookatthistableforaclearoverviewofallthechordssofar.

Table12:Triadchords

Table13:Triadchordsintervalstructure

Thisconcludesallchordtriads.Theyarethemostbasicchordsoftheharmonybuiltinthirds–called:Tertianharmony–whichvastmajorityofchords thatwe hear today are based on. They are not hard to learn and should bememorized. There are also the 1st and 2nd inversions for each of these triadchords,butwehaveyettogoovertheinversions.

7thChords(Quadads)More complicated than triads, because of an extra note, 4-note chords, orquadads, canbe explained simply as extended triadsby another3rd—usuallythe7thofsomekind.That’swhythey’reoftencalled:7thchords.Also,7thchordsgenerallycontain4distinctnoteshencewhythey’reconsideredasquadads.

Quadadsarebuiltinmoredifferentwaysthantriads(sincethereisanextranote,whichmeans therearemorepossiblecombinations). Ingeneral,however, they

arealldifferentversionsofthe7thchords(whichconsistofaRoot,a3rd,a5th,anda7th).

Quadad harmony hasmore things going on—more notes clashingwith eachother;it isthereforemorecomplexandsophisticated.Quadadsareusedwidelyacrossallgenres,butespeciallyinbluesandjazz.

7thchordsareasfollows:

Major7–thesechordshaveamajor3rdinterval,followedbyaminor3rd,whichisfollowedbyanothermajor3rdontop.ThismeansthattheyhaveaRoot,Major3rd,Perfect5thandaMajor7th(we’vealreadyseenthisoneatthebeginningofthischapter).

Chordformulais:1357.

InC,thenotesofCMajor7chord,orjustCMaj7,orevenCM7,wouldbe:CEGB.

Minor7– thesechordsarecomposedofaminor3rd, followedbyamajor3rd,followedby anotherminor 3rd. So theyhave the followingnotes:Root,minor3rd,Perfect5thandaminor7th.

Chordformulais:1b35b7.

InC,Cminor7,orCm7,wouldbe:CEbGBb.

Dominant 7 – these chords are like in themiddle between the previous two.TheyhaveaRoot,Major3rd,Perfect5thandaminor7th.Somajor3rdisfollowedbytwominor3rdintervals.EventhoughtheyareverysimilartoMajorandminor7thchordstheysounddifferentoftenaddingtensionwhichtendstoresolveinachordprogression.

Chordformulais:135b7.

Cdominant7,orjustC7(asit’susuallywritten),hasthenotes:CEGBb.

Minor7b5–thisnamemayseemscarybutit’sactuallyjustaminor7thchordwithaflat5th.Itiscomposedofa:Root,minor3rd,diminished5th(Tritone),andaminor7th.Thismeansthattheyhaveaminor3rdintervalfollowedbyanotherminor3rd,whichisfollowedbyamajor3rd(theoppositeofDominant7).These

areveryunique soundingchords, commonlyused in jazz, sometimes inblues,butnotasmuchinpop,rockandsimilarstyles.

Chordformulais:1b3b5b7.

Cminor7b5,orCm7b5,hasthenotes:CEbGbBb.

Diminished7–alsocalledFullDiminished, thesechordsgoonestepfurther.Theyarecomposedonlyof stackedminor3rd intervals,which iswhy theyarecalled symmetrical chords. Their interval structure is always the same, nomatter if you’re ascending or descending in pitch. In practice, thismeans thatyoucanmovethesechordsupordownbyaminor3rdinterval(3semitones)asmuchasyouwant,andthenoteswouldremainthesame,onlyindifferentorder.Eachnoteinthiswaycanactasarootnote.Thisisoftenusedinplayingtogetacoolsoundingsequences,andjazzplayersinparticularliketoexploitthisidea.Any kind of chords that have the same intervals across all their notes aresymmetrical.Augmentedtriads,forinstance,madeupoftwostackedmajor3rdintervalsarealsosymmetricalchords.

The sound of diminished 7 chords is jarring, dark and unstable, but alsointeresting andoftenused (carefully) fordramatic effect.Diminished7 chordsshould not be mistaken with diminished triads, which are just called‘diminished’.TheyconsistofaRoot,minor3rd,diminished5th,andMajor6th.

Chordformulais:1b3b5bb7*.

*NOTE:bb7isadoubleflatted7th,whichmeansthatitisthesameasthe6thscaledegreeinpractice.

Cdiminished7,orCdim7forshort,hasthenotes:CEbGbA.

Major6–thesechordshaveacool,distinctivesoundandareusedcommonlyinjazz, and occasionally in some other styles. They can be used to spice up aregularmajortriad,orasasubstituteforaMajor7th,whichcansometimesclashwiththemelodyifit’splayingtherootnote–becausethe7thnoteinaMajor7thchord isonlya semitoneapart from the root.Theiruse is specializedand it isimportanttoexperimentandtrustyourearsonwhenitsoundsgoodtousethem.

Theyconsistofamajor3rd,followedbyaminor3rd,andthenamajor2ndinterval(whichis2semitones).Theyhavethenotes:Root,Major3rd,Perfect5th,Major6th.

Chordformulais:1356.

CMajor6,orjustC6wouldbe:CEGA.

Minor6–finally,minor6thquadadsarethesameMajor6th,exceptwithaminor3rd. They have a minor 3rd interval followed by a major 3rd, which is thenfollowedbyamajor2ndinterval.Theycontainthenotes:Root,minor3rd,Perfect5th,Major6th.

Chordformulais:1b356.

Cminor6,orCm6,wouldbe:CEbGA.

Table14:Quadadchords

Table15:Quadadchordsintervalstructure

This concludes the main quadad chords. These of course are not all possiblecombinationsofintervalsthatquadadscanconsistof,therearequiteafewmoreyoucanmake,forinstance:Dominant7chordwithaflat5th(13b5b7).Thesemayormaynotsoundgoodindifferentsituations,soalwaysuseyourearasaguideandrememberthegoldenrule:“Ifitsoundsgood,itisgood”.

3FundamentalChordQualitiesAswe’veseen,thereareverymanydifferentchordqualities,butthereisaneasyway to categorize them all according to their sound and function in a chordprogression.Thisalsogoesforextendedandalteredchordswe’regoingtolookatafterthissection.

In essence, there are three fundamental chord qualities that all other chordqualitiesfallinto.Thereare:

1. Majorchords2. Minorchords3. Dominantchords

Herearesomerulesandguidelinestoknowwhichfamilyachordbelongsto:

IfachordhasaMajor3rdandaMajor7th thenit isdefinitelyintheMajorfamily.Thesechordsaregenerallyhappysounding,andgenerallyspeakingtheirfunctionistoprovidestabilityinamajorkeyandgivecontextformelodicdirectioninachordprogression.

Ifachordhasaminor3rdnote in it, thenit isconsideredtobeapartof theminorfamily. These chords are generally sad sounding, the opposite ofMajor, and theirfunctiongenerallyspeakingisalsotoprovidestability,butinaminorkey.

IfachordhasaMajor3rdalongwithaminor7th,thenitisdefinitelyinthedominantfamily.Dominantchordsareusuallyusedasquadads—theyaremajortriadswiththeadditionofaminor7th.Thesechordsareusedinallbluesandmanyothergenres—theycreatealotoftensionwhichtendstoberesolvedinachordprogression.

Fromthesethreebasicchords,allotherchordscanbeattained.Byalteringnotesofthosechordsoraddingnotestothem(usuallyintheformof“extensions”—thirds stackedon topof thechords), and thenby subtractingothernotesawayfromtheresultingchords,itispossibletogenerateeveryotherchordthatcanbeused.Forallthesereasons,manymusicians,eveninjazz,considereverychordamemberofeitherthemajor,minorordominantfamily.

TheComplexityofExtendedchords(9’s,11’sand13’s)Chordsgrowandevolvebeyondanoctave,andwhen theydoso–when theycontain a notewhich is a third up from the 7th (and therefore higher than theoctave) – they are usually called extended chords. These chords are seen assimpleextensionsof triadsandquadads (withquadadsbeing theextensionsoftriads);andsincethesearegenerallybuilt in thirds, thebasicextensionsof the7thchords(1357)aredifferentvariationsofthe:

9thchordsor9’s(7’swithastackedthird),

11thchordsor11’s(9’swithanotherstackedthird),

13thchordsor13’s(11’swithanotherstackedthird).

Whenextendingchords,we first lookat thescaleandextend itsnotesbeyondtheoctave.Wecansimplywritethisas:

Theoctaveistheeightnoteina7-notescale.Sowhenascalestartsagainat1,wecanwritethenumber8insteadindicatingthatthisistheoctavewithwhichthescalestartsagain—onlyanoctavehigher.Thenwejustcontinuewritingthenumbersinorderfromthere.Thismeansthatthe9thnotewillbethesameasthe2nd,10thwillbethesameasthe3rd,11thsameas4th,13thsameas6th,etc.

Ifwehaveourusual1357chord,andextenditbyathird,wewouldlandonthe9th;ifweextendthatbyanotherthirdwewouldgettothe11th,andifextendthatbyathirdwewouldgettothe13th.

Sotheorderinwhichthechordsextendis:

Triads(135)->7thchords(mostoftenasquadads)1357->9’s(13579)->11’s(1357911)->13’s(135791113).

Tosumupsofar:

Adding3rds to3rd-based triads gives us 7th chords.Because these chords (usually)containfournotes,they’renowquadads.Withtriads,7thchordsformthefoundationofthe3rd-based(Tertian)harmony.7thchordsarenotconsidered“extendedchords”,buttheyareviewedastriadextensions.Forachordtobeanextendedchord,ithastocontainthenotesthatarebeyondtheoctave.

Adding3rds to7’sgivesus9’s.Thesecanbe5-notechordsbutusually somenon-essential notes of a chord that don’t affect the soundmuch are omitted. This alsogoesfor11’sand13’s.

Adding3rdsto9’sgivesus11’s.

Andadding3rdsto11’sgivesus13’s,whicharenowfullyextendedchordsbecausetheycontain7distinctnotesinthem.

It’simportanttoknowthatinpractice,notallchordsareplayed,orvoiced,withallofthesenotesbeingincluded—sothatitispossibletoplaya7thchordforinstance(whichconsistsofaroot,a3rd,a5thanda7th)byplayingonlyaroot,a3rdanda7th,andleaveoutthe5th.Itisverycommonfornotestobeleftoutofthechordinthisway,andtherearedifferentreasonsfordoingso.Sometimesitis physically impossible to play all the notes in a chord, but also sometimesleavingoutthenotesthatarenotcrucialwillmakethechordsoundclearerandmorepronounced.Having toomanynotes inachordmakes it soundcrowded,unclear,andconfusing.Soremovingthesenon-essentialnotesandreducingthechordtoaquadad(oreventriad)isfavorablebecauseitmakesthechordsoundmore focused, clearer, and simplybetter, because there are less notes clashingwithoneanother.Therearecertain“rules”aboutwhichnotescanbeleftoutofachordandwhichcannot,we’llgettotheminabit.

Notethatwestopatthe13thnotebecauseIfweweretoaddanotherthirdtoourextendedchord,wewouldlandonthe15thnote,andthisnoteisthesameasthe1st first note of the chord only two octaves higher. What this means is thatstackingthirdsafterthe13thwouldonlygetusthesamenoteswehadinour135 7 chord. Since this wouldn’t give us any new notes there is no point inextendinganyfurther.

Anotherimportantthingtoknowisthatthecorepartofthechordisuptothe7thnote.Therearemanyvariationsofthesechords,aswe’veseen,andeachhasa name. Any further extensions beyond the 7th are handled and treateddifferently.Thisisdoneinawaysothatthereareonlythreebasicvariationsofeachextendedchord:Major,minorandDominant.

Theextendedchordsareasfollows:

Major9–theseareverycool,dreamysoundingchords.TheyconsistofaRoot,Major3rd,Perfect5th,Major7th,Major9th(samenoteastheMajor2ndonlyanoctavehigher).TheyarecomposedofintervalslikeaMajor7chord(major3rd–minor3rd–major3rd),withanotherminor3rdaddedontop.

Chordformulais:13579.

CMajor9,orCMaj9,wouldhavethenotes:CEGBD;althoughthe5thnote(Ginthiscase)isoftenleftoutofthischord(aswellasallotherextendedchords).

Minor9– similarly toMinor7chords theseshare thesame intervals;we justhavetoaddanothermajor3rdontop.

TheyconsistofaRoot,minor3rd,Perfect5th,minor7th,Major9th.

Chordformulais:1b35b79.

Cminor9,orjustCm9,wouldbe:C,Eb,G,Bb,D.

Dominant 9 – these chords are used often in funk (dominant 9 is sometimesreferred to as the ‘funk chord’), and of course, jazz. Here, again, we’re justaddinganinterval–major3rdinthiscase–ontopofadominant7chord(togettothe9thfromtheminor7th).

ThesechordsconsistofaRoot,Major3rd,Perfect5th,minor7thandaMajor9th.

Chordformulais:135b79.

Cdominant9,orjustC9,wouldbe:CEGBbD.

Personally,all9’saresomeofmyfavoritechordstoplayonguitar.

Major 11 – these chords consist of a Root,Major 3rd, Perfect 5th, Major 7th,Major9thandPerfect11th(sameasthePerfect4th).

Chordformulais:1357911.

CMaj11wouldbe:CEGBDF.

Minor11 – these contain aRoot,minor 3rd, Perfect 5th,minor 7th,Major 9th,Perfect11th.

Chordformulais:1b35b7911.

Cm11wouldbe:CEbGBbDF.

Dominant11–thesecontainaRoot,Major3rd,Perfect5th,minor7th,Major9th,Perfect11th.

Chordformulais:135b7911.

C11,wouldbe:CEGBbDF.

Because11’sare6-notechordstheycanbeveryimpracticalanddifficulttoplay,but theycanbereducedto4-notechordssimplybyleavingout the5thand the9th,whichare(usually)non-crucialnotesforthesechords.

Major13 – these contain aRoot,Major 3rd, Perfect 5th,Major 7th,Major 9th,Perfect11th,Major13th(sameasMajor6th).Thatwasalotofnotes.

Chordformulais:135791113.

CMaj13hasthenotes:CEGBDFA.

Minor13–containaRoot,minor3rd,Perfect5th,minor7th,Major9th,Perfect11th,Major13th.

Chordformulais:1b35b791113.

Cm13hasthenotes:CEbGBbDFA.

Dominant13–lastly,thesechordscontainaRoot,Major3rd,Perfect5th,minor7th,Major9th,Perfect11th,Major13th.

Chordformulais:135b791113.

C13hasthenotes:CEGBbDFA.

13’sareoftendifficultchordstouseandplay.It’slikeyou’replayingafullscaleas a chord. They occur with less frequency (usually with one or more notesomitted),butwhentheydotheycanspiceupanyprogression,sometimeswithastartlingeffect.

Table16:Extendedchordsintervalicstructurewithintervalslistedin2octaves.*

*NOTEthatafterthefirstoctave(P8)allintervalesarethesameonlyhigherbyanoctave(to anynumberyou just add7).These intervals that are larger thanoneoctaveare calledCompoundintervals,andthe15thnote(P15)iscalledaDoubleOctave.

Lookingat theTable16youcan seehow the9th,11th and13th, are “fixed” tobeing: Major 9th, Perfect 11th and Major 13th note, no matter whether theextendedchord ismajor,minorordominant.Sinceextensionsafter the7th arealwaysthesenotes,wejustcallthem:9th,11thand13th.Ifanyoftheseextendednotesischangedbyahalf-stepupordown,thenwhatwehaveissomethingthatiscalledanAlteredchord.Thosecanreallymaketheheadhurt,butwe’lldealwiththeminaseparatesection.

RulesforLeavingOuttheNotesinExtendedChordsAswe’ve said, some of the notes in complex chords like 9’s, 11’s and 13’s,couldbe(andaremostoften)omittedwhilestillretainingthedistinctivequalityofa9th,11thor13thchord.Thefollowingrulesaremorelikeguidelinesandlessliketherules.Youcanreallyuseanycombinationofnotesthatyouwantaslongasitsoundsgoodtoyou.Infact,anyruleinmusiccanbebrokenifitsoundsgood.

ThemostimportantnotesinachordareitsRoot,3rdand7th—thesenoteshavetobepresentmostofthetime(no7thinatriadofcourse).

Havingsaidthat, the3rdcanbeexcludedwhen there issomeclashingbetween thenotes.Thiswouldcreateasuspendedtypeofchord.Strangely, the root note alsodoesn’t have tobeplayedunder somecircumstances.For instance, sinceRoot is the lowest note in a chord it can be left out in a bandsituation where you have a bass player or someone else who is playing the root.Otherwise,thechordssoundbetterandlessmessywithit.

If you leave out the 7th, it will result in getting different kind of chords, called:Addedtonechords(moreontheminthenextsection).

5thnoteinachordcanbeleftoutmostofthetime,unlessitisoneitscharacteristicnotes.

9thchordsshouldhave:1379.The5thnotecanbeeasilyleftouthere.

13thchordshouldhaveatleast:13713—wecanexcludethe5th,9thand11th.

11thchordsshouldhaveatleast:13711—wecaneliminateboththe5thandthe9th.

Problemwith11’sSome11th chords,namelyMajor11andDominant11,are specialbecause thePerfect11thnoteisanoctaveupfromthePerfect4thnote,whichmeansthattheyarethesamenote(4+7=11).Perfect4thisasemitoneupfromtheMajor3rd,andthesechordscontainbothofthosenotes.

For example, C dominant 11 contains the notes: C (R),E (M3), Bb (m7),F(P11),andwecanseethattheFnote(P11)isonlyasemitoneupfromE(M3);

andeventhoughit’sactuallyanoctaveandasemitoneupfromE,thiscancauseaclashbetweenthesetwonotesandproduceanunpleasantsound.

Thisisoftenavoidedbysharpingthe11thnote,thusgetting:Dominant#11chord(13b7#11)orMajor#11chord(137#11).ChordslikethesearecalledAlteredchords,whichwe’vementionedbefore.

Anotherwaytoavoidthiswouldbetocompletelyremovethe3rd,whichcreatesasuspendedtypeofchordbecausethe3rdhasbeenreplacedwiththe11th.Thesechords could be named for example: Major7sus11 (1 5 7 11), andDominant7sus11(15b711).Therearedifferentwaysyoucangoaboutnamingcomplicatedchordssuchasthese—alwaysfollowlogicwhendoingso.

Itshouldbealsosaidthatthesekindofnoteclashesdon’thavetobeavoidedatall.Ifsomethingsoundsbadintheory,likeinthisexample,itdoesn’tmeanthatitwillsoundbadwhenyouplayitonyourinstrument.Aswesaid, the“rules”canbebrokenifitsoundsgoodintherightcontext.

AddedToneChords–What’stheDifferenceInthelastsectionwementionedthatthe7thcanbeleftoutofthechord,andthisusually results in getting different type of chords, called: Added tone chords.Added chords (`add’ for short) are viewed as simple triadswith one ormoreaddednotes.Thenotesthatareaddedinthiswayareusually:

Major2nd—add2(1235)—RM2M3P5

Perfect4th—add4(1345)—RM3P4P5

Major9th—add9(1359)—RM3P5M9

Perfect11th—add11(13511)—RM3P5P11

Major13th—add13(13513)—RM3P5M13

Outof thesechords theadd9’s areprobably themost common.Theyareusedofteninpopandrocktospiceuptheregulartriadchords;Cadd9chord(CEGD)istheaddchordthatmostbeginnersfirstlearnonguitarbecauseit’seasytoplay.

Add4 is a typical chord that should sound bad in theory because of the clashbetweenM3andP4,whichareasemitoneapart,butinrealitythisisoneofthecommonly used chords on guitar that sounds good, even though it shouldn’t;specifically, Dadd4 chord (D F# G A) because of its convenient position onguitar.Itdoeshavesomedissonancetoit,butthatcanalsobeagoodthingwhenwewantit.Notethatadd4andadd11areessentiallythesamechordsbutwithadifferentnoteorderorchordvoicing.Add11(Perfect11th)isanoctaveupfromadd4 (Perfect 4th), and is positioned higher than Perfect 5th in a chord. Chordvoicingsareexplainedalittlebitfurtherinaseparatesection.

Noticehowall these chords aredifferent from theoneswe’vehad so far.Forexample,anadd9chordissimilar toasus2chord,becausethemajor9th is thesamenoteasthemajor2nd,onlyanoctavehigher.Butaddedtonechordscontainthe3rd,whilesuspendedchordsreplaceitwithsomethingelse(mostcommonlywiththe2ndor4th).Thesamegoesforsus4andadd11chords.

In music theory, nomenclature for some concepts is not very consistent —differentmusiciansmaysometimesname the same thingdifferently.Onesuchinstance iswhen aMajor 11 chord is sometimes incorrectlywritten as add11.Thisiswrongbecauseaddedtonechordsdon’thavethe7th,whileregularMajorextendedchordsdo.ThisalsohappenswithMajor9’sandMajor13’s,sodon’tletthisconfuseyouifyouseeit—makesuretocheckthestructureofachordtoknowwhatchordyou’redealingwith.

Also, what sometimes causes some confusion is distinguishing any Majorextendedchord(9th,11thor13th)withaDominantextendedchord(9,11or13);forexample,CMajor13andC13—theformerisamajorchordcontainingtheMajor7th,whilethelatterisanabbreviationofadominantchordwiththeminor7th.

DemystifyingtheAlteredChordsAltered chords are very complex chords that can have many differentpossibilities,definitionsandwaysofthinkingaboutthem.Thisiswhytheycanbeveryconfusing,difficultandinconsistentinthewaydifferentmusiciansandmusic theory professors interpret them. But they are well worth the effort

becauseonceyouunderstandthemyoucanreallymakeupanychordyouwantand understand the harmony better. Make sure you’re comfortable witheverythingwe’vehadsofar(especiallywiththeextendedchords),beforetryingtotacklethealteredchords.

Let’s simplify it at thebeginningandsay thatalteredchordsareanyextendedchords that have one or more of their notes changed chromatically. Like theextended chords, they can also be just: Major, minor or Dominant. Theirextensionsarestillthe9th,11thor13th,butinanalteredchordthesenoteshavebeenchangedbyasemitoneuporasemitonedown.

Thesechangesarecalledchromaticalterationsand theyare:b9,#9,b11,#11,b13,#13.Thisisthewaywewritethemdown.

However, since there are three versions of Altered chords (major, minor ordominant), not all of these alterationsmake sense in each version, and this isbecause of the different notes in the core part of the chord that each of thesethreequalitiescontain.Ifyouremember,thecorepartofthechordisuptothe7thnote,orinotherwords,the7thchordsarethecorepartofanextendedchord.Tounderstandallthisandshowwhichalterationsarepossibleforwhichchord,let’sgoovereachversion.

MajorChordAlterationsb9and#9Major7chordconsistsofthenotes:RM3P5M7.IfweextendthischordtotheMajor9thandalterthisnotesothatitisasemitonelower,meaningb9,wewouldget an altered chord with a name that we can simply write as:Major7b9, orMaj7b9*.

InC,thenotesoftheCMaj7b9wouldbe:CEGBDb.

*NOTE that the altered chord names are traditionally written on the sheet with thealterations put in parenthesis and superscripted next to a chord that is altered, like this:Major7(b9).Itdoesn’treallymatterwhichwayyouchoosetowriteitaslongasit’svisible.Thoughifachordhasmorethanonealteration,whichispossible, it ispreferable towritetheminatraditionalway.

b9noteis theminor9th interval,whichis thesamenoteas theminor2nd.ThisintervalisonlyasemitoneupfromtheRoot,andthiscausesareallydissonant

sound.Sob9isavalidalterationforaMajortypechordbecauseitisauniquenote.

Butwhatifwealterthe9thbyasemitoneup(#9)intheMajor7thchord?

Ifyou lookat theTable16:Extendedchords intervallic structure,youcanseethat the #9 is actually aminor 10th, which is the same note as theminor 3rd.MajorchordscontaintheMajor3rd,sothisproducesaclashbetweentheMajor3rd and the minor 3rd. All of these chords can be many different things andinterpreted in many ways depending on the harmony, and that’s why they’recomplex.

Youcanwritethisas:Maj7#9.

CMaj7#9hasthenotes:CEGBD#.

IfyouleaveouttheMajor3rdhere,youwouldgetasuspendedchordthatisnotreally suspended because it has theminor 3rd (minor 10th)— thiswould be aminorchordwithaMajor7thnote—theoppositeoftheDominant7chord.

b11and#11Let’s seewhatwould happen ifwe had a b11 in ourMajor 7 chord. Firstweextendthischordbytwothirds:tothe9th,andthentothe11th.ThiswouldgiveustheMajor11chordwiththenotes:RM3P5M7M9P11.

Again,ifyoulookattheTable16youcanseethatthePerfect11thisthesamenoteasthePerfect4th.Ifwealterthisnotebyasemitonedown,wegettheMajor10thwhichisthesameastheMajor3rdnote.SinceourunalteredMajor11chordalreadycontainstheMajor3rd,thereisnopointinthisparticularalteration.

Ontheotherside,#11isthesameastheAugmented4th.ThatwouldgiveusatwosemitoneclashbetweenP4,Aug4andP5;butinthiscasewewouldleaveoutthefifth.

Howdowenamethischord?Wecan’tnameitMaj11b11becausethatwouldbeveryconfusing.Whatwecandoisbackdownathird,tothe9th,andthenwrite:Maj9#11. In thiswaywe simply indicate that this is aMajor 9th chordwith asharped11thnote.InC,thenotesofthischordwouldbe:CEGBDF#.

b13and#13

Whenitcomestothe13’s,weextendtheMajor7chordtotheMajor13bythreethirds.TheMajor13chordwould thenhave thenotes:RM3P5M7M9P11M13.

IfwelowertheMajor13thnotebyasemitone(b13)wewouldgettheminor13th,which is the same as theminor 6th note,which is a unique note in the initialchord.Wename this altered chordbybackingdown a third and thenwriting:Maj11b13,or(traditionally)Maj11(b13).InC,thenotesare:CEGBDFAb.

#13wouldbetheminor14th,whichisthesameastheminor7thnote.Thisisalsoa unique notewe can have in aMaj13 chord.The name of this altered chordwouldbe:Maj11#13.InC,thenotesare:CEGBDFA#.

Table17:PossiblechromaticalterationsforaMajortypechord

MinorChordAlterationsb9and#9Minor7chordconsistsofthenotes:Rm3P5m7.Whenweextendthischordtothe9th,andloweritbyasemitone(b9),wegetaminor7chordwithab9,sowewriteit:m7b9.

b9isauniquenoteinthischordbecauseand,ifyouremember,itisthesameastheminor2nd.

InC,thenotesofthischordwouldbe:CEbGBbDb.

Ifweraisethe9thbyasemitoneup(#9),wegettheminor10thnotewhichisthesameastheminor3rd—whichisalreadyfoundinourunalteredchord.That’swhythereisnopointindoingthisparticularalteration.

b11and#11Extendingtheminor7chordtotheminor11resultsinthenotes:Rm3P5m7M9P11.Loweringthe11thbyasemitone(b11)givesaMajor3rdnote.Again,inorder toname thischord,webackdowna third, to the9th,andcall it:m9b11.ThisisanotherchordthatcontainsboththeMajor3rd(Major10thactually)andtheminor3rd.ThenotesofCm9b11chordwouldbe:CEbGBbDE.

Raising the11th bya semitone (#11)gives theAug4thnote.Wecall it simply:m9#11.ThenotesofCm9#11wouldbe:CEbGBbDF#.

b13and#13Minor13chordhasthenotes:Rm3P5m7M9P11M13.Thefirstalterationistheb13,whichistheminor13th–equaltoaminor6th.Thenameofthischordthenis:m11b13.InC,thenotesare:CEbGBbDFAb.

The second alteration is the #13,which is equal to aminor 7th. But sincewealreadyhaveaminor7thintheinitialchord,thereisnoneedforthisalteration.

Table18:Possiblechromaticalterationsforaminortypechord

DominantChordAlterations

Dominant chords are unique in a way because the chromatic alterations areusuallydoneonthesetypesofchords.Thisisbecausethesechordsaredesignedfortension,whichtheyaddwhentheyoccurinachordprogression.Thepurposeof adding altered notes to a dominant chord is to provide evenmore tension,whichthenwantstoresolvebadlytoastablechord.Itisforthisreasonthatyouwilloftenseealterednotesonadominanttypechord.

b9and#9Dominant7chordconsistsofthenotes:RM3P5m7.

b9noteisequaltoaminor2nd.Thenameofthischordis7b9.C7b9wouldbe:CEGBbDb.

Ontheotherside,#9ontopofthedominant7isspecialbecauseitisoneofthemostpopularalteredchordsusedinfunk,blues,rockandjazz.It iscommonlyreferredtoastheHendrixchord(specificallyE7#9becauseoftheopenEstringonguitar).#9isequaltoaminor3rd,andhavingthisnotealongwithaMajor3rdandminor 7th produces a really funky sounding chord. InC, the notes of thischordare:CEGBbEb.

b11and#11b11asweknowbynowisequaltoaMajor3rd.Thisnoteisalreadyapartofthedominant7thchord.

#11isequaltoanAugmented4thnote.Thenameofthisalteredchordwouldbe:9#11.InC,thischordwouldhavethenotes:CEGBbDF#.

b13and#13Finally,b13inachordgivesustheminor6thnote.Thenameof thisdominantchordwouldbe:11b13.ThenotesinCare:CEGBbDFAb.

Raising the13th by a semitone gives us theminor 7th,which is already in thedominantchord.

Table19:PossiblechromaticalterationsforaDominanttypechord

Tosummarize:

Thereisnob11alterationonaMajortypechordbecausethatnoteisalreadyapartofthechord.Thereareno#9and#13alterationsonaminortypechord,andTherearenob11and#13alterationsonaDominanttypechord,forthesamereason.

AlterationPossibilitiesandtheUseofb5and#5Wecanaddanyof thechromatic alterations toa7th chordwithouthaving theusualextensionsinit.Forexample,ifwewanttoaddb13toaminor7chord,wedon’thavetoextenditallthewaytothe11th,andthushavethe9thandthe11thinthere.Wecanjustsimplyaddtheb13ontopoftheminor7chord—resultinginam7b13chord,withthenotes:Rm3P5m7m13.

Anotherexample,Ifwewanttohaveadominant7chordwitha#11,wedon’tneed to have a 9th there. Just adding the #11 on top of the dominant 7 chordwouldresultin:7#11chord,withthenotes:RM3P5m7Aug11.Also,notethatwhenever there is no chord quality preceding the first number in the chord’sname,likeinthiscase,alwaysassumethatitisadominantchord.

We can also havemore than one alteration in a chord, as long as theymakesense.Forexample,Maj7b9#11b13.Thischordnamelooksmessy,sotheusualway towrite it on a sheetwouldbe:Maj7(b9 #11 b13),whichdifferentiatesmore

clearly the core part of the chord—Maj7, and the alterations that are put inparenthesis.

Onanothernote,youmightsometimesseeb5and#5aschordalterations.Thisisoftendoneinjazz.b5isthesamenoteas#11and#5isthesameasb13.Thesearejustdifferentnamesforthesamething,theuseofwhichmostlydependsonpersonalpreferenceofacomposer,arrangeroramusictheoryprofessoryou’respeakingtoo.Theruleofthumb,however,isthat#11isusuallyseenonaMajortype chord, while b5 is seen on minor and Dominant type chords to stayconsistentwiththeuseofflatsthatoccurinthesechords.Inotherwords,thisisdonetoavoidhavingbothsharpsandflatswhenyoulistoutthechordnotes.Forexample,inaCm7#11chord,withthenotes:CEbGBbF#,youcoulduseb5insteadandnameit:Cm7b5.Thenotesofthischordwouldthenbe:CEbGBbGb.Samethinggoesfor#5andb13.

Also,ifacomposerorarrangerdecidesthatachordwiththesenotesistravelingdownwardsonthenextchord,they’regoingtowriteoutachordnamewithflatsand use b5 and b13.On the opposite, if they decide that a chord is travelingupwardstheywouldmostlikelyusesharpssuchas#5and#11tonameachord.

Lastly,themostcommonalterednotesonachordare:b9,#9,#11(b5)andb13(#5).Thesemostlyoccurinjazzondominanttypechords.

BorrowedChordsvsAlteredChords–ClassicalvsJazzViewRememberwhenwesaidthatAlteredchordscanbedifficulttograsp?Well,thereasonisthattherearebasicallytwowaysoflookingatthem:classicalandjazz.

Earlierinthischapterwementionedthateachscaleproducesasetofchords,allbuilt in thirds on each of its notes and organized around the root note of thatscale,whichisthekeythatthosechordsbelongto.Wehaveyettogooverthisin full detail in the next few sections, but this is important to remember nowbecauseintheclassicalwayoflookingatthealteredchords,anychordthathasbeenalteredsothatitcontainsoneormorenotesthatarenolongerpartoftheoriginal scale,meaning that the chord no longer fits the key, is considered analteredchord.

Achordlikethisthatsoundssurprisingand`outofkey’toalistenerinamusicalpiece isalsocalledaborrowedchordornon-diatonicchord.This is simplyachordthatisborrowedfromaparallelmode,hencethename.Parallelmodes,ifyouremember,sharethesamekey(sametonalcenter)buthavedifferentparentscale.Thisprocessofborrowingchords fromaparallelmode is calledmodalinterchangeormodalmixture.

Forexample,wehaveachordprogressionthatisinthekeyofCmajor:

Cmaj7–Am7–Fmaj7–G7

IfwechangetheFmajorchordintheprogressiontoanFminor,sothatitis:

Cmaj7–Am7–Fm7–G

WewouldstillbeinthekeyofCmajormostly,butwithonechordthatbelongstoCminorkeyinstead,andthatwouldbeFm7chord.CMajorandCminorareparallel modes, and thus we have simply borrowed a chord from a parallelaeolianmode(naturalminorscale),inthiscaseCminor.Thisborrowedchordintheclassicalviewisalsoconsideredanalteredchordbecausethemajor3rdnoteoftheFchord(FAC),hasbeenloweredbyasemitonetoAb,thuscreatinganalteredFmajorchordinthecontextoftheoriginalkey.

Inthemoremodern–jazzview,alteredchordsareaswehavedescribedthemsofar.Here,thealteredchordshavedifferentalterationsthatmostofthetimedon’tbelongtotheoriginalkey,butsometimestheydo.Forexample,inourpreviousprogression,wecanaltertheFmaj7sothatitis:

Cmaj7–Am7–Fmaj7#11–G7

ThisFMaj7#11chordconsistsofthenotes:FACEB,allofwhicharefoundinthe key of Cmajor. In the classical view this would not be considered as analteredchord,whileinthemodernjazzviewthisisdefinitelyanalteredchord.Keepinmindthisdistinctionanytimeyouusealteredchords.

AlteredHarmony–HowAlteredChordsareUsedandWhereDoTheyComeFromRememberourweirdfriendtheAlteredscale?Thisscaleifyoudon’trememberis the 7th mode of the melodic minor scale. Altered scale is useful for many

reasons and jazz players in particular like to use it to playmore sophisticatedchordsandleadlinesoverthosechords.

Chromaticalterationsaremostoftendoneonadominantchordthatresolvestothemoststablechordinachordprogression.Thischordinthecontextofchordfunctionsinprogressions(whichwehaveyet togoover)iscalledfunctioningdominantchord.Becausethepurposeofthischordistoaddtension,weoftenaddevenmoretensionanddramabyalteringitwithalterednotes.Resolvingthisaltered dominant chord to the next chord which is stable produces a verypleasant,`cominghome’typeofsound.

Youcanalsoplay lead linesover this altereddominant chord, andusealteredscalespecificallyoverthatchordbeforeitresolves.Thiswillresultinsomeverysophisticated lead lines that never sound ordinary – lines which jazz playersoftenuseintheirsolos.

Solet’sseehowtobuildtherelevantalteredscalefromadominantchord,let’ssayC7.

C7chordhasthenotes:

Nowwe’regoingtoaddallofthealterednotesthatarepossibleforadominant7chord:b9,#9,b5(sameas#11),#5(sameasb13).Notethatweexcludethe5th(Ginthiscase)becausethatisoneofthenoteswe’regoingtoalterwithb5and#5.

Nowwehave:

Nowthescalewegotbyaddingthealterednoteslooksverymessy.Wewilltidyit up using enharmonic equivalents so that we can arrange all notes inalphabeticalorder.

WhatwehavecreatednowessentiallyistheCalteredscale.Sincethisscaleisthe 7th mode of themelodicminor scale, we know that it is only a semitonebelowtheparentmelodicminorscaleofthismode.Thismeansthat theparentmelodicminorscaleofanalteredscaleisfoundonits2nddegree.InthekeyofC, that would be Db. So the parent melodic minor scale of C altered is Dbmelodicminor,andCalteredisthe7thmodeofDbmelodicminor.

Parentmelodicminorscaleisveryeasytofigureoutinthiscase–youjusthaveto look one semitone above the root of a dominant 7 chord to find it. Forexample,parentmelodicminorscaleofGalteredscale(builtoutofG7chord)isAb melodic minor. Why would you want to do this? Well, this is veryconvenient because it is usually easier to think and visualize the scale in thecontextofamelodicminorratherthananalteredscale.

Notethat this isonlydoneinpracticeondominant typechordsbecausetheyahavespecificfunctioninaprogression,whichistobuilduptensionrightbeforeitgetsresolved.

Have you noticedwhich noteswere left unchanged by the alterationswe hadabove?It’stheM3(E)andb7(Bb).Ifwehadallnotesunalteredwewouldget:

Doyourememberwhichscalethisis?

It’stheMixolydianmode.ItisalsosometimesreferredtoastheDominantscalebecause it contains theRoot,M3rd andm7, all ofwhich are amust have in adominantchord.Whatalteredscaleessentiallydoesisitaltersallnon-essentialnotesinadominantscale,exceptfor1,3andb7.That’swhyalteredscaleworksbestandismostoftenusedoverdominantchords.

Major andminor type altered chords have their uses too, but these aremuchrarer.Theyareusedmostlytoproducemoreexotic,differentcolor,soundsthatspiceupaprogressioninaninterestingway,usuallyas`borrowedchords’iftheyareoutofkey.

ChordsBuiltin4thsNotalltriadshavetobebuiltfromstacked3rds.We’vealreadyseenthatinthecaseofsuspensions,thereareotherintervals:2ndsand4ths,thatarestackedontopofoneanother. It ispossibleeven tobuild triads fromthegroundfloorbasingthemcompletelyonanon-3rd interval.Usually, this is donewith4ths. In thesecases,chordsarebuiltbystacking4ths:Perfect4ths,flat4ths,sharp4ths,invariouswaystomaketriadsorquadads.

The resulting chords— usually used in jazz and modern classical music —consist, ingeneral, of roots, 4ths,7ths and10ths (1 4 7 10), and theyhavequitedistinct soundsand servequitedistinct functions.Cquadadbuilt in4thswouldbe:

Thesechordscanbeusedinplaceoforinadditionto3rd-basedchordstoachieveavarietyofeffects,butthatusuallymeansmovingintotherealmofsomeveryadvancedharmony.

Let’snowshiftgearsforalittlebitandexplaininmoredetailchordsrelationshiptoscales.

HowChordsComefromScalesAsweknowbynow,chordscomefromscales.Theyaregeneratedbyscalesandareliterarymadeupofnotesfromthescaletheycomefrom.Whatthismeansisthatagivenscalewillimplyacertainlistofchords,thosechordsallbeinginthesamekeyasthatscale.

Chordsthatcomefromamajor(diatonic)scalearecalleddiatonicchords.Eachmajor scale key (remember— 12 notes so 12 keys) has its own set of sevenchords—allofthosechordsbeginandarebuiltonadifferentscalenote.

Figuringoutall thechords inamajorkeyissimple.Let’ssaythatwewant tofigure out all the chords that are in the key ofCmajor. Firstwe number aCmajorscaleandgoalittlebitbeyondanoctave(uptothe13th):

Chords, aswe knowby now, aremost often built in thirds sowewill simplybeginbystackingthirdsjustasbefore.Wewillstartbyaddingthe3rdandthe5thnoteoneachscaledegree.

Thiswillresultingetting7differentsetsof3notes,andthenwehavetoanalyzewhatchordthosenotesmakeup.Forexample,firstnoteinCmajorscaleisC.Whenyouadd the3rdand the5thnote to it,youget thenotes:CEG.SecondnoteinCmajorisD,afteraddingthe3rdandthe5th(countingfromDasthefirstnote),youget:DFA,etc.

Table20:StackedthirdsinCmajorscale

Nowweneed to analyze thesegroupsof3notes and seewhich chordqualitytheymakeup.

HowtoAnalyzeDiatonicChords1. Thefirstgroupofnoteswehaveis:C,E,G;Whenwehaveagroupofnoteslikethisandwewanttofigureoutwhatchorditis,westartbycomparingthenotestothemajorscaleofthebottom-lowestnote.

Inthiscase(CEG)it’sC,sowetakealookattheCmajorscale.WeseethatthesenotesareallfoundintheCmajorscale—they’rethe1st,3rdand5th.

Weknowthatchordwhichhas135chordformulaisamajorchord,sothismustbeCMajorchord(figuringoutthischordisprettyobvious).

2. Nextgroupofnotesis:D,F,A;Again,westartbycheckingandcomparing thenotes to themajor scaleof thebottomnote.Inthiscaseit’sD,sowechecktheDmajorscale.

NowwecanseethatDistheRootnoteandAisthe5thnote,butF–the3rdnoteinourchord–isnotfoundinaDmajorscale.

InsteadwehaveF#.This tellsus thatournote (F) is flattedbyasemitone(ahalf-stepdownon thenotecircle).Whenwestack thirds (135) inaDmajorscale,weget thenotesofaDmajorchord:DF#A,butsinceour3rdnote isF, itmeans thatourchordformulasequenceisactually:1b35.

Andwhatkindofchordhasaformula:1b35?

Minorchord,ofcourse.SothismustbeDminorthen.

3. Nextgroupofnotesis:E,G,B;

WechecktheEmajorscaleandrepeatexactlythesameprocess.InEmajorthe1 3 5 notes are:EG#B.Since our 3rd isG, itmeans that, again, this note isflattedbyasemitone,andtheformulasequenceforEGBis:1b35.Thistellsus that the3rdchord isanotherminorchord,and it’sEminor (in thekeyofCmajor).

I’llletyoufigureoutthechordforthenextthreenotegroups:FAC;GBD;ACE;

You just have to follow the same process as described for the first two notegroups.

Ifyouhaveanytrouble,alittlebitfurtherinthissectiontherewillbeacompletelistwithallCmajorscalechordssoyoucanchecktomakesureyougotitright.

Ijustwantedtoexplainthelastgroupof3notesstartingonthe7thdegreeoftheCmajorscale—BDF.

Whenwecheckthemajorscaleofthebottomnote:

— we can see that both the 3rd (D) and the 5th (F) in our note group are asemitone lower than the 3rd and the 5th in theBmajor scale. Thismeans thatinsteadof135,wehave1b3b5.

Doyourememberwhattypeofchordhasthiskindofformula?

You’veguessedit—it’sadiminishedone!

AssemblingDiatonicChordsTo summarize what we have so far here’s a list of chords that we’ve got byanalyzingthenotes:

Table21:DiatonicchordsinCmajorscale

Eachkeyofthemajorscaleproduces3Majorchords,3minorchords,andhasonediminishedchordwhichstartsonthe7thscaledegree!

Thereisreallyonlyonedifficultywithallthisandit’sthatintherealworldthenotesarenotalwaysgiveninthiscorrecttriadorder.

Sometimesachordinversionisused(wetalkabout thosenext)wheretherootnoteisnotthelowestnoteinachord.

Forexample,youcanhavenotes:FAD,anditmightseemconfusingtofigureoutthechord.Itcanbemanydifferentthings,butthisissimplytheinversionofDminor(DFA).

Here’sanotherexample:BG#E.Canyouguess this chord? It’sEmajor,butwiththereversenoteorder.

Recognizing these chords by their notes evenwhen they’re in an inversion issomethingyou’regoingtobecomebetteratasyougainmoreexperienceplayingandfiguringstuffoutbyyourself.

Goodstartistogetusedtothecommonchordnotegroupssothatwhenyouseeonewithadifferentnoteorderyoucaninstantlyrememberwhatchordthatis.

Thecommononesare:CEG(Cchord),GBD(G),FAC(F),ACE(Am),EGB(Em),DF#A(D),AC#E(A),BD#F#(B),EG#B(E),BbDF(Bb),BDF#(Bm),DFA(Dm).

Inamoreadvancedharmonywheremorecomplexchords(withmorenotes)areused, itwillbeharder todo thisbecause somenotes canbe leftout.This cancreatealotofconfusionastowhattypeofachorditis,buttherearemethodstofigureouteventhose,it’sjustalittlebitmorecomplicated.

Comingbacktoourscalechord,youhavetorememberthateverymajorscalekeywillproducethissamesequenceofchordqualities.

Hereisthemajorscaletriadchordsequence:

Thissequenceneeds tobememorized.Eachmajorkeywillproduce this samesequenceoftriadchords.

Notethatscaledegreesareusuallywritteninromannumerals.Thisisimportantbecauseofthechordprogressionswe’regoingtotalkaboutlater.

The diatonic quadads chord sequence is similar, but with a little bit differentchordqualities:

Weknowthatthese7thquadadsarethechordsyougetafteraddinganotherthirdon topof triadchords.Youcaneasily figureout thediatonicquadadsonyourownandcomeupwiththesamechordsasinthissequence.Justincase,ifyouneedanyhelp,let’sdoittogetherfortheVchord(Dominant7)andfortheviichord(min7b5),becausewehaven’thadthemindiatonictriads.

Dominant 7 chord is the chordwe get if stack the thirds starting from the 5thscaledegree.InthecaseofCMajorscale,the5thdegreeisG,sowebuildourdominantchordontopofthisnote.Wetakethe1st,3rd,5thanda7th(fournotesbecauseitisaquadadchord),butstartingfromtheGnote.Wegetthenotes:G,B,DandF.ThenwechecktheGmajorscaleandseethatGistheRoot,BistheMajor3rd,DisthePerfect5th,butthe7thnoteisF#,andwehaveF.Thismeansthatthe7thnoteisflattedbyasemitone,andwhatwehaveisthechordformulaforaDominant7chord:135b7.

Inquadad form,min7b5 is thechordwegetwhenwe stack the thirds startingfromthe7thmajorscaledegree.IfwedothisinthekeyofCmajorwegetthenotes:B,D,F andA.Thenwecheck thesenotes inBmajor scale–B is theRoot,D#thethird(wehaveD),F#isthe5th(wehaveF),andA#isthe7th (wehaveA).Soallnotesaftertheroothavebeenflattedbyasemitone.Thismeansthatthechordformulaforthischordis:1b3b5andb7.Intriadformthiswasadiminished chord (or half-diminished tobeprecise), butwhenwe add anotherthirdontopitbecomesmin7b5.

Notethatourdiminished7th,orfulldiminishedchord,withtheformula:1b3b5bb7,isnotadiatonicchordbecauseitdoesn’tappearinthisdiatonicsequenceof4-notechords.

WecandothisexactprocesstofigureoutthechordsthatarefoundinaminorScale,butwedon’thaveto.Weknowthatminorscaleissimplythe6thmodeofamajorscale,soallwehavetodoistakethemajorscalechordsequenceandre-orientitsothatwestartfromthevichord.

Bydoingsowegettheminorscaletriadchordsequence:

InthekeyofAminor(the6thmodeofCmajor)thatwouldbe:

Amin(i),Bdim(ii),CMaj(III),Dmin(iv),Emin(v),FMaj(VI),GMaj(VII).

You can apply this minor chord sequence to any natural minor key and youwouldgetthechordsinthatkey.

Minorquadadssequencefollowsthesamelogic:

Lastly,keepinmindthatthisisnottheonlywaytoassemblechordsthatsoundgoodtogether,andveryoftenimprovisorsandcomposersusechordsthatarenotrelateddiatonicallyornotgeneratedbyadiatonicscale,butitisoneeasywaytoknowandensurethatwhatyouplaywillsoundgood.

TransposingfromOneKeytoAnotherThe necessity to play in a bunch of different keys is not uncommon for amusician.Beingabletochangekeysonthespotisareallyusefulskill tohavefor a variety of reasons — especially if you want to play chords on yourinstrument.

Often times the reasonwedo this is becausewewant to play in a keywhichbetter suits a singers voice (doesn’t matter if we sing or someone else), or itmightbejustmoreconvenienttoplayinacertainkeydependingonasituation.

Inanycase,havingthisskillisquiteusefulandimportant,especiallyifyouareplayinginaband.

Luckily, since you now know the sequence of chords that each major scaleproduces,switchingfromonekeytoanotherisveryquickandeasy.

If we have a chord sequence playing, for example: C—Am—F—G,wefigureoutthatthesearetheI—vi—IV—VchordsoftheCmajorkey.

IfwewanttoswitchkeystoG,firstweneedtofigureoutthechordsinthekeyofG,andthenapplythischordprogression.

1. Gmajorscaleis:G,A,B,C,D,E,F#2. Afterapplyingtheformula:Maj,min,min,Maj,Maj,min,dim,wegetthefollowing

chords:GMaj(I),Amin(ii),Bmin(iii),CMaj(IV),DMaj(V),Eminor(vi),

F#dim(vii).3. ThenallwehavetodoisapplytheI—vi—IV—Vchordsequencetothekeyof

G,andwegetthechords:G—Em—C—D.

SowhatwasC—Am—F—GinthekeyofCisnowG—Em—C—DinthekeyofG.

Thiscanbedoneinallkeysandwithanychordprogression.

ChordInversionsandChordVoicingsThearrangementofnotesinachordiscalledachordvoicing.Itrepresentstheorderandthefrequencybywhichthenotesappearinachordwhenweplayit.Byfrequency,Imeanhowmanytimesthenotesarerepeatedinachordthatisplayed.

Forexample,anEMajortriadconsistsofthenotes:EG#B.Thisisanexampleofabasicchordvoicing.Thenotesaregoingfromlowertohigherinorder,sothatE–theRoot,isthelowestnote,G#istheMajor3rdandhigherinpitchthan

E,andB–thePerfect5thisthehighestnoteinthisvoicing.However,sometimeswecanplayachordinwhichtheorderofthenotesisdifferentthanthisone,sothat,forexample,wecanhave:EBG#,anditmaynotbeobviousatfirstthatthis is still anEmajor triad, butwith a different voicing.E (Root) is still thelowestnote,butnowG#(Major3rd)isthehighestnoteinthisvoicing.

This isoften thecaseonguitarwhereachordcanhavemanydifferentshapesandwaysitcanbeplayed,eachwithadifferentchordvoicing(andalsodifferentfingeringchoices).IfwetakeourEmajortriadagainandplayitonguitarasabasic open chord shape, we can see that the order of the notes played fromlowest to highest is: E(R), B(P5), E(Octave), G# (M3), B(P5), E(DoubleOctave).ThisisanexampleofachordvoicingwhereEnoteappears3times(in3octaves),B(P5)appearstwice,andtheG#(M3)appearsonlyonce.

Wecanseethatonechordcanhavemanydifferentvoicings,androotisalwaysthebass(lowest)note.Buttherearespecialcaseswhenit’snot.

Most all chords are third-based. The general form of a chord is such that itcontainsarootfollowedbyaseriesofstackedthirds(majororminor)thatcreatethequalitiesofthatchord.Itispossible,however,toproducechordsthatdon’thavethisstructurebutarestillbasedonthirds.

Thisisdonebyre-arrangingthenotesofastackedthirdchordinawaysothatthe lowest note in the chord— the bass note — is no longer the root note(usuallythatmeansthattherootnoteiscontainedelsewhereinthechord).Thesechordsarecalled“Inversions”.

Essentially,wecansaythatachordinversionisvoicingachordnoteotherthantherootasitslowestnote.

The simplest inversions are triad inversions (because those are the simplestchords).Foranytriad,sincetherearethreedistinctnotes,therearetwodistinctinversionsthatcanbeproduced(inadditiontotheoriginalchord,inwhichtherootnoteisthebassnote).

MajorTriadInversionsCMajortriadcontainsthenotesC,EandG.TheCisthenthechord’srootand,mostoften,itsbassnote.Inthatcase,thechordisnotininversion.

1. The first inversion of the C major triad contains the same notes, but now the E(Major3rd)isthechord’sbassnote.Mostcommonlythechordisplayedinthenoteorder:E,G,C.Thisnewchord,relativetoitsnewbassnote(E)containsaminor3rd

(G)andaminor6th(C).

2. The second inversion of aCmajor triad hasG (Perfect 5th) as its bass note. It isgenerallyplayedG,C,E(in thatorder);andcontains, relative to itsbassnote(G):Perfect4th(C)andaMajor6th(E).

MinorTriadInversionsMinortriadinversionsfollowthesamerulesasmajortriadinversions.

1. An A minor triad (A, C, E) in first inversion is generally played C, E, A; andcontains (relative toCas thenewbass):Major3rdandaMajor6th. It’s interestingthatthischordininversionisactuallyCMajor6(butwithoutthe5th),withthenotes:C(R),E(M3),A(M6).

2. Insecondinversion,thechordisE,A,C;andrelativetoEitcontainsaPerfect4th

andaminor6th.

Thesetriadinversions—inthecaseofmajorandminortriads—havespecialnames:

Thefirstinversionofamajororminortriadiscalleda“6”chord.Aswehaveseenthisisbecauseitsbassnoteisthe3rdoftheoriginaltriadanditcontains,relativetothenewbassnote, a3rd (Major3rd in aminor chord inversion, andminor3rd in amajorchordinversion)anda6th(Major6thinaminorchordinversionandminor6thinamajorchordinversion).The second inversionofamajororminor triad is calleda“6/4”chord, since thischord,whosebassnote isa5th, contains a4th anda6th above thatbassnote.Thisinversion essentially gives us a 6sus4 chord (R, P4, M6) in the case of a majorinversion, and augmented sus4 triad (R,P4,Aug5– same asm6) in the case of aminorinversion.

InversionsofDiminishedandAugmentedChords

Herewehavesomethinginterestinggoingon.Diminishedchordsarebuiltonlyout of stacked minor 3rds and Augmented chords out of stacked Major 3rds.Because of that, diminished and augmented chords are called symmetricalchords. The consequence of that is that inverting augmented triads and fulldiminishedchordsresultinmoreaugmentedtriadsandfulldiminishedchords.

In other words, a full diminished chord in inversion is just that same chordrepeatedupordownaminor3rdinterval(3semitones).Likewise,anAugmentedtriad chord in inversion is just that same chord repeated up a Major 3rd (4semitones).

Notethattherearesymmetricalscalestoo.Scalessuchasadiminishedscaleandwholetonescalehavethiskindofstructures.Infact,thefirstscalewehadinthisbook—theChromaticscale,isalsoasymmetricalscale.

Inversionsof7thsandExtendedChordsIt ispossible to invert7ths andextendedchords inavarietyofways toendupwith harmonically complex chords. For any quadad, since there are 4 distinctnotes, there are three distinct inversions (that follow the same logic as triadinversions)inwhichtheRootisnotthelowestnote,anditgoesonasmorenotesareadded.

NormalRootposition(1357)–Rootisthelowestnote

1stinversion(3571)–3rdisthebassnoteandRootisthehighestnote

2ndinversion(5713)–5thisthebassnoteandRootisthesecondhighestnote

3rdinversion(7135)–7thisthebassnoteandRootisthesecondlowestnote

These chords, most often used in contemporary classical music and jazz, areusefulformanyreasons,mostobviouslyassubstitutionchords.

Keepinmindthatyoucanhaveanychordvoicing,meaninganynoteorderinachord, but as long as the Root is positioned as the lowest note then it is notconsideredaninversion.

HowtoFindRootNotePositioninanInvertedChordChordvoicingsareoftenarrangedinawaysothatjustbylookingatthenotesitisfarfromobviouswhatchorditis.Luckily,thereisaneasymethodtofindoutwhere the root note is in an already inverted voicing that youmight get. Themethod is to simply rearrange the notes until they are stacked in thirdsalphabetically,andthisisbecausevastmajorityofthechordsarebuiltinthirds.

Let’ssaywehaveachordvoicingwiththefollowingnotes(inorderfromlowesttohighest):A,F#,A,D,F#, andwewant to figureoutwhere the root is andwhatchordthisis.

1. Firstwerecognizethatthereareonlythreedistinctnotesinthischord,sothismustbea triadof somekind.Wealsodisregardany#’sorb’sbecausewe justwant tofigureoutthethirdsalphabetically.

2. Thenwestackathirdontopofeachnote,startingfromthelowest,whichinthiscaseisA.AthirdupfromAifwecountalphabetically(A,B,C–1,2,3)istheCnote.WecheckifthisnotematchesthenotenexttoAinourchord.Itdoesn’tsincethenextnoteisF#.

3. Thenwemoveontothenextnote–F#.Wedisregard thesharp;soa thirdupfromF(F,G,A–1,2,3) isAnote.This isgoodbecauseAmatchesthenextnoteinourchord.ThismeansthatF#couldbethestartingnote.ThenweaddathirdupfromA,which,again,istheCnote,anditdoesn’tmatchthenextnote,whichisD.ItseemsthatF#isnottherootnote.

4. ThenwemoveontoD.AthirdupfromDisF.Itmatches.WeaddathirdtoF,andgetAnote.Matchagain.

Since this is a triad it is enough to get twomatches in row (for quadads youwouldneedthreematches).Nowwejusttakebackthesharpsorflatstoallnotesthathadthem.Inthiscase,onlyFhadasharp.Thenoteswegotbyrearrangingtheminthirdsare:DF#A,andthesearethenotesofaDMajorchord.SinceAnotewasatthebottomasthelowestnote,itmeansthatthisisthe2nd inversionofDMajorchord.

Thisprocess isquitestraightforwardandyoucanuse itanytimeyou’reunsurewhatchordyou’refacing.Whenitcomestotriadsyoujusthavetowatchoutforthosesuspensions(2ndand4th). Ifanyof thenoteswithastackedthirddoesn’t

match,trytocountupalphabeticallybyasecondandafourth.Forasus2chordfirst findanotematchwith the stackedsecondand thenwitha stacked fourthnote.Forasus4chordfirst findamatchwith thestackedfourthandthenwithstackedsecondnote.

As the number of the notes in a chord increases it gets progressively moredifficult to figure out the chord, plus a chord can sometimes have severaldifferentnames–thechoiceofwhichwilldependontheoverallharmonyyou’regiven(ornot).

SlashChordsSlashchordsaresimplythemethodweusetonotateinvertedchords.

Theylookastwoletternamesseparatedbyaforwardslash,forexample:

Here, thenoteon the top left represents thechord,and thenoteon thebottomrightrepresentsthechordnotethatisinthebassasthelowestnote.Inthiscase,G is in the bass of theCMajor7 chord.This chord has the notes:C(1),E(3),G(5),B(7),sowhatwehaveisthe2ndinversionoftheCMaj7chord.

Inaband situationbassplayerusuallycovers the lowestnoteof slashchords;andthenachordplayercanjustplayaregularnon-invertedchord.

Slashchordsarenotjustusedfornotatinginvertedchords.Theyaremostofthetime,buttheycanhaveotherusesaswell.

Onesuchinstanceiswhenwehaveaslashchordinwhichthebottomrightnoteisnotapartofthechordonthetopleft.Forexample,G/F#istellingusthatwehave toplayaGmajor triadon topof theF#note in thebass.This isusuallyregardedasbadnotationpracticebecauseyoudon’tactuallyrealizeatfirstwhatchorditisthatyou’replayinginachordprogression.Thislimitsyouroptionsasaperformer,andmakesithardertomakegooddecisionswhenitcomestovoiceleadingandhowtomovefromonechordtothenext.

VoiceLeading

Withallthechordswehadsofaryoumightwonderwhatisthepurposeofchordinversions, and rightfully so.But there is onemain reasonwhymusicians usethem,anditcomesdowntovoiceleading.

Voiceleadingisanoldertermthatcomesfromchoralmusic.Thisisthemusicwrittenforchoirs–amusicalensembleconsistingofonlysingers.Inthistypeofmusic, eachvoice (singer)hasauniquemelody line, and theway thismelodylinemovesandinteractswithothervoicesinachoiriscalledvoiceleading.

What’sinterestingisthatthistranslatestootherconceptsinmusic.Forexample,if instead of singers we had four different instruments each playing a uniquemelodyline,thosemelodies–consistingofindividualnotes–wouldlineuptocreate andoutlinechords.Voice leadingwouldbe theprocessbywhich thosemelodiesmoveinharmony.

Voiceleadingalsotranslatestoplayingchordsonasingleinstrument.Here,itisall about howwe connect chords together one after another to create smoothmelodiclinesforeachnoteinachordasitmovestothenextchord.

Let’ssayweplayacoupleof4-notechordsinachordprogression.Wecanthinkof each note as a separate melody line that moves as one chord changes toanotherchord.Thepointofvoiceleadingistocreatemelodiclinesforeachofthe chord notes that are smooth, easy to play and good sounding, so that theoverallchordprogressionsoundsbetterandmoreappealingtoourears.Inordertodothis,wehavetopayattentionwhateachofthechordnotesaredoing.

In the early days, composers noticed that moving between the notes that arecloser toeachothersoundsbetter.Sogenerally,whencomposingorarrangingharmonywewanttoavoidawkwardintervalsandjumpsthataredifficulttoplayanddon’tsoundasgood.

From this comes themain principle of voice leading which states that as theharmonychanges,eachvoice(chordnoteforexample)shouldideallymovenomorethanonewholestepupordowninpitch.Anotecanremainthesamebetweentwochords,oritcanmovebyahalf-steporawholestep,butnomorethanthat.Thisisconsideredagoodvoiceleadingpractice.Thiswouldproducesmooth soundingchordchanges that aremoremelodic, andeasier toplayandlistento.Agoodanalogyforthiswouldberhymingofthelyricsinasong–thewordsthatrhymearelikethechordnotesthatmovenomorethanawholestepasthechordharmonychanges.

Let’ssaythatwehaveaverypopularchordsequence,called12-BarBlues.Thissequence,consistingofonly3chords–I,IV,andVinanykey–isbasedononeofthemostfamiliarsoundingchordprogressions.Oneofthemainreasonsthisprogression sounds so memorable is because of good voice leading. Let’sanalyze what the chord notes are doing as they change throughout theprogression.WewilldothisinthekeyofE.

IchordinthekeyofEisE,withthenotes:EG#B

IVchordisA,withthenotesAC#E

VchordisB,withthenotes:BD#F#

Ina12-BarBluessequence,thesechordsmoveinthefollowingway:

E–A–E–B–A–E–B–E.

(Note that these chords are played for different periods of time – we’re justlookingatthechangeshere).

Inthefirstchange(EtoA)Enoteremainsthesame,G#goesahalf-stepuptoA,andBmovesbyawholestepuptoC#.

Inthesecondchange(AtoE)it’sallthesamejustinreverse.

In the thirdchange(E toB)Egoesahalf-stepdown toD#(it isalsoawholestepdownfromF#),G#goesawholestepdowntoF#,andBremainsthesame.

Inthefourthchange(BtoA)BnotemovesawholestepdowntoA(itisalsoawholestepdownfromC#),D#movesahalf-stepdowntoC#(itisalsoahalf-stepdownfromE),andF#movesawholetonebacktoEnote.

Inthesecondtolastchange(EtoB)inthissequence,ifweweretointroduceanAnote toaBchord,which is aminor7th – thusgetting theB7chord (this isoftendone inon theVchord toprovide stronger resolution to the I chord);Awould resolvenicelyon the final change (B toE) toG#andBnotes in theEchord.

Wecan see that there isn’t a single intervalbetween thenotes in thesechordsthatislargerthanonewholestep.Butwhatifwewanttocreatedescendingorascendingbasslines(whichisoftendoneinvoiceleading),ortocreatespecificmelodieswithinthechordsastheychange;oreventohaveapedalnote–whichis a single note played in one place that sustains consonantly and dissonantly

throughoutthechordprogression?Thisiswherechordinversionsanddifferentchordvoicingscomeintoplay.

In order to effectively voice lead, you often need to invert chords and usevoicingsthatallowyoutofollowvoiceleadingprinciples.Forexample, ifyouwanttohaveadescendingbassline,youcaninvertthechordssothatthelowestnoteofeach isnomore thanawholestepawayfromthebassnoteof the lastplayedchord.Chord inversionscanalsobeused ifyouwant to remain inonepositiononyourinstrumentandplayallyourchordstherewithoutjumpingupordownwithyourhand.Thisisveryusefulforplayingapedalnote–youwouldneedtoinvertallchordssothatyouremaininonepositiononyourinstrumentthroughouttheprogression.

Forallthesereasons,studyingvoiceleadingandinversionsisincrediblyusefultoanymusician,especiallytocomposersandarrangers.

Polychordsitispossibletocombinechordstoproducenewchords.Theseareusuallycalledpolychords.Often,thesechordsarecomplexanddifficulttoplayover,buttheyareusefultosomeimprovisorsandcomposersforavarietyofreasons.

Polychords,asthenameimplies,representtwochordsplayedatthesametime,withonebeingplayedontopoftheother.Theyareverysimilartoslashchords,butdifferentinafewimportantways.

Insteadofwith a forward slash, polychords are notated as a fractionwith onechordontopandtheotheronthebottom.Thechordthat’sonthebottomisthelowerpartofthepolychord.Inotherwords,thetopchordisplayedontopofthebottomchord.

Here’showanotatedpolychordusuallylookslike:

HerewehaveaGMajor7chordplayedontopofAminorchord.Whenwelistouttheirnotestogether:

–WhatweessentiallygetistheAminor13chord,andthisisbecausethenotesofGmajor7(G,B,D,M13),aretheminor7th,Major9th,Perfect11thandMajor13thinthekeyofA.

Let’scheckoutaharderexample:

InthiscasewehaveaGMajorchordplayedontopofDminorchord.Let’slistoutthenotesofbothchordsandanalyzethem.

Dmhasnotes:DFA,andGmajhas:GBD.Ifwegroupthemtogetherweget:DFAGB.

All of the notes are stacked in thirds alphabetically (we leave out the last Dbecauseitisrepeated),butAtoGisaweirdjump.WechecktheGnoteinthekeyofDmajor(wealwayscheckthekeyofthebottomnote)andseethatitisthePerfect4th.Inextendedchordharmony,Perfect4thanoctaveupbecomesaPerfect11th.BnoteinthekeyofDisMajor6th,andthatisequaltoaMajor13th.Whatwehaveis:DastheRoot,Fistheminor3rd,AisthePerfect5th,GisthePerfect11th,andBistheMajor13th.

Sincewehaveaminortriad,no7th,andtwoaddednotes–thisisanaddedtonechordwithtwoaddedtones;youcanwriteitlikethis:Dm(add11add13).

We can conclude that polychords are just a shorter way of writing long andcomplexextendedchordsofanykind–includingthealteredones.Althoughthispresents a problem because whenwe see a polychordwe don’t know at firstwhatkindofchordwe’rereallydealingwith.Inotherwords,weusuallydon’tknow the relationship of the notes in the top chord to the key of the bottomchord,unlessweanalyzethenotes.Likewiththeslashchordsthathaveanon-chordbassnote,usingpolychordslikethismakesitmoredifficulttofigureouttheharmonyandmakegooddecisionswhenplaying.

Polychords actuallymakemuchmore sense in the context of polytonalmusicwhere you have two or more tonal centers happening at the same time and

you’retryingtocreatetwoseparateharmonies.Moreonthatlaterinthebook.

ChordProgressions(Part1)Achordprogressionis,simply,aseriesofchordsthatisplayedtogetherin

amusicalway.Anysongstructureisbasedonachordprogression,andthat

progressiontakesthelisteneronajourneyoftensionandresolve.

Chordprogressionshaveaform:

1. There is a chord (or chords) that is the centerof theprogression, called the tonic.Thischord(orchords)isoftenplayedfirstandit isalwaysthecenterofgravityoftheprogression—everythingelsewantstoresolvetoatonicinwayoranother.

2. Then there is the part of the progression that moves away from the tonic, whichinvolvesplayingoneormore“subdominant”chords.

3. Andthereis thepartof theprogressionthatmovesbacktowardthetonicinwhich“dominant” chords are played. These chords have the strongest pull to the tonicbecausetheyaddlotsoftension.Themostbasicunitofachordprogressionistheresolution:themovementfromonechord that isnota tonicchord toa tonicchord,establishingand resolving tension,creatingmovementandproducingaharmonicdirection.Aresolutionlikethis—twochords,resolvingtothetonic—iscalledacadence.A special instance of this is themovement from amajor chord on the fifth to thetonic:aV-I(inamajorkey)orV-i(inaminorkey).Ifneitherofthosechordsisaninversion,thentheresolutioniscalledaPerfectcadence,anditisthefoundationofmostofthebasicchordprogressionsinWesternmusic.Whethertheprogressionisinamajorkey(inwhichcasethetonicchordismajor(I)andthediatonicchordsofthatkeyareindexedtothemajorscaleofthatroot),orinaminorkey(inwhichcasethetonicchordisminor(i)andthediatonicchordsofthatkeyareindexedtotheminorscaleofthatroot),thechordbuiltonthefifth(thedominantchord)ismajor.

This isbecause inorder for the resolution from theVchord to the tonic tobestrong,the3rdoftheVchordneedstobemajorsothatitcanresolveuptothe5thofthetonicchord.Thismaysoundcomplicatedbuttakesometimewithit.

Often times, these dominant chords are played as 7th chords (dominant 7thquadads), in which a minor 7th is added to a major triad, thus adding more

tension.Chordprogressionsarewritten(likechords)usingromannumeralswithdashes in between. Numerals for major and dominant chords are capitalized,whiletheminoronesaren’t.

CommonChordProgressionsThereareseveralfairlycommonprogressionsthatrepeatinsongaftersong.Thebasic chord progression that makes use of cadences is most simply a I-IV-Vprogression (which repeats), in which the major IV chord acts as thesubdominant,themajorVchordactsasthedominant,andthemajorIchordactsasthetonic.

InthekeyofCforexample,thisprogressionI-IV-Vwouldbe:C—F—G.

Anothercommonprogression,especiallyinjazz,isii-V-Iprogression(inwhichthe minor ii chord acts as the subdominant, the major V chord acts as thedominant,andthemajorIchordactsasthetonic).

InthekeyofCtheprogressionii-V-Iwouldbe:Dminor—G—C.

Chordprogressionsalsoincludeminorversionsofthoseprogressions:i-iv-v,ii-v-i.

Othercommonprogressions,inrockandpopmusic,arevariations(moreorless)ofI-IV-V,suchas:I-IV-I-IV-V-IV-I.

Here’salistofsomeverycommonchordprogressionsyoucanfindinsongs:

1. I—vi—IV—V2. I—V—vi—IV3. I—V—IV—V4. I—IV—V5. iii—vi—ii—V6. I—IV—I—V7. I—V—ii—IV8. I—vi—ii—V9. I—V—vi—iii10. I—iii—IV—V

You can just pick a key and play any of these chord progression and it willsoundgreat.

More complicated progressions include, for example, iii-vi-ii-V-I (in whichdiatonicchordsareplayedonthe3rd,6th,2nd,5thandtonicofamajorkey),I-vii-vi-V,andiii-vi-V-I,amongothers.

Noticethatinallofthesecases,movementisestablishedawayfromsometonicchord (usually to some sub-dominant chord) and then, passing through adominantchord(usuallytheVchord),acadenceisproducedastheprogressionresolvesbacktothetonic.

ExtendingandSubstitutingChordProgressionsAmusicalpiecedoesn’talwaysneedtofollowastrictchordprogression.Oftentimes there are some interesting stuff happening, non-diatonic chords beingintroduced,keychanges,etc.

It isalsopossible toextendchordprogressionsbyaddingsmallerprogressionswithin the principle progression, often using temporary harmonic centers tomultiplytheoverallnumberofchords.

One version of this is something, used often in jazz, inwhich a dominant 7thchordisusedafifthabovesomediatonicchord.AcommonversionofthisistofindaV7chordusedabovetheVofthetonic(thisisacalledaV7/V,or“fivesevenoffive,”chord).

Oneverycommontrickistosimplyalterthechordofaparticularscaledegree.

Forexample,insteadofplayingtheusualminor(ii)inaprogression,having‘II7’wouldmeanthatthischordhasnowturnedintoadominant7thchord.

Oneexampleofsuchprogression(commoninjazz)wouldbe:

I7—vi7—II7—V7

Sometimes, chords are strung together that ascend or descend a scalediatonically (or chromatically) in order to move from one part of the chordstructure to another.Between these two techniques: adding chords a 5th above

existingchordsandmovingdiatonicallyorchromatically,thereisahugespaceofpossibilitiesavailabletoacomposerorimprovisor.Notallofthispossibilitieswillsoundgoodhowever—it’simportanttoalwaysletyourearsguideyou.Itisalsopossible tosubstitutechords inorder tovaryaprogression, repeating itdifferentlytoarriveatalongeroverallprogression.Thesimplestformofthisistosubstituteonetonic,dominantorsub-dominantchordforanotherofthesamefamily

Diatonicchords thatcouldactas tonic,andare therefore in the“tonic family”are:1st,3rdand6thchords.

2ndand4thchordsarebothinthe“sub-dominantfamily”.

5thand7thchordsarebothinthe“dominantfamily”.

It is alsocommon inpopmusic (inBeatles songs inparticular) to substituteamajor chord for a minor chord in a progression. This is often called “TheBeatlestrick”.Thisisatechniquethatcomestopopmusicbywayoftheblues,inwhichmajorordominantchordsareusedontheI,IVandVeventhoughthesong is in aminor key (since theminor pentatonic scale is the foundation ofblues).

Forexample:

I—IV—iv—I

MovingTonalCenters(TonalCentersVsKeys)Whenwetalkaboutextendingprogressionsbyestablishingtemporaryharmoniccenters,weareinvokingthedistinctionbetweentonalcentersandkeys(orkeycenters). It is possible for a song to be in one key but to havemultiple tonalcenters. Inotherwords, I can revolvearoundCmajor, and thenCminor, andthenBmajor, but Imight still be playing in the keyofAmajor if that is thetrajectoryoftheprogressioningeneral(andifthesonghasnotchangedkeys—ormodulated).

Thisisdonemostcommonlyinjazz,wheresometimesasongthatiswritteninaparticularkeywillmove throughmany tonal centers, sometimesveryquickly.

Famously,forinstance,JohnColtranehadcompositionsthatmovedthroughasmanyasninetonalcentersinjustafewbars.

WhatIsModulationandHowIsItUsedDistinctfromtonalcentersarekeycenters.Whenakeyischanged,wesaythatthesonghasmodulated.Inthesecases,ratherthanatemporaryharmoniccenterbeing established and then passed through (en route usually to the key of thesong), the entire harmonic structure of the progression shifts up or down bysomeinterval.

Therearenohardandfastrulesinpoporrockthatgovernthewaymodulationoccurs, but in general it occurs at the beginning of a repetition of someprogression and usually that entire repetition occurs in themodulated key.Tosmooth the transition, it is sometimes easy to replace the chord immediatelyprecedingthemodulationwithadominantchordfromthenew(modulated)key.

Modulationsarecommoninpopmusic,countryandrock,particularlyattheendofa song,wherea refrainmaybe repeateda full stepabove theoriginal root.Thisisone,simple,formofmodulation—repeatingaprogressionexactlyasitwas,onlyhigherorlower.

Mostoften,thisoccursupratherthandown,anditusuallyoccursinhalfsteps,wholesteps,ormajor3rd(twostep)intervals.TheendoftheTitanicthemesongisanexampleofthissortofmodulation.

ChordArpeggiosChordsaremadeupofdifferentnotes;weusuallyplaythesenotesatthesametime, but we can also play them individually, and that’s when we’re playingarpeggios.Arpeggiosaresimplythenotesofachordplayedoneatatime,inanyorder,ratherthanallatthesametime.

Arpeggiosaresimilartoscalesinawaybecausewhenwelearnascalewelearnabunchofnotesthatfitoverasequenceofchordsinsomekey.Whenweplaythesescalenotestheywillsoundpleasantoverthosechords.Ontheotherhand,

whenwelearnarpeggioswelearnabunchofnotesthatfitusuallyoverasinglechordinachordsequence.Sogenerallyweplayarpeggiosoverasinglechordinachordprogression,andwechangearpeggioswheneverachordchanges.

Arpeggios are very useful when we improvise a melody over a chordprogression.Wemayuseaparticularscaleforthisprogressionandthenifatanypoint a chord comes up that doesn’t fit the key of the chord progression, ourscale notes would not fit over that chord and will sound unpleasant. In suchinstance we can switch to playing arpeggios just for that single chord thatdoesn’tfitthekey,anditwillsoundreallygood.

Onesuchexamplewouldbeifyouhadaprogression,let’ssay:i—VII—VI—V7 (which is a common progression used in flamencomusic, also called:Andalusiancadence).InthekeyofAmthechordswouldbe:Am—G—F—E7.

HereyoucanuseAminorscale tosoloand itwouldfitperfectlyoverAm,GandFchords;butwhenE7comes,justforthatonechordyouwouldswitchtoplayingEdominant7arpeggio—meaningthenotesofE7chord:EG#BD,inanycombination.

This is another,more beginnery, way to use arpeggios. The general tendencyhowever is tograduallymoveonto thinkingandplayingmorechordally—totreateachchordinaprogressionseparatelyandplaymorechordnotes inyoursolos. Thisway your soloswill soundmore appropriate,moremelodic,moreuniqueandlessgeneric.Jazzplayersdothisallthetime.

Ifyouthinkaboutitandanalyzesomeofthemostfamoussolosinhistory,forexamplethoseinsongslike:HotelCalifornia,StairwaytoHeavenorSultansofSwing, you will notice that one of the things that makes these solos socaptivating comes down to the note choices that are mostly arpeggios of thechordsplayinginthebackground.

Arpeggiosarealsousedtooutlinetheharmonyofasonginawaysothatyoudon’thavetoplaychordsintheusualsense(allnotesatthesametime).Youcanjust pick out individual chord notes and play them as the progressionmoves,usuallyinacertainpattern.Thiswillmakeitsoundalmostasifyou’replayingthe chords even though you’re just playing their notes individually. Anothergoodthingaboutarpeggiosisthatyoucanoftengetawaywithplayingdissonantchords thatwould otherwise sound awful if all their noteswere played at thesametime.

Inconclusion, learnhow tousearpeggiosonyour instrument; learnwherearethenotesandhowtofindthemquickly, learncoolrhythmicpatternsbywhichyou can play individual chord notes, and use them in your playing.When itcomestosoloingandimprovisation,studythechordsthatyou’replayingover,analyzethecontextandtheeffectthateachnotehasoverachordthatisplaying.Noticehowbyfocusingmoreonthechordnotesyoursolosstarttosoundmoreenticingandcaptivating.

Part4

AllAbouttheRhythm

TheImportanceofHavingaGoodRhythmFew things in music (and perhaps in life) are as important as rhythm. As somany jazz, funk and blues musicians know, it is possible to play virtuallyanythingandhaveitsoundgoodifyou’vegotthegroove,theswing,thefeel,thevibe,theflow.

Developingrhythmismorethansimplyunderstandingthenumbers—itisaboutputting hours in with your instrument, really becoming comfortable with it,perfectingyourtechnique,establishinganinternalclock,etc.

Some of this is nearly impossible to develop passively on your own, and soplayingwithothermusicians(whohavegreatrhythmskills)asoftenaspossible,loopingyourself(recordingyourplaying)andusingyourloopstopracticeover(this will help diagnose rhythmic problems) and playing to a metronome(especiallywhenyouare first learningsome techniqueorpattern)areallquiteimportant.

Playingslowandfocusingon timingrather thanonspeed isalsoan importantpartofdevelopinggoodrhythm.Ifyou’replayingslowyou’llbeexercisingyourtiming,andifyou’replayingfast(er)yourfocuswillbemoreonyourspeed.Thecatch is that great sounding speed playing and impressive technique are onlydeveloped through very slow and engaged repetition (you have to have thetimingdownfirst)andwithgradualspeedincreases.

For all these reasons, understanding rhythm is a largepart ofmusic theory—howtimeisdividedinmusic,howapulsefunctions,howamusiciancancreateandresolvetensionortellastoryrhythmically.Understandingandinternalizing

these thingsmaybe themost importantpartofbeingaperformerorcomposerand sounding good, and itmay aswell be themost rewarding aspect of yourplaying.

UnderstandingTime,Beat,BarandTempoInmusictheory,theword“time”referstothepulseorthebeatofthemusicanditstimesignature.Thebeatofthemusicisthemostfundamentalunitoftime.Itiswhatwetapourfoot,nodourheads,orclapourhandsto.Itisdefinedbythetimesignatureofapiece.

A“bar”,alsocalleda“measure”,isanotherfundamentalunitthatmeasuresthetimeofapieceagainstwhichnote/beatdivisionsareunderstood.Inotherwords,a bar is one complete cycle of the beats, and it is always defined by the timesignature. Bars are a convenient way of keeping the music organized intosmallerchunks.

Tempo isanothercrucialelementinmusic.Itdescribesthespeedatwhichthebeats happen— the pulse of the music. It is usually expressed in beats perminute, or BPM. It simply tells us the number of beats in one minute (forexample80bpmmeans80beatsperminute).

Knowingaboutthetimeandthetempoofapiecealreadytellsyoumoreorlesshow to play over it, it alreadymakes themood of the piece apparent. If youknownothingmoreaboutapiecegoingin,itispossibletoimproviseincareful,sophisticated and powerful ways, using your ear to guide your harmonic andmelodicsense.

Atthesametime,ifyoudonotunderstandwhatthetimeofapiece,itiseasytogetlostinthefray(whetheryouareplayingacomposedpieceorimprovising).Understandingtimeisofparamountimportance.

TimeDivisionsInmusictheory,timeisdividedmathematicallyaccordingtosimpleratios.Thisistrueoftimesignatures,aswewillsee,anditistrueofthewaythatnotesorbeatsaredividedingeneral.Wesaythatanynote,heldforsomeamountoftime,hasaparticularvalue,andthatvalueisexpressednumerically.Sothisnotevalueissimplyaspaceoftimeinmusicwithaparticularlength.

Inmusic,therearenoteswiththefollowingvalues:

Wholenote(anoteheldforthelengthofastandardbarincommontime–moreonthissoon)Halfnote(heldforhalfaslongasawholenote)Quarternote(heldforaquarterofawholenote,orhalfofthehalfnote)

Eighthnote(an8thofawholenote,orhalfofthequarternote)

Sixteenthnote(a16thofawholenote,orhalfofthe8thnote).

These are themost common note values. There are also notes that are longerthanwholenotes(butrarelyused):

Doublewholenotes(heldforthelengthoftwobarsincommontime)Longa(anoteheldforthelengthoffourbarsincommontime)Maxima(anoteheldforatotallengthofeightbarsincommontime)

Andtherearenotesthatareshorterthan16ths.Thoseare:

32ndnote(anotewiththevalueequaltothehalfofthe16thnote)

64thnote(halfof32nd)

128thnote(halfof64th)

256thnote(halfof128th)

Itisnotverycommontoencounternotessuchaslongaormaxima,ornotesanyshorter than 16ths or 32nds except for sometimes in compositions played at aslowertempobutwithveryfastruns.

At any point in amusical piece it is possible to play lots of notes (16th’s and32nd’s) that sound really fast while still keeping time and retaining the slowtempoofthepiece(60bpmorless).Itisalsopossibletoplayonlyafewnotes

(wholeandhalfnotesforexample)eventhoughthetempoofthetuneisreallyfast(120+bpm).Inbothcasesthetempogivestheoverallsubjectivefeelforthespeedofthetune.

Inaddition tobasicdivisions,anyof thesenotescanbecomeadottednote (anotewithasimpledot‘.’nexttoit),whichindicatethatthelengthofthenoteis1.5timesthenormallength.Forexample:

Dottedwholenoteisonewholenote+onehalfnotes(orthreehalfnotes)Dottedhalfnoteisonehalfnote+onequarternote(orthreequarternotes).Dottedquarternoteisonequarternote+oneeightnote(orthreeeightnotes).

Dottedeightnoteisoneeightnote+onesixteenthnote(orthree16ths).

Dottedsixteenthnoteisonesixteenthnote+one32ndnote,etc.

Therearealson-tuplets,suchastripletsandpentuplets(orquintuplets),inwhichsomenumberofnotesarefitevenlyintoagivenamountoftime.8thnotetriplets,forinstance,fit3noteswherethereareusuallytwo8thnotes(we’llgettotheminabit).

TimeSignaturesExplainedTimesignature,alsocalledametreormeter,describesthestructureofabarofmusic. It tellsus thenumberof thebeats inabar,and thenotevaluesofeachbeat.Inadditiontothetempoofapiece,thetimesignaturetellsamusicianmoreorlesswhatthemusicwillfeellikerhythmically,whichisveryimportant.

Timesignaturesareexpressed,aswehavealreadyseen,intermsofratios,andtheyareconnected to thenotedivision ratios thatwehavealreadyseen.Timesignature is always located at the beginningof themusical staff for amusicalpiece.Itiswrittenastwonumbers,onebeneaththeother.

Themostcommontimesignatureinmusictodayis:4/4(alsocalled:Commontime).

Thefirstnoteinthisratio(topnoteifyou’relookingatthemusicalstaff)tellsusthenumberofdividednotesinabar,anditcanbeanynumber(note:thisdoes

not tell youhowmanynoteswill actuallybe in themeasure,onlyhowmanynotesofaparticularlengthwouldfitinthemeasure).Soin4/4timethefirst4meansthattherearefourbeats/notesinonebar.

The second note (bottom note if you’re looking at the staff) tells us the notevalueofthosedividednotes.Thissecondnote,whichcanonlybe2,4,8,16,andsoon, tells theperformerthe“feel”or thepulseof thesong(is itpulsedin8thnotesor inquarternotes?),andalongwith the firstnumber tells theperformerhowlongeachbariswithrespecttothatpulse.

In4/4,thesecond4tellsusthatwe’redealingwithquarternotes.

4/4TimeInessence,4/4timetellsusthattherearefourquarternotesinonebar.Hereitisrepresentedvisually:

Figure16:Inthistimethebeatshaveavalueofonequarternote

Wecanalsosubdividethosebeatsintoeightnotes:

Figure17:Herethebeatsarestillquarternotes—we’rejustsub-dividingthembyplayingtheand’sinbetween

‘and’or‘+’ ishowwepronouncetheoff-beats—whicharenotesin-betweentheregularmainbeats.

Andintosixteenthnotes:

Figure18:Sixteenthnotesin4/4

Wehavenowsubdividedthebeatintofournotesperbeat,orsixteennotesperonebar,in4/4time.

‘e’ ishowwepronouncetheoff-beatbetweenthemainbeatandthefollowing‘and’.

‘a’ishowwepronouncetheoff-beatbetweenthe‘and’andthefollowingmainbeat.

Sowereadlikethis:oneeeandahtwoeeandahthreeeeandahfoureeandah,(newbarstarts)oneeeandahtwoeeandah,andsoon.

Toput this intopracticeandgetasenseof it,here’saverybasicexerciseyoucando.Itstartsverysimplebutitcangetascomplexasyouwant.

You’llneedametronomefor this.Thereare freedigitalappversionsonline ifyoudon’thaveaphysicalone.First,chooseaspeedonthemetronome,let’ssay60bpm,andthenplaythisexerciseataneventempoalongwiththemetronomeclick (which represents the beat). You can simply clap your hands at first ormake any percussive sound, or if you prefer you can play a single note or achordonyourinstrument.

Ifpossible,useametronomethathas‘accent’feature.Theaccentwill indicatethe start of eachbarwith adifferent ‘click’ sound.Thiswillmake it easier tounderstandbars.Metronomeclickistheretohelpyounoticewheneveryoufallof thebeat.Youneed tomake sure that you’replayingon thebeat and reallylockinwiththemetronome.Themainbenefitofthefollowingpracticeisthatit

helpsyoutounderstandhowbeatisdivided,andyoulearnhowtofeelthepulseandinternalizetime.

(I)First,here’swhatyou’regoingtoplay:

1. Wholenotes—claponceonthefirstbeatofeachbar.Dothisforupto4bars.2. Halfnotes—twoclapsperbar,oneonbeat1andthesecondonbeat33. Quarter notes — four claps per bar, one on every single beat (playing quarter

notes).Seefig16.4. Eightnotes—eightclapsperbar,oneoneverybeatplusonthe“and’s”whichare

in-betweennotes.Seefig17.5. Sixteenthnotes— sixteen claps per bar, which means four claps per every beat

(playingsixteenthnotes).Seefig18.

Playeachofthenotesforupto4bars.‘

(II) After you’ve played all notes you can alternate between them bymakinglarger jumps.Forexample, inonebaryoucanplayhalfnotes,and in thenextimmediatelyswitchtosixteenthnotes,andgobackandforth.Practiceregularlyswitching between whole notes, half notes, quarter notes, eight notes andsixteenthnotes, inanycombinationandatvarious tempos(especially theslowones,<60BPM,as they’re thehardestbut themostbeneficial toyour timing),and make sure that you keep the time by playing on the beat. That’s whymetronomeistheretokeepyouincheck.

(III)Afteryougetcomfortablewiththis,insteadofplayingintwoormorebars,youcannowtrytocombineeverythinginasinglebar.Thisiswherecommonrhythmicpatternsstarttoemerge.

Hereareafewexamples:

1. Playaquarternote (oneclaponbeat1), then twoeightnotes (twoclaps–oneonbeat2andthesecondonthe‘and’after thebeat2),foursixteenthnotes(4claps–oneonbeat3,secondon‘e’,thirdon‘and’,fourthon‘a’,andfinallytwoeightnotesonbeat4.

12and3eanda4and…andrepeatforfourbars.2. Halfnote(beat1and2),eightnote(beat3),quarternote(beat4).

1(2)3and4…andrepeatforupto4bars

(IV)Createatleasttwoofyourownrhythmpatternsbycombiningthenotesinthesameway.

(V)Nowyoucan start combiningentirepatternsacross severalbars.Playoneexercisedpatterninonebar,andinthesecondbarswitchtoanotherpattern.Playatleastfourdifferentpatternsin4bars.

This is only the beginning. There aremanymore ways to combine the noteswhich is done by: skipping the beats and playing on the off-beats (calledsyncopation),utilizingdottednotes, rests, triplets andothern-tuplets (moreonthissoon),polyrhythmsandpolymeters. In thiswayyoucanplayprettymuchanythingrhythmically.

We can also derive a few foundational rhythmic structures (some of whichyou’ve already learned) which are like the pieces of a puzzle. When youcombine these pieces you can create virtually any rhythmic pattern that youwant.Onceyoulearntheseunitsyouwillbeabletohearandrecognizepatternswithnoeffort,aswellasimproviseandcreatenewpatternseasilyonthespot.Youwilllearnaboutthissoon.

Beforethat,let’sseewhathappensin6/8time.

6/8Time6/8isanotherverypopulartimesignature.Ittellstheperformerthatthereare6eightnotes inonebar,or sixbeatspermeasure.Unlike4/4which is a simpletime,thisisacompoundtime(moreonthisinthenextsection).

Figure20:Inthistimeabeathasavalueofoneeightnote

Thistimesignaturehasnowdefinedthebarinadifferentway.Nowthereare6beats (6evenlyspacedmetronomeclicks inonebar),orsixeightnotes inonebar.Inotherwords,onebeatisnowaneightnoteandtherearesixoftheminabar.Thisgivesusthesenseofthelengthofonebarandtheoverallfeelofthepulse–it’spulsedin8thnotes.

HowtoCountin6/8Becauseofthedifferentbeatvalue,thenotesarenowcountedinadifferentway.

Eightnote—hasavalueofonebeatanditisthebasicunitforcounting:

123456,123456,123456,123456,etc.(onetwothreefourfivesix…)

If you play a note (or tap) on all six beats in ameasure, you’re playing eightnotes.Asyoutry thisyoucancount(sayout loud)eachof thebeats.Youcanalsoaccentbeat1 ineachmeasure togetabetterfeelwhere thebarstartsandends.

Dotted quarter note –We know that this note equals three 8th notes. Sincenotesin6/8aregroupedintwogroupsofthreeeightnotes,youcancountthemeasilywithdottedquarternotes.

123456,123456,123456,123456,etc.(onetwothreefourfivesix…)

Thismeansplayingonlyonbeats1and4asyoucountallthebeats.Soitwouldbesomethinglike:Taptwothreetapfivesix,Taptwothreetapfivesix,etc.

Dottedhalfnote–thisnotehasavalueofthreequarternotes,whichissixeightnotes,andthatfillsupourbarin6/8.Inotherwords,adottedhalfnotenowfillsupthewholebar.

123456,123456,123456,123456.etc.(onetwothreefourfivesix…)

Youcanpracticeitbycountingeachbeatbutplayingonlyonbeat1ofeachbar.

Sixteenthnotes in6/8 –On theother (shorter thanonebeat—spectrum,weknowthatoneeightcanbedividedinto2sixteenthnotes.Sohaving16thnotesin6/8simplymeansaddingtheandsbetweeneachofthebeats.

1and2and3and4and5and6and,etc.(oneandtwoandthreeandfourandfiveandsixand…)

32ndnotesin6/8–todivideevenfurtherissimple.Wejustadd‘e’and‘a’likewiththe16thnotesin4/4.

1eanda2eanda3eanda4eanda5eanda6eanda

Simple,CompoundandComplexTimeSignaturesThereare3mostcommontypesoftimesignatures:

1. Simple2. Compound3. Complex.

Simpletimeisthenamegiventomusicaltimethatisdivisiblebyunitsof2.Inother words, any time you are tempted to count “one two one two” you aredealingwithsimpletime.Thisincludestimesignaturessuchas4/4and2/4.

Forexample,takea4/4measure.Themeasurehas4beats,andtheyaredividedintotwogroups—eachwithastrongbeatandaweakbeat.

So the measure contains, in order, the following beats: strong, weak, strong,weak.

Whenwecountthemeasure,andclapourhandstoit,weclaporputanaccentonthestrongbeats,andsothemeasureasawholeisdividedintotwoparts.Thatmakes4/4anexampleofsimpletime.

Compound time is the name given to music time that is divisible by 3.Wheneveryoucounttoapiece“onetwothreeonetwothree”youarecountingtocompoundtime.Thisincludestimesignaturessuchas3/4and9/8.

Take for example 3/4 time. In 3/4, there are three beats in one measure —Strong,weak,weak.

Whenwecountit,wecountitin3,likeawaltz—1,2,3;1,2,3.Thismakes3/4anexampleofacompoundtime.

This also includes 6/8 time,whichwe’ve already looked at.Both 6/8 and 3/4time are very similar. Themain difference is that in 6/8 you are playing twogroupsof triplets,making it closer to 2/4 (where there are twoquarter notes).Therewillalsobeadifferenceinstrongandweakbeats.

In6/8thereare6beats:Strong,weak,weak,strong,weak,weak.

Unlike3/4,in6/8measurethesecondstrongbeat(underscored)youcansayis‘lessstrong’thanthefirststrongbeat.

Inthissense,3/4iscloserto9/8,whichhas9beatsinonemeasure(threegroupsof three) with the first beat being the strongest: Strong, weak, weak, strong,weak,weak,strong,weak,weak.

Complextime is, simply,any timenotdivisibleby2or3.This includes timesignaturessuchas5/4,7/4or7/8.

Take,asanexample,5/4.Thistimesignatureisoftenviewedas:Strong,weak,weak, strong,weak.Thisway it is divided into twoparts:Strong,weak,weak(3/4),andstrong,weak(2/4).

3/4+2/4equals5/4,whichiswhythisisacomplextimesignature—itconsistsof 2 parts (two time signatures), that are unequal, and themeasure is countedfirst asagroupof3and thenasagroupof2.The firstnumber—5, isneitherdivisibleby3nor2.

In 7/8, there are seven eight notes usually subdivided into three parts:Strong,weak,weak, strong,weak, strong,weak.Again, this is a complex time simplybecause it consists of 3 time signatures (can you tell which ones?) that areunequal,andthefirstnumber(7)isnotdivisibleby3nor2.

Musicians use different time signatures in all sorts of songs. Pop music isgenerallyin3,4,or6.Jazzplayers,classicalcomposers,andmathrockplayersuse most all of them at different times. Time signatures essentially, are justdifferent ways that music arranges itself according to what is called for —sometimesyouplayanascending triad,sometimesdescending;sometimesyouplayin4,sometimesin7.

Tripletsandn-TupletsTuplets are a way of altering the way, temporarily, that a series of notes iscounted.Theyareanotherwayofsubdividingthebeat.

Thesimplesttupletisatriplet,inwhichthreenotesareplayedduringthetimeitwould normally take to play two such notes. For instance, three quarter notetriplets (themost common tuplets) are equal in length/value to one half note.Theytakeup2beatswhilenormallytwoquarternoteswouldtakeup2beats.

3halfnotetriplets=4quarternotes(oronewholenote)

3quarternotetriplets=2quarternotes(oronehalfnote)

3eightnotetriplets=1quarternote

3sixteennotetriplets=1/2quarternote(oroneeightnote)

332ndnotetriplets=?

I’llletyoufigureoutthelastone.

Rememberthatonequarternoteisonebeatin4/4?InthisCommontime,one8thnotetripletis33.3333…%ofonebeat,sothreeofthoseareequaltoonequarternote; and the same goes triplet note rests. The notes in tuplets are dispersedevenly over the interval in question, effectively creating a temporarypolyrhythm.

Themost common tuplets are 3-tuplets or triplets, but there are also 5-tuplets(quintuplets), 6-tuplets (sextuplets), 7-tuplets (septuplets), 8-tuplets (octuplets),9-tuplets (nonuplets), etc.These tuplets areusuallyharder toplayandare lessusedmainlyduetotheiroddness.

PolyrhythmsandPolymetersItispossibletocreatewildlycomplicatedtimesignatures,andsinceacomposerorimprovisorcanmovebetweentimesignatures(usingoneforsomenumberofbars and then changing it to something else) it is possible to create difficult,sophisticatedrhythmiclattices(asin“mathrock,”somemetal,andsomejazz).

Itisalsoworthnotingthatdifferenttimesignaturescanbestackedontopofoneanother.Whenthisisdone,eitherapolyrhythmorpolymeter—somewhatofanadvancedconcept—results.

Polyrhythmsaretwobarsofthesamelengthbeingplayedatthesametime,thathavedifferenttimesignatures(forinstance,abarof3/4andabarof7/4,whichtakeupthesameamountoftime).

Polymetersworkbycombiningtwodifferent timesignaturessothat thelengthof each pulse is the same (resulting in bars of different lengths that can cycleagainsteachotherinandoutofphase).

Bothofthesethingsareusedinmodernmetalandmathrock,inmodernjazz,incontemporaryclassicalmusic,andinavant-gardeimprovisation.

Accents,Syncopations,Dynamics,TempoChanges…Onceyouknowaboutthetimeofapiece,youneedtoknowhowtoplaywithit.It isn’t possible, not often, tomake something interesting happen if all you’redoing is playing the exact pulse of the music. Sometimes some notes areintentionally missed out and off-beats are played to produce a compellingrhythmicstructure.Thisiswheresyncopationcomesin.

Syncopationmeanssimplyplayinginbetweenthespacesthatthetimesuggests(we’vealreadyseenthisinthepreviousexercise).Playingforlongerorshorter,taking rests, skipping beats, etc. This is the first step toward feeling andexpressingthegrooveofasong(evenifthatsongislooselyorganized).

It is also possible to create n-tuplets, polyrhythms and polymeters on the fly.Thistakesmoreskill,andagreatintuitiveunderstandingoftime,buttheresultsareworththeworkittakestobeabletoexecutethem—anydrummerwilltellyouthat.

Aplayercanadjustthespeedorvolumeofthesong,speedingup,slowingdown(eitherbyfittingmorenotesintothesamespaceorbyadjustingthetempoofthepiece).Thiscanbedonecompositionallyorimprovisationally.

Finally,aperformerorcomposercanusedynamicstoaccentvariouspartsofameasure. This is often done in funk, blues, and jazz to highlight parts of themeasurethatwouldotherwisefadetothebackground.

Bydrawingattentiontodarkpartsofameasure,playerscanexposethegrooveofthesongforallthatitimplies—allofthefalsestartsandhalf-resolutions,the

stutters,thehiccups,ghostnotes,thethingsthatmakeagroovegroove.

BuildingBlocksofRhythm—CreateanyRhythmPatternEasily(WithAudioExamples)Aswe’veseenbynow,themainunitoftimeisabeatandthisbeathasdifferentvalues (or time lengths) definedby the time signature.We’ve also seen that abeatcanbesubdividedindifferentways.Bycombiningthesesubdivisions,itispossibletocreatefundamentalrhythmicunitswhich,whencombined,cancreatevirtuallyanyrhythmicpattern.Withthisarsenalofrhythmsunderyourbeltyouwillbeabletomoreeasilyhear,recognizeandplayallmostcommonrhythmsoutthere.Youwillalsobeabletousetheseblockstocreateyourownrhythmicpatternsandevenimprovisewiththemasyouplay.

For new guitar players a very common issue is playing different strummingpatterns.Thosestrummingpatternsare just rhythmpatterns thatcanbebrokendown into individual “mini-patterns” or blocks of rhythm. In this section youwill see how easy it is to use these blocks to create rhythm patterns (on anyinstrument) and combine them into complicated rhythm structures. It isimportant to familiarize yourself with these fundamental patterns and simplybecomemoreawarewhenyou’reusingwhichinyourplaying.

TohelpyoudothatI’veprovidedaudioexamplesforeachoftheserhythmssoyou can actually hear how they sound and practice along on your instrument.EachpatternisinCommontime,lastsfor4bars,andisplayedonguitarusingapitched note—C4ormiddleC (found on 5th fretG string), at a slow tempoalongwiththemetronome.

Thefollowingexamplesaredividedintothosewithoutsyncopation(easier)andwith syncopation (harder). Therewill also be one exercise at the end of eachsectionwhichwillhelptoputallthisintoperspective.

Lookingatthemostpopularsimpletime–4/4,onebeatisonequarternote,andthereareeightbasicwaystocombinesubdivisionsthatamounttothelengthof

onebeat.We’llstartfromthere.

Note that the following rhythmsare easier towriteusing the traditionalmusicnotation.Thisbookexplainstheorywithoutnotation,butthat’swhyyoucanfindthese examples written in musical notation in my How to Read Music forBeginnersbook(relatedtothisone),whichisallaboutunderstandingthataspectofmusic.

1. Thefirstrhythmunitisasimplequarternote.Inabaritlookslikethis:1234

Playingquarternotesin4/4issimple—it’sjustonetaponeachbeat.Afterhearingthepatterntrytoplayalongwitheach.Here’showthisonesounds:

Quarternotesaudioexample->http://goo.gl/JrVHPW2. Eightnote—onequarternoteisdividedintotwoeightnotes.

1and2and3and4andAsweknowbynow,eightnotesaresimplyplayingonthebeatsaswellasonthe‘ands’inbetween.

8thnotesaudioexample->http://goo.gl/cTd87u

3. 16thnotes–onequarternoteissubdividedinto4sixteenthnotes:1eanda2eanda3eanda4eanda

Nowweintroducee’sanda’s tosubdivide thebeat intofour.Note that1,2,3,4are themainbeats(theonesplayedalongwiththemetronomeclick)andanythinginbetweenisconsideredanoff-beat.

16thnotesaudioexample->http://goo.gl/5LLCSC

4. 8thandtwo16thsThisiswherethingsstarttogetmoreinteresting.Wecanmixsixteenthandeightnotestofilloutonebeat.

Inabarthispatterniscountedinafollowingway:

1(e)anda2(e)anda3(e)anda4(e)anda()–wheneversomethingisinparenthesislikethisitsimplymeansthatitisnotplayedon, if you’re tappingorclapping;or thenoteplayedbefore is still sounding, if you’replayingapitchednote.Likewise,ifanyoftheelementsareboldeditmeansthattheyareplayed.

Sonowweplayaneightnotewhichisthenfollowedbytwo16thnotes(anda).

8th–16th–16thaudioexample->http://goo.gl/R235EB

5. Two16thsandone8thTheoppositeofthepreviousone,wenowhave:

1eand(a)2eand(a)3eand(a)4eand(a)Here,twosixteenths(1e)areimmediatelyfollowedbyaneightnote(and).

16th–16th–8thaudioexample->http://goo.gl/wTXXuD

6. 16th,8thanda16thMaybealittlemoredifficulttograspthantheprevioustwo,thispatterniscountedlikethis:

1e(and)a2e(and)a3e(and)a4e(and)a

A16th(1)isimmediatelyfollowedbyan8thnote(e)andthenwehaveanother16thnoteattheend(a).

16th–8th–16thaudioexample->http://goo.gl/UNQiyh

7. Dotted8thanda16th

Wearenowaddingdottednotesintothemix.Dotted8thnote,ifyouremember,isequaltothree16thnotes,soittakesup75%ofthebeat,andthenwehavea16thnotewhichis25%percentofthebeat(in4/4).

1(e)(and)a2(e)(and)a3(e)(and)a4(e)(and)a

A dotted 8th note (1) is followed by a 16th at the end (a). Both ‘e’ and ‘and’ are inparenthesissotheyarenotplayedonbecauseofthedotted8thatthebeginning.

8th.–16thaudioexample->http://goo.gl/1EJMRz

8. 16thandadotted8thSameasthepreviousone,onlyinreverse:

1e(and)(a)2e(and)(a)3e(and)(a)4e(and)(a)

Here,a16th (1) is immediately followedbyadotted8th (e)whichcovers theoff-beats‘and’and‘a’.

16th–8th.audioexample->http://goo.gl/TjsnsW9. EightnotetripletsBesidesubdividingthebeatintotwo8thnotes,orfour16thnotes,wecanalsosubdivideitintothreeevenlyspacedout8thnotetriplets(onetakingup33.3333…%ofthebeat).Wecountthemlikethis:

1ea2ea3ea4eaor

1triplet2triplet3triplet4triplet

This pattern will be more difficult to get used to but is very well worth the effort –practicingswitchingbetween regular subdivisions in2or4andsubdivisions in3, inabar,willdowondersforyoursenseoftiming.Here’showeightnotetripletssound:

8thnotetripletsaudioexample->http://goo.gl/hgKKPg

4-BarRandomSequenceExercise1Here is a random sequence of the patterns shown so far combined together randomlyacross4bars.

4-BarSequenceExercise1audioexample->http://goo.gl/dLoj3sYourchallengenowistolistentothissequenceandworkoutwhichrhythmpatterns(1-9)havebeenusedineachofthebars,inorder.Thisisagreatexercisetodevelopyourear and the ability to hear, recognize and reproduce rhythmic patterns. The correctanswerwillbeprovidedattheendofthisbookintheCheatSheetsection.Usethatonlyforcomparingyouranswers.

Next,takeanyofthepatternsshownandcombinetheminanywaythatyouwish.Yourtaskistosimplyplaywiththepatternsandcomeupwithyourown4-barsequencethatyoulike.

AddingSyncopationGoing one step further, we will now add syncopation, which is denoted by rests. Byincorporatingrestsintopreviousrhythmicblockswegetmorefundamentalrhythmunits.Restsinmusicarespacesoftimeduringwhichthereisanabsolutesilence–nonoteoranypercussivesoundisbeingheard.Thereisarestequivalentforallofthenotesshownsofar:wholenoterest,halfnoterest,quarternoterest,etc.(wetalkmoreaboutrestsinmyHowtoReadMusicforBeginnersbook).

Theseexamplesarealittlebittrickiertoplayandmastermainlybecausewemaynotbeused to playing or accenting off-beats, but with some practice and patience they willpresentnoproblem.

10. Syncopated8thnotesHerewehaveaneightnoterestfollowedbyaneightnote.Itcanbecountedlikethis:

|1|and|2|and|3|and|4|and||—thesebracketsservetoshowarested(notplayed)note.Onamusicsheetitwouldbeshownasan8thnoterest.Ifwe’reclappingortappingeverythingthenyoutreatthese

bracketsastheregularbrackets:();butifyou’resingingorplayingapitchednotefortheseexamples,thenthesespacesoftimearesilent.

You’llnoticethatthisisacommonreggaerhythm.Here’showitsounds:

Syncopated8thsaudioexample->http://goo.gl/yr7aqe

11. Syncopated16thnotesNowwehavea16thnoterestfollowedbythree16thnotes:

|1|eanda|2|eanda|3|eanda|4|eandaAs with the previous pattern all of the strong beats (1 2 3 4), which fall on themetronomeclick,areskipped.Thetrickistofeelthisbeatinternally,andthenplaytheoff-beats(eanda).

Syncopated16thnotesaudioexample->http://goo.gl/xFDo8m

12. 8thnoterestandtwo16thsThispatternissortofacombinationoftheprevioustwopatterns.Itiscountedlikethis:

|1||e|anda|2||e|anda|3||e|anda|4||e|anda

8thnoterest(50%ofthebeat)isfollowedbytwo16thnotes(another50%).

8thnoterest–16thnote–16thnoteaudioexample->http://goo.gl/Gyt2Hx

13. 16thnoterest,16thnote,andan8thnoteTheoppositeofthepreviouspattern.Itiscountedlikethis:

|1|eand(a)|2|eand(a)|3|eand(a)|4|eand(a)Beat1isskipped(notheardorplayed),youplay‘e’and‘and’.The‘and’isaneightnotesoitisheldforthedurationof(a)ifyou’replayingapitchednote.Ifyou’reclappingortappingallthis,then(a)istreatedthesamewayas|1|—it’snotplayed.

16thnoterest–16thnote–8thnoteaudioexample->http://goo.gl/si5qG2

14. 16thnoterest,eightanda16thnoteAlittlebittrickierthanthepreviousones.Wehavea16thnoterest(25%)followedbyan8thnote(50%)anda16thnote(25%).Itiscountedlikethis:

|1|e(and)a|2|e(and)a|3|e(and)a|4|e(and)a‘e’isaneightnotehereandifyou’replayingapitchednoteitneedstolastuntil‘a’.

16thnoterest–8thnote–16thnoteaudioexample->http://goo.gl/5FeUXG

15. Dotted8thnoterestanda16thnoteNowwehaveadotted8thnoterestanda16thnote.Sowe’rejustplayingonthelastoff-beat‘a’.Itiscountedlikethis:

|1||e||and|a|2||e||and|a|3||e||and|a|4||e||and|a

8thnoterest.–16thnoteaudioexample->http://goo.gl/owmMgr

16. 16thnoterestandadotted8th

The opposite of the previous one. Now a 16th rest is followed by a dotted 8th. It iscountedlikethis:

|1|e(and)(a)|2|e(and)(a)|3|e(and)(a)|4|e(and)(a)Inthisbarthe‘e’noteisheldfor75%ofthebarwhile1,2,3and4arenotplayedorheardatall.Ifyou’replayinganotewithapitchon‘e’thenthisnote(sinceitisadottedeightnote)isheldforthedurationof‘and’and‘a’.

16thnoterest–8thnote.audioexample->http://goo.gl/VfXfA4

17. Syncopated8thnotetriplets

Herewehave8thnotetripletsbutwithan8thnotetripletrestonthemainbeats(1234).Itiscountedlikethis:

|1|triplet|2|triplet|3|triplet|4|triplet

Notethat likean8thnotetriplet,one8thnotetripletrestisalso33,3333…%ofthe beat. In music notation and on the staff 8th note triplet rest has the samesymbolastheregular8thnoterestbutitiscontainedwithinthebracketsdenotingtriplets.

Alsonoticethesubtledifferencebetweenthispattern,andpattern12and13,andhowbeat subdivisionsare spacedoutdifferently.Thisone soundsmore likeawaltz:

Syncopated8thnotetripletsaudioexample->http://goo.gl/1RWGze

4-BarRandomSequenceExercise2Here’sanotherrandomsequenceofrhythms(ormini-patterns)shownsofar,thistime including syncopation.Aswith theExercise 1, your task is to listen andfigure outwhich rhythms are used in all 4 bars.Again, therewill the correctanswerundertheCheatSheetsection.

4-BarSequenceExercise2audioexample->http://goo.gl/3KwQ24

NotethatbothExercise1andExercise2sequencesarenotmeanttobesuper-precise, andwhat’smore, they’recompletely random,hencenotverymusical.Thisisdoneintentionallytomakeitlessobviousandmoredifficult,andtoshowhow you can recognize patterns and extract them from a random sequence of

notes. This will greatly helpwith transcribing rhythm (figuring it out by ear)fromsongsandothermusicalcompositions.

Afterfiguringthisout,yourtaskistocomeupwithyourown4-barsequenceofpatterns thatyoulike,but this timeincludeanyof thesyncopatedpatternsyoulearned.

You can now hopefully see how combining all these beat subdivisions is notdifficult,anditgivesgreatpossibilitiesforwhatyoucanexpressrhythmically.All thesepatternsare fundamentalandareusedmoreor lessoften inpractice,howevertheyarenotexhaustive–youcanderivemoremini-patternsusingthesubdivisions you learned like combining pieces of a puzzle. As an extrachallengeyoucantrytocomeupwithyourownrhythmblocks.

Part5

MoreWaysofCreatingMovementinMusic

Timbre/ToneAcomposerorperformercanusenoteselectiontobuildandreleasetension,tocreate movement. They can also use, as we have seen, note duration — bymanipulatingtime,theyareabletoachieveallmannerofcomplications.Thereare, however, other ways ofmoving throughmusical space, other axes, othertools,othervehicles.Oneoftheseistimbreortonecolor.

Timbreandtonerefernottothepitchofasound,andnottoitsvolume,buttowhat thesoundsoundslike.Theyarethecharacteror theformofasound, thecolororqualityofasound.

Thoughtheyareoftenusedinterchangeably,“timbre”and“tone”aresometimesusedtorefertodifferentfeaturesofasoundscolor.

Inthesecases,thetimbreofasoundisindexedtowhateverinstrumentthesoundisproducedwith—aviolin’sAnoteisdifferentfromasaxophone’sA,andthedifferencebetweenthosetwosoundsisthetimbre.

Thetone,ontheotherhand,isthespecifictonalqualityofthesoundcomingoutofthatinstrument,affectedbythecompositionoftheinstrument,thetechnique,theamplificationandanyeffectsused.

In general, the timbre or the tone of a sound (and herewe are imagining thatthosetwothingsarethesame)isoneofthewaysacomposerorperformercancontrolthewayapieceofmusicfeels.Tensionisbuiltandreleasedbywayoftimbrejustasmuchasbywayofpitchorduration.

DynamicsDynamics refer to the volume of a sound, as well as to how that volume isexpressed(doesitcomeonquickly,doesitlinger,etc.).

The dynamic movement in a piece of music— getting louder getting softer,increasingordecreasingthesustain,attackordecayofthetonesinthatpiece—contribute to the overall sense of drama and tension, the propagate musicalmovement,injustasprofoundawayasthetimbre,thedurationandthepitchofthesoundsdo.

Playingwithdynamicsandphrasing(thephysicalwayinwhichamusiclineisphrased/played)isintrinsicallyrelatedtowhatmanycall“playingwiththefeel”.

ConsonanceandDissonanceItisonethingtoknowhowtomakemusicsoundgood—soundnice,pleasing,easytolistento.It isonethingtobeabletoplayconsonantmusic(musicthatsoundslikeresolution,thattendstowardreducedtension),butitisanothertobeabletotrulycreatemovementinapiece.

Realmovementrequiresthat,moreoftenthannot,dissonantsoundsaremade—that is, sounds that tend towards tension, sounds that are difficult, surprising,evenharsh.

Makinguseofharmonicandmelodicideasthatpromotedissonance,playingontherhythmofasongandusingsyncopationinunexpectedways,usingtimbre,toneanddynamicstocreatetension...Theseareallwaysofhelpingtoproducemovementinmusic.

Drama

Musicisalanguage,andapieceofmusicisanarrative.Thereischange,risingandfallingaction.Thereareclimaxes.Thereisdevelopment.Thereareperiodsoftensionandperiodsofrelease.Thereisdrama.

Itisnecessarytouseallofthetoolsatyourdisposaltocreatewhateverkindofdrama you are trying to create. It is possible to remainmostly at the level ofharmony and melody, creating movement with note selection, moving andchanging harmonicmaterial, even perhaps abandoning harmonic structures alltogether(asinsomefreeimprovisationandmodernclassicalmusic).

Butit isalsopossibletousetime,tone, timbreanddynamicstotellastory, tomoveanaudiencebymovingthesound—pushingair,pushingwaves,pushingfeelings...Moving,changing,dramatizing.

ExtendedTechniquesIt is worthmentioning, briefly, that there are ways of creating drama that gobeyondtraditionaltechniques.Itisalwayspossibletoplayyourinstrument(ortocomposeforaninstrument)inwaysthatarenon-standard,thatwereneverinthebeginningintendedforthatinstrument.

A saxophone player can play artificially high or can produce rich harmonics,they can over-blow, they can breathe and whisper, they can speak or yell. Aguitarist can use a bow, can play muted notes or harmonics, can scrape thestrings (even using a tremolo bar is a kind of extended technique), can playdrumsonguitar(checkoutsomeTommyEmmanueldrumsolos)orguitarlikepiano.Apianoplayercaninsertobjectsintotheirstrings,changingthetimbreoftheirinstrument.Therearealwayspossibilities.

In some forms of music, most notably avant-garde, experimental, and “free”music, extended techniques are used to manipulate the story that a piece ofmusic tells.But someof these techniques, such as (on the guitar) tremolo baruse,effectuse,andartificialharmonicsaredeeplyapartofmainstreammusic,and whatever the music or the instrument you play, understanding extendedtechniquesmeanshavingonemorewayoftellingastory.

Part6

PuttingMusicalStructuresTogether

Thefirststeptowardbuildingtheoreticalmasteryinmusicislearningyourwayaround the ground floor—understanding the fundamental elements ofmusic,the theoretical structures that we work with in music theory, and how thosestructureswork together insomebasicways.This,however, isonlyenoughtogetyoutounderstandwhatmusic ismadeof,andnot inanysensehowmusicworks.Understandingmusic ismore— infinitelymore— thanunderstandingthediscreteelements thatmakeitup.Music isamoving, living,pulsingbody,andjustlikeourbodiesitssystemsareirreducibletoanysetofsimpleelements.

The end game ismore than understanding— it ismastery—and that comesfrom being able to manipulate musical structures, putting them to work andmakingthemworkforyouinwhateverwayyouwouldlike.That,however,isalongwayoffformostpeoplewhoarelearningmusictheoryforthefirsttime.Abasicintroductionisneededfirst,whichmoreorlesscontainstwoparts:

1. A rundown of the foundational elements of music theory, its basic structures(covereduptothispoint);

2. Away to put those structures together in order to gain a greater understanding ofwhatishappeningintheactual,materialactofmusic-making.

That second task is what this section is about: letting you in on some of thesecrets ofmusical systems; showingyouhowmusical elements and structuresmakesensetogether;andgettingyoureadyforthenextstep,whichisabroaderperspective — a more advanced conversation about how to manipulatetheoreticalstructuresinyourownplayingandwriting.Thepointofthissectionis not to get you the whole way there, only to get you moving in the rightdirection.

Tothatend,wewilldiscuss,first,abroaddistinctionbetweenimprovisationandcomposition(withaneyetowardthinkingabouthowimprovisersandcomposers

usemusic theory), second, a general taxonomyofmusic theory (or at least ofharmonyasitisunderstoodtheoretically),andthird,asetofmusicalideasandstructuresthatareindispensableinyourjourneytowardtheoreticalmastery.

WhatisaComposition?Wepracticingmusicianstakeforgrantedsomanytheoreticalobjects,andnoneperhapsmore than thisone—composition.Weassume thatweknowwhat itmeanstocomposesomething,andthatwhatwethinkofascompositioniswhateveryoneelsethinksofascomposition.Wethinkthereisaneasyanswertothequestion“Whatisacomposer?”andthatweknowjusthowcomposersmakeuseofmusictheory.

It’sworthbeginningwithsomethingsimple.Whatiscomposition?Whatdoesitmeantobeacomposer?Atfirstglance,itlookslikeit’sjustamatterofwillfulcreation:tocomposeistocreateintentionally.Andso,composingmusic(beingacomposer)isjustamatterofbeingsomeonewhointentionallycreatessound.That,however,doesn’treallycoverit.

First, there is non-compositionalmusic (such as improvisation),which is also,presumably created intentionally. And second, there is sound that is createdintentionally—suchashonkingacarhorn—thatwewouldnevercallmusic.So there has to be two things added to what we have already said: 1. thatcomposerswrite things that aremeant to be repeated,more or less exactly astheyarewritten;and2.thatcompositionsaremorethanmeresound.

Thefirstofthesethingsissimpleenough—compositionsarerepeatable—andatleastatfirstblushthisiswhatseparatescomposersfromimprovisers.Butthesecondthing—thatcomposedmusicismorethanmeresound—isalittlemorecomplicated.

Andhereiswheremusictheoryenters.Music,itissaid,isnotsimplysound,butorganizedsound.Andwhilethisdefinitionisinsomecasestoosimpletobetrue,itserveshereasageneralguide.Whenwetalkabouttheorganizationofsoundinamusical sense,whatweare talkingabout is theoretical structures—mostbasically, harmony, melody, and rhythm. These are the things that musicianscreate, and are not simply sounds. We create organizations and structural

arrangements of sounds that are consonant or dissonant, that follow somemelodicorder(howevercomplex)andthatoccurintime(mostoftenofaregularpulse).

So this is what composers do — intentionally create repeatable musicalstructures.Andthosestructurescanbediscussed,analyzed,andevengeneratedbymusictheory.

ImprovisationasInstantaneousCompositionIfcompositionistheintentionalcreationofrepeatablemusicalstructures,thenitshouldbeeasyenoughtoknowhowtothinkaboutimprovisation.Itshouldbethesamething,onlynow,ratherthanbeingrepeatable,itismeanttobeplayedonlyonce.

Butthisis tooeasy.Surely,wecanimagineacomposerwritingapiecethatisonlymeant to be playedonce; and thiswouldn’t be improvisation.And all ofthis takes forgranted the idea that themusic that improvisers improvise is thesamething,ormoreorlessthesame,asthemusicthatcomposerscompose.

Improvisation, in general, resists the kind of theoretical analysis that wasdesigned for centuries for composition. This isn’t because improvised musicdoesn’t have harmony, melody, and rhythm, but because it uses those thingsdifferentlythancomposition.Thedifferenceisallabouttime.

A composer has time — time to think, time to write, time to arrange andrearrange, edit and re-edit. And this changes the way they work with musictheory.It’slikepaintingaportraitfromapicture,whichwillneverchangeandnevergoaway—composerscanworkandreworktheverysamepartsofapieceuntil what is left is a reflection of, in general, richly complex theoreticalstructures.

But an improviser does not have time. Improvisation is often said to beinstantaneouscomposition,andwhile,aswearesaying,itmaybemisleadingtocall it akindof composition, it certainly is instantaneous.Thismeans that the

wayan improviserworkswith theory isdifferent.Rather thanpainting fromaphoto, theyarepainting fromabriefmemory—aquick image thatpassesbytheirmind. Thismeans that they cannot pause and reflect on theway they’reusingtheory;theysimplyhavetouseit,andthey’vegotonechancetodoso.

Animproviserusedtheoryinshorthandandmnemonicdevices.Whatwemeanby that is that they have memorized various harmonic devices (and othertheoretical structures) and they know just how to use them, apply them, alterthem,andcombinethem.Muchofthetheoreticalworkinimprovisationisdonebehindthescenesandwellbeforehand—intheyearsordecadesofpracticeandstudy.Thismeans that theory for improvisation isn’tquite the sameanimalastheory for composition. It consists of all the same structures, but its use isdifferent.

NoteRelativismArosemaybearosemaybearose,butanoteisnotanote.Notmerely,thatis.

ThereissomuchmoretoanA440thanbeingatonethatsoundsat440hertz.Inmusic,whatmatters farmore than a tone’s absolutepitch is its relativevalue.What thatmeansis thatanAmaybedifferent in thiscasethanin thatcase.Itmay,andlikelywill,servedifferentfunctions.Andthatiswhatmakesanote—itsfunction,notitsdefinition.Noterelativismmeansthatwhatanoteis,whatitreally is, is something that relies on other notes, and that its value is alwaysrelative.

Let’stakeanexample.Let’ssayIamplayinginthekeyofEminor,andIplayanAminorchord.TheAofthatAminorisservingmultiplepurposes:itisthe1noteofthechordIamplaying,whichisaminorchord;itisthebassnoteofthatchord,againstwhichalloftheothernotesIamplayingaredefined;anditisthe4th note in theEminor scale.All of these thingsdefinewhat thatA is at thatparticulartime.

ButnowimaginethatIamplayinginBbmajor,andIamplayingaDm7chord.IamstillplayinganA,onlynowitisdifferent.Itisthe5noteofthechordIamplaying,whichisamin7chord;itisnotthebassnoteofthatchord;anditisthe

seventh note in the Bb major scale. It is entirely different and therefore itsfunctioninthesemusicalstructuresisfundamentallydifferent.

The point is that notes are relative, and that this is the foundational truth ofharmony.Tostudymusictheoryisnottostudyasystemofimmovableobjects,buttostudyasystemthatisalwaysinmovement,thatischangingandbecomingnewateachmoment.That’soneofthethingsthatmakesitsohardtobeamusictheorist — you are trying to capture something that fundamentally wants toeludecapture.

In the process of learning theory, one of the most important things you canrealizeisthatmusicismovingandthatharmonyisrelative.Onceyoubegintosee that notes are different depending on their changing functions, it will beeasiertoputyourselfinthecorrectheadspace.

HowChordsFunctioninaKeyEverykeyhassevenbasicchords(oneforeachnoteinthescale).Eachofthesechords has a function. But for all seven of them, there are only three basicfunctions,onlythreebasicgroups:tonic,dominant,andsubdominant.

Tonicchordsarethemoststableandtheyestablishakey.Theyaretheonesthatchordprogressionsmovetoinordertoreleasetension.Theyarethefirst,third,andsixthdegreesofwhateverscaleisathand.

Dominantchordsarethemosttense,andtheywantstronglytoresolvetosometonic chord. Dominant chords are the farthest, harmonically, away from thetonic,butthatmeansthattheypointbacktowardthetonic,andsotheirfunctionistoleadtheprogressionbacktothekeycenter.Thesearethefifthandseventhdegreesofthescale,andanychordsbuiltonthosedegrees.

Subdominant chords are the chords that establish movement away from thetonicandtowardthedominantbeforethedominantchordswanttoresolvebackto the tonicchords.Tonicchordsestablishakey,whereassubdominantchordsmoveawayfromthatkey.Thesechordsaretense,butnotinthesamewaythatdominantchordsare,andtheytendtomovetowarddominantchords(although

theycanalsoswitchdirectionsandmovebacktowardtonicchords).Thesearethesecondandfourthdegreesofthescale.

Let’stakeanexample,usingthekeyofC.

InCMajor,andchordbuilt from theCmajor,Eminor,orAminor triadsareconsideredtonicchords.Allofthesechordswillestablishthekeycenter.

AnychordsbuiltontheDminororFmajortriadswillmoveawayfromCmajorasatonic.Thesearethesubdominantchords,andtheyarealwaysonthesecondandfourthdegreesofthescale.

Finally, any chords built on theGmajor orB diminished triads are dominantchords. These are always on the fifth and seventh degrees of a scale. Thesechordswillestablishthemosttension,buttheywillalsopointrightbacktotonicchords,sincetheywanttoresolveinthatdirection.

HowNotesFunctioninaChordThenotesofachordfunctioninpredictableways,justlikethechordsofakey.Thebasicstructureofachordatitssimplest,thetriad,isthemoststablepartofthatchord,withthe1and5beingthemostconsonant.Thisiswhyitispossibletoplaynothingbutpowerchords(alsoknownasfifths)andsoundgood.

The3 is a stable note in a chord, but not as stable as the1or 5.The3does,however,servetodeterminewhetherthechordismajororminor.

Thefirstextensionofatriadisa7.Thisisthenextmoststableintervalafterthe3, and it serves aswell to color the chord and determine its family—major,minor,dominant.

The last three extensions — 9, 11, 13 — do not, in general, establish thefoundationofthatchord,nordotheydeterminewhetheritisamajor,minor,ordominantchord.Theyarealsofarlessstablethanthe1,3,5,or7notes(thosefour are called “chord tones” precisely because of their stability). Theseextensions do, however, color the chord in different directions— aminor 6thsoundsquitedifferentthanamajor6th,forinstance.

TypesofHarmonyHarmony is at once the most basic and the most advanced concept in musictheory.Itisthebedstoneofwhatwethinkaboutwhenwetheorize,anditcanbemade to be more complex than most people expect. When we talk aboutharmony,weare talkingabout theway thatnoteshang together,whether theyare consonant or dissonant, andwhat sorts of structures they can be arrangedinto.Weare also talking about all of that atemporally—outsideof time.Forharmony,itdoesn’tmatterhowlongnotesareheld,justthattheyareallhangingtogetherinastructure.

ItcanbesaidthatHarmonycanbeeither:

1. Tonal2. Modal3. Polytonal4. Atonal

Here’sabriefoverviewofeach.

TonalHarmonyMostofthemusicintheWestiswhatiscalled“Tonal”music,andit is intheprovinceoftonalharmony.Tonalmusicismusicthathasatonic,orakeycenter—a note that acts as the center of gravity for the piece or for the part of thepiece you’re talking about. And tonal harmony is how we understand theharmonyoftonalmusic—itmakessenseofchordsandscalesrelativetosomekeycenterortonic.Tonalharmonycanbeeither:chordal,scalarorchromatic.

ChordalChordal music is music whose primary harmonic vehicle is the chord. Weanalyze it by analyzing the way that the chords move and interact with oneanother.Themost basic unit in chordalmusic is the chord, and generally thismeansthatwearetalkingabouttriadsandtheirrelationships.

Scalar

Scalar music is music whose primary harmonic vehicle is the scale. Weunderstand thismusic by analyzing theway that notes and chords are derivedfrom the scales that contain them. Themost basic unit of harmonic in scalarmusicisascaleratherthanachord,thelatterbeingderivedasamemberoftheformer.Thismeansthatgenerallywearetalkingaboutsomescaleormode(orseriesofscalesandmodes)ratherthansomesetoftriads.

ChromaticChromaticmusic is similar in principle to scalarmusic, only the scale that isusedisthe12-tonechromaticscale.Thismeans,intheory,thatthemusicisfreetoleavethespaceoftonalityandmoveintoatonalharmony(seeatonalsectionbelow),butinpracticeitisoftentiedtosomecenterofgravity.

Modalvs.TonalHarmonyTonalmusic,aswehavesaid,ismusicinwhichthereisanotethatactsasthecenterofgravity.Thiscasebechordalorscalar(orchromatic),butinallofthosecases, there is one note that weighs the music down at any one time.Modalmusicisdifferent—ittakesascaleormodeasaplacetobeginandtreatsallofthenotesinthatscaleasthepointsofgravity.Inasense,theentirescaleisthe“key”or“tonic.”

PolytonalityPolytonalharmonycanbeeithertonalormodal.Inpolytonality,morethanonekeycenterisestablishedatagiventime.Thiscanoccurtonally,aswhenmorethan one note is used as a center of gravity, or it can be done with modalharmony, when more than one mode is used at one time. In either case, theresultingharmonyiscomplexandoftenquitedissonant.

AtonalHarmonyInatonalharmony,thereisnokeycenter.Thismusic,popularizedinthewestinthe 20th century by composers such as Arnold Schoenberg and Anton VonWebern, treatsall12 tonesas thoughtheywerecentersofgravity.Privilege is

given to tones, not as they interactwith some key center, but as they interactwithoneanother.Thismusicisoftendifficulttolistento,butsomeofitisquitebeautiful.

QuestionstoPonderNowthatwehavebeguntoassembletheblocksofmusicalstructures,itistimetomove to the next step. It is time tomove toward themanipulationof thosestructures.Thisiswhatadvancedmusictheoryis—awayofthinkingaboutthemanipulationofmusicalstructures.Youalreadyknowthenamesofthings;youalreadyknowthebeginningsofhowtheyfittogether;nowitistimetotakethenextandbiggeststeptowardmasteringthosestructures.Thisisanever-endingprocessandwillcontinuefortherestofyourlife.

Whileyoubeginthisprocess,herearetwothingstothinkabout:whereharmonybegins;andthedepthofthechromaticscale.

BeginningwithaScalevsBeginningwithaChord(attheFoundation).Onequestionthatisworthmullingoveriswhetherharmonybeginswithachordorwith a scale. In tonal harmony,we understandmost everything in terms ofchords and their functions. But in modal harmony it is just the opposite —everythingiscashedoutintermsofscalesandtheirfunctions.Sortingout thistanglewillgetyouthatmuchclosertomastery.

ChromaticScaleasOriginvsChromaticScaleasExtensionThechromaticscalecanbeapowerfultoolifyouallowittobe.Itcanbeseenasthemastersetofallextensions—achordorscaleextendingineverydirectionasfarasitwillgo.Butitcanalsobeseenastheorigin,thescalefromwhichallothersarecut.Thiswayofseeingchromaticismisdecidedlymodal,andmakesallmusic, inasense,chromaticmusic.Again, figuringouthowto thinkaboutthiswillhelpyouasyoumoveforward.

Part7

GoingBeyondtheFoundations

Formanybeginningmusicians,it is thehardestthingintheworldjust towraptheirheadsaroundthefoundationsofmusic theory.Tolearn tounderstand thebuilding blocks of harmony, melody, and rhythm (chords, scales, modes,arpeggios,rhythmicfigures,melodicpatterns,etc.)andtolearntomakesenseofa sheet ofmusic— these things can seemoverwhelming.But as a student ofmusic progresses (and that is what we all are: students of music, alwayslearning)thosethingsseemlessandlessforeign.Whereoncetherewasmysteryandopacitytherecomesasenseofclarity.

Concepts such as modality, which seemed so strange at first, begin to seemobvious, less intellectually taxing; andas thisoccurs, themusicianprogresses.Theirknowledgeiseasierandeasiertoapply,anditbecomeseasierandeasiertothink, tobreathe, toemoteon their instrument.The instrument itselfno longerseemsunwieldy,anditnolongerappearsasamediumthroughwhichexpressionoccurs; instead it is thatonand inwhich thoughtsandfeelingsappear.Theoryhappensonone’sinstrument,directly,withoutanyintermediary.

Butas thisoccurs, asmastery ismoreandmorea thing that seemsattainable,new questions emerge. It is no longer enough to know, for instance, all 21foundational seven-note scales. It begins to be necessary to learn how to usethose scales — how and when to play what, and where. It begins to seemobvious that those scaleswork togetherwith the chords that are by now rote,onlyitisn’tclearhowthatoccursorwhy.

It begins to seem as though new chords need to be constructed, newcombinations ofmelodic and harmonic patterns need to derived, newways ofworkingwithtonalityneedtobeemployed,andevennewwaysofconceivingofharmonyaltogetherneedtobeunderstood.Onlyitisn’tatallclearwhatanyofthatmeans.Whenthisstartstohappen—whenitisnolongerenoughtopossessthebuildingblocksbutrathertoknowhowtoconstructthingsoutofthem—itistimeformoreeducation.

The content that lies ahead is for intermediate and advanced music theorystudentswho already possess the knowledge necessary to understandmore orlesswhatmusiciansaredoingwhentheyareplaying.Whatthissectionwillstarttoansweris:

Whyaretheyplayingthatway?Howcanwemoveforwardandusethestructuresofharmonytoestablishnewwaysofplaying?Howcanweunderstandmoreandmorecomplexandsubtlemusic?How can we become more complete musicians, better composers, richerimprovisers?

Andmostimportantly:

Howcanweusetheknowledgewehavealreadygained?Howcanwecombinewhatweknowandhavepracticedinnewandexcitingways?Howcanwe, perhaps, learn tomove beyond the limits ofwhatwe already know,eventothepointofbreakingwhatwethoughtweresteadfastrulesintheprocess?

This is for intermediate and advanced players who want to learn to thinkdifferentlyaboutmusic,withwiderperspective.

While geared toward improvisation, it is certainly useful for the composingartist.Whilederivedlargelyfromthehistoryofjazzfrom1959forward,italsoprovidessuitablemeanstoanalyzingtheharmonicstructureofsomeofthemostimportantclassicalpiecesfromthelate19thandearly20thcenturies.

Wewillbeginbydiscussingandrevisingchordprogressions,understoodastheactivityandapplicationofindividualchords.Wewillthenquicklymovetowarddiscusses the principles of chord substitutions and reharmonization beforepausing for a lengthy conversation about improvising over chord progressions(including,butnotlimitedto,therelationshipbetweenchordsandscalesandthechord-scalesystemof improvisation,nowwidely taughtatuniversitiessuchasBerkelee).

That will end the conversation about what is generally known as “tonalharmony”, and the final chapterswill be dedicated to understandingways ofmoving beyond simple tonality — first, in terms of modal harmony aspioneeredbyMilesDavisinjazzandDebussyinclassicalmusic;andsecond,intermsofatonalmusicaspioneeredbyOrnetteColeman.

Specialtreatmentwillbegiventowhatissometimescalled“freemusic”,whichis a form of improvisation inspiredmost often by themodal harmony of lateJohnColtranerecordingsandtheatonalharmonyofOrnetteColeman.

Finally, the chapter on atonality will close with a section on playing beyondtraditionalmusical categories (by focusing on timbre, volume, speed, density,etc.,ratherthanonharmony,melody,andrhythm)andasectiononthespiritualaspectsofmodalandatonalmusic.

Fewthingscangivemorelastingjoythanthesustainedmeditationonadvancedmusic theory. Unlike basic theory, the world of advanced harmony is one ofinterpretationandcreativity.Therearenoclearanswers,andthereareveryfewsimple ways of understanding any of what we will discuss. Everything hereexistsinshadesofperspective.

WhatIampresentinghereisonewayofunderstandingtheprogressionbeyondsimple music theory, one way of thinking about how to move forward andbeyond the same musical patterns you have been practicing for what likelyseems like forever. This is the path to true creation, and it is paved withuncertainty.Forthatreason,itissometimeshardtomakesenseofwheretogo,what to think. But if you allow yourself to become immersed in the stuff ofadvanced music theory, than you will be rewarded with a lifetime of richcreation.Iinviteyoutoputintheeffort.Itisworthit.

ChordProgressions(Part2)Chord progressions are the foundation of most tonal harmony. In jazz, forinstance, it was not until the 50s that players began to move modal, or evenscalar.Thewaythatpeoplewroteandplayedwasmoreorlessentirelychordal.Achordprogression,asstatedbefore,issomeseriesorsystemofchordsthat,ingeneral,tendstowardsometonic.

Chord progressions are simple things by nature. There are only a few basicprogressions,whicharethencombined,movedaround,andalteredaccordingtoonly a few basic rules. The foundation of every progression is a cycle —movementawayfromandmovementtowardthetonic,orcenter,ofthekey.Thisoccursmostbasically throughcadences,ofwhich themost foundational is the

V7-I cadence, inwhich a dominant seventh chord is played a fifth above themajorIchord,followedbythatchorditself.Minorversionsofthiscadenceexistas well: V7-i. Though many types of cadences exist and do many differentthings,allofthemsharethestructureofthisbasicone—theyallbuildtension(theV7here)andtheyallreleasethattension(theIhere).

A simple chord progression consists of a tonic chord, a subdominant chord, adominant chord that follows the subdominant chord, and a tonic chord thatresolvesthedominantchord.BasicexamplesofthisaretheIV7-V7-I7foundinthebluesandtheii-V-Ifoundinjazz.Manyvariationsexist,butmoreorlessallofthetimetheyfollowthesamestructure.

Basic progressions are often extended according to a simplemechanism: Themathematicalstructureofaprogressionisusedtogettheprogressionfromsomechordtothefirstchordinwhateverprogressionisbeingextended.Thissoundscomplicated,butit’srathersimple.

1. First,youbeginwithaprogression—forinstance,aii-V-IinAMajor.ThosechordsareBm-E7-AMaj.

2. Then, a progression is chosen, from which we will borrow the mathematicalstructure.Let’ssayweuseanotherii-V-I.Weusethestructureofthatprogression(afourthupandthenafifthdown)tostartontheiiiofAmajorandendontheii,whichwillbethebeginningofthefirstii-V-I.

3. So the full progression will be iii-vi-ii-V-I, or C#m-F#m-Bm-E7-A Maj. Morecomplex progressions, such as this one, can be further combined with otherprogressions by using it (or another progression) as the basis for extendingprogressions (just like the ii-V-I here was used as the basis for extended theprogressionwestartedwith).

Additionally,progressionscanbemademuchmorecomplexbymakinguseofnewtonalcenters.Aii-V-IcanbeplayedinAmajor,followedimmediatelybyaIV-vii-IinGMajor,andsoon.Thisestablishesanewtonalcentereachtimetheprogressionisre-oriented,makingimprovisingoverthesechangessomewhatchallenging.Itis,however,commonpracticeinjazz.

Finally,thereischordsubstitution.Wehavealreadytalkedaboutthisabitbutwewillbediscussingthisat length in thenextsection,usingthe ideatobeginthinkingabouthowtoimprovisewithandoverchordprogressions.Fornowitisenough tosay thatchordscanbeexchanged forotherchords inaprogression.Thesenewchordswillservethesameharmonicfunctionintheprogression,but

theywill have different harmonicmaterial in general (since they are differentchords).

Perhaps the most basic example of chord substitution is chord familysubstitution, inwhich one chord from the same key is substituted for anotherchordofthesamefamily(atonicchordforatonicchord,adominantchordforadominantchord).Anothercommonchordsubstitutionisthetritonesubstitution,inwhich a dominant 7th chord is substituted a tritone away from the originaldominant7thchord.

ChordSubstitutionsWhencomposersworkwithprogressions,orwhenimprovisersplayoverthem,theyaregenerallythinkingintermsofchordsubstitutions.Achordsubstitutionis when one chord is replaced by another, and it allows us to extend aprogressionindefinitely.

Chord substitutions are at once the easiest thing to think about and the mostcomplicated. In the most basic sense, what a chord substitution is is areharmonization, and since reharmonizations are the foundations for melodicvariation, chord substitutions are themost basicway of generating new ideas(both on the fly and in a composition). But they are also sometimes terriblycomplicated, and performing them improvisationally can be extremelychallenging.Mostofwhatadvancedplayersthinkaboutwhentheyarethinkingabout improvising with a chord progression is something having to do withchordsubstitutions.

We have already said that a chord substitution happenswhenwe replace onechord with another, different, chord that serves a similar function in theprogression.Oneverybasicwayofdoingthisis,aswehaveseen,toreplaceachord in aprogressionwithanother chordof the same family—a tonic for atonic,adominant foradominant,a subdominant fora subdominant.But thereare many other ways of substituting chords, some of which are much moreadvanced.

For eachwayof substituting a chord, there is anopportunity toboth extend aprogressioncompositionally(aswegeneratenewprogressionsfromanexisting

progression)andaway to reharmonizea substitution improvisationally (aswecome up with new chords and melody lines to play over existing chordprogressions).

Beyondchordfamilysubstitution,thereareafewotherbasicwaystosubstitutechords. One of themwe have alreadymentioned: tritone substitution. This iswhen a dominant seventh chord is substituted a tritone apart from an existingdominantseventhchord.

Thereisnotritonesubstitutionequivalentformajorandminorseventhchords,but there is something thatworks for those chords in a similarway:Aminortriadorminorseventhcanbesubstitutedthreehalfstepsbelowamajortriadormajor seventh, andamajor triador seventhcanbe substituted threehalf stepsabove aminor triad or seventh. This is sometimes called a relativeminor (ormajor)substitution,anditalmostalwaysworkswell.

Beyond thosesimplemethodsofsubstitutingchords, therearealmost limitlessoptions.Thereare,however,afewbasicrules.Inessence,aneasierwaytoshowchordsubstitutionsmethodsisbydividingthemintothosethatchangeanddon’tchangethechord’sroot.

NotChangingtheRootQualityAdditionOneeasywaytosubstituteachordistosimplyalterthatchord,keepingitsbassnote.This isnot somuchsubstitutionaswecommonly talkabout it,but it is,strictlyspeaking,awayofreplacingonechordwithanother.

Themost basicway to alter a chord is through quality addition, inwhich thechordremainsintactbutisaddedto.Anewqualityisintroduced.Forinstance,aMaj7chordcanbecomeaMaj7#11chordbyaddinga#11notetoit.

QualitySubtractionAnother easy way to alter a chord without, usually, changing its root is tosubtractaqualityfromit.Amin7chordcanbecomeamin(triad),a5chord,oramin7chordwiththe5thomitted.Ifyouaredealingwithanextendedchord,thenyoucanalwaysremovetheextensionsandendupwitha7thchord.

Tosummarize:thesimplestkindofchordsubstitutionisthroughqualityadditionandsubtraction.Inessenceormorequalitiesareaddedtoortakenawayfromachord,andtheresultingchordisputinplaceoftheoriginal.Anotherexample,aC7canbecomeaC9,oraC13canbecomeaCadd13.

QualityAlterationIt is also possible to generate a new chord by altering the qualities that arealready in it. Notes can be raised or lowered, generally by a half-step. A 13chord can become a 9(#11)(13) by raising the 11, or a min9 can become amin7b9byloweringthe9.

FamilyAlterationThelastwaytochangeachordwithoutchangingitsrootistoalteritsfamily.Ingeneral, as stated before, there are three families of chords—major chords,minorchords,dominantchords.

Youknowwhichfamilyyou’redealingwithbylookingatthe3andthe7:

Ifthe3isab3,thenitisaminorchord.Ifthe3isamajor3andthe7isamajor7,thenitisamajorchord.Ifthe3ismajorandthe7isminor,thenitisdominant.Ifthereisno3orno7,thenitisgenerallyobviousbylookingattheothernotesinthechord(forinstance,amin6chordisminor).

Whenit isn’tclearjustthinkofthescalethatincludesthatchord—ifithasamajor3rdandaminor7ththenit’sadominantchord,etc..

AMaj6chord is theonly time thingsget confusing— this canbeeithermajorordominant,which justmeansyouhavemoreoptionswhendealingwith that chord.Somethingsimilarissometimestrueofstackedfourthchords,butthatisforanotherday.

Whenwealter the familyofachord,wechange it frommajor tominor, fromminor to dominant, or in anyotherway tomovebetween families.The chordstaysthesameexceptforthenotesthatwouldmakeitbelongtoacertainfamily.Forinstance,amin9becomesa9oraMaj9.Inthosecases, therootandthe5staythesame.

ChangingtheRootInversionYoudon’talwayswantthebassnoteofyourchordtostaythesame.Sometimes,often times, the reasonyou’re substituting is to createnewbassmovement. Inthesecases,youneedtomovethechordcompletely.Thesimplestwayofdoingthisistoinvertit.Youendupwithallofthesamenotesonlyinadifferentorderandwithadifferentbassnote.Putthe3onthebassend,forinstance.Thiswillgiveyouanentirelynewchordtoworkwith.Forexample,aCMaj7canbecomeaEmb9.

Itisworthpausinghereforamoment.Betweenqualityadditionandsubtraction,quality alteration, family alteration, and inversion, there is a vast array ofpossibilities.Ifyoucombinethesetechniques,youcangeneratealmostlimitlessnewchordstoworkwith.Andthisisalmostalwaysgoingtosoundgood.

Thegeneralrulewhenworkingwithchordsubstitutions(atleastthetraditionalrule) is tomakesure that thenewchordhasat least2notes that theoldchordhad.Ifyoudothat,youcan’treallygowrong.Evenifyoudon’tdothat,thereareplentyofcaseswherewhatyouplaywillsoundgood.

It isn’t altogether uncommon for players to add and alter multiple qualities,invert the resulting chord, and then subtract some qualities from that chord,endingupwithasubchordthatiscompletelydifferentthantheoriginal(havingonly 1, or sometimes nonotes in commonwith it).Doing this can still soundgreat,itjustmeansyouhavetolistencarefullyandknowwhentoreelitinandcomebacktotheoriginalprogression.Asalwayswiththeoryyouhavetolearntouseyourearsasaguide.

SlashChordsSimilar in notation to inversions, slash chords are a great tool for chordsubstitution.Whereastheinversionsarewrittenlikethis—Am7/C—denotinginthiscase,Casthebassnote,slashchordsarewrittenlikethis—Am7/Cm—denotinginthiscasethatanAm7chordisbeingcombinedwithaCmchordsothattheCmchordisonthe“bottom.”

This way of combining chords is important for polytonality, and will bediscussedagainlater.Fornowwecanrestatsayingthatit ispossibletoaddachordtoapre-existingchordandendupwithachordsubstitutionthatisaslash

chord.Thisisawayofalteringachordwithoutadding,subtracting,orchanginganyofitsqualities,althoughitcanbecombinedwithanyofthosetechniques.

TritoneSubstitutionAspecialkindofsubstitutionisthetritonesubstitution.Inthiscase,adominantchordisreplacedbyanotherdominantchordatritoneaway.Forexample,aC7becomesanF#7.

ChordProgressionSubstitutions

ChordAdditionRatherthanalteroraddtoanexistingchord,itispossibletosimplyaddchordstoaprogressiontoachievearesultsimilartostraightforwardsubstitution.Thisisstilla formofsubstitution,only it isaprogressionsubstitutionrather thanachord-by-chordsubstitution.

The chord or chords that are chosen to be added are generally ones that helpbridgebetweenonechordandanother,butitispossibletoaddchordsthatservetheir own distinct harmonic purposes and even temporarily change the keycenterofthesong.

Anexampleofasimplechordadditionisasfollows:givenaiv-V-IinGmajor,youcansimplyadda ii chordat thebeginning, leading into the ivchordwithanothersubdominantchord.Or,alternatively,youcouldaddatonicchordatthebeginning—forinstance,avichord.Youcouldalsochoosetoaddatritonesubbetween theV and the I, ending upwith something like this: vi-iv-V7-bII7-I,playingthefirstfourchordstwiceasquicklyasoriginallywrittentobesuretotakeupthesameamountoftime.

ChordSubtraction

Theoppositeofchordaddition,butcousintoitinprinciple,ischordsubtraction.Withsubtraction,weagainreplaceoneprogression(orsectionofaprogression)with a newone.We can, ifwe choose, keep the chords unaltered, so that theonly changewe aremaking is thatwe are eliminating certain chords from theprogression.

This is usually done so that what remains are the most important chordsharmonically—theIandichords,theVchords,etc.Itispossible,however,toretain only subdominant chords and non-I tonic chords. This makes theprogression far less stable and far more harmonically ambiguous, which issometimesdesirableasitleavesmoretothelistener’simaginationandprovidesmoreroomforinterpretationonthepartofasoloist.

SeriesSubstitutionA special case of progression substitution is series substitution, in which aspecific harmonic series or cycle is substituted for another, usually morecommon,series.Forinstance,theremaybealonger,quicker,morecomplicatedseriesthatreplacesaii-V-I.

AfamousexampleofthisistheColtranecycle.IntheColtranecycle,pioneeredbyJohnColtraneonhis“GiantSteps”album,aii-V-Iisreplacedbyaseriesthatmovesquicklythroughthreetonalcenters,eachamajorthirdapart.Forinstance,aii-V-IinCmajor(Dm-G7-CMaj)isreplacedwith:Dm-Eb7-AbMaj-B7-EMaj-G7-CMaj.

In thatprogression, the tonicchordsareAbMaj,EMaj,andCMaj.These threetonal centers are cycled throughquickly in the same time it takes normally tomovethroughaii-V-Iinonetonalcenter.Ingeneral,thesetypesofprogressionsubstitutions are used to add complexity to a piece, although that isn’t alwaystrue.

ModalReductionModal reduction, pioneered by Miles Davis, is a special kind of chordsubtraction inwhichallof thechordsaresubtractedexcept theonesneeded todefine themodalcentersof thepiece.Amodalcenter isdifferent froma tonal

center in that rather than identifying therootor tonicofachordprogression itidentifiestheharmoniccenterofascale.

So the chordsBm,DMaj,E7, andAMaj all share the samemodal center, notbecause AMaj is the tonic chord, but because they all contain notes that arefound in theAmajor scale. In this case, those chordsmight all be eliminatedexceptfortheAMajchord.Alternatively,iftheywerealleliminatedexceptforthe Bm, then themodal center would be the Bminor scale or perhaps the Bdorian mode. In this way, reducing a progression modally can encourage thesoloiststoplayandthinkincertainways.

In a modal reduction, it is common for all of the chords except the I and Vchords(andsometimesjusttheIchords)tobeeliminated,sothatwhatisleftissimplyaskeletonthatcanbefilledinbyascale.Thepointhereisnottocreateharmonic movement with a chord progression, which moves away from andback toward a tonic chord, but to allow the players a maximum amount offreedomwithinaparticularkeybyestablishingamodalcenterthatcanbefilledin,changed,andstretchedinavarietyofways.

Thisisthefoundationofmodalharmony,whichwillbediscussedlater.Fornowitisimportantonlytoknowthatbyreducingachordprogressiontoitsessentialskeleton,anewkindofharmonicfreedomandloosenesscanbeachieved.Thiswas theway ofmodal jazz in the 1950s, and it changed theway jazz playersthoughtaboutchordsandsolosforever.

ModalSubstitutionOnceyouhaveestablishedaprogressionasaseriesofmodalcentersratherthantonalcenters,thepossibilitiesforchordsubstitutionopenupdramatically.Modalsubstitution is awayof substitutingonechord for anotherwhenbothof thosechordsarecontainedinthesamescaleormode.

Therewillbemoretosayaboutthislater,inthechapteronmodalharmony,butjustnowitiseasytoseehowthisworksinprinciple—onechord,forexampleaCm7,isunderstoodrelativetosomemodalcenter,forinstanceDPhrygian,andso any chord contained inDPhrygian is allowable as a substitution chord forCm7.Eachtimethishappens,itisasthoughamodalcenterisbeing“cut”andinverted— some notes of the scale are being eliminated and what is left isrearrangedintosomenewchord.

Thepossibilitiesforreharmonizationherearenearlyendless,particularlywhenyoustarttoconsiderthedifferentwaysasingleprogressioncanbeharmonizedmodally(forinstance,thatsameCm7chordcanbeseenaspartofCPhrygianorBAeolianratherthanDPhrygian).

ModalInterchangeFinally, there ismodal interchange.This isnot somucha technique forchordsubstitutionas it is formodalcentersubstitution,but theresult isstill thatonechordor setofchords is replacedbyanother.Whatwemeanbymodalcentersubstitution is that rather than using a new chord that shares the samemodalcenterastheoldone,wereplacethemodalcentercompletely,evensometimesinaway thatmakes themusicaltogetherdissonant,and thengenerateachordbasedonthatnewmodalcenter.

Wewillcoverthisagainsoon,butfornowyoucanseethewaythatdoingthisopens up the harmony of a song completely to its limit. There is virtuallynowhereyoucannotgowithInterchangeandmodalsubstitutionwhentheyarecombined.

PolytonalSubstitutionsApolytonalsubstitutionoccurswhenachordorpartofachordfromsomeotherkeycenter isusedinaprogression.This isoftendonebywayofslashchords.Forinstance,aC7becomesaC7/DMaj

AWordonChromaticismChromaticism is an important concept in modern composition andimprovisation.Itisessentialtounderstandingbothjazzandclassicalmusicsincethe second half of the 20th Century. There are many applications ofchromaticism, andwewill speak of it againwhenwe talk about improvisingover a chordprogression,buthere—with respect to chord substitutions— itplaysaroleaswell.

Chromaticism,simplyandgenerally,istheintroductionofthe12-tonescaleinto

theharmonyofa song,chord, scale,etc. Ingeneral, thismeansalteringnotes,scales,orchordsbyahalf-stepupordown.

Inthecaseofchordsubstitution,thiscantaketheformofqualityalterationinwhichoneormoreofthequalitiesofadiatonicchordarealteredchromatically.Inthecaseofchordaddition,itcantakethecaseofaddingachordahalf-stepaboveorbelowanexistingchord.In the case of modal substitutions, you can sometimes move an entire chord(contained in the scalebeingused)upordownchromatically.This is aversionofwhatiscalled“sliding,”whichwillbediscussedlater.

Techniques such as modal interchange and chromaticism are ways of greatlyextendingtheharmonicrangeofasong.Betweenthesetechniquesliesvirtuallyeverychoiceyoucouldevermakewiththeharmonyofapiece.Whatisleftistounderstandthewaythatwideopenchordsubstitutionscanbeusedinthecontextofimprovisation—howcanweplaywithandoverthechordsofasongusingtheseharmonictechniques?

MoreSubstitutionExamplesIt isworth pausingover all these substitutions for amoment andgiving someexamples.Thiscanbeadifficultconcepttomaster,butitisquiteimportant,andexampleswillhelpyouseehowchordsandevenprogressionsaresubstitutedinpracticeratherthansimplyintheory.

Eachofthefollowingexamplestakesthisprogressionasitsstartingpoint:Am7-D7-GMaj7-CMaj7-F#m7b5-B7-Em7.

QualityAdditionandAlterationThefirstkindofsubstitution—qualityaddition—issimpleenough.Here,wetakeachordor two (ormore) from theprogressionandaddqualities to them.Am7becomesAm9,forinstance.GMaj7becomes,perhaps,GMaj11.

Toalterthefamiliesofsomeofthechords,simplychangetherelevantqualities.CMaj7becomesC7.B7becomesBm7.Andsoon.

Inversions

Youmaywanttochangethebassmovementoftheprogressionbyalteringthebassnotesofoneormorechordsthroughinversion.Thisisnotasdifficultasitseems,inpractice.Itisjustamatteroftakingoneofthenotesinthechordthatisn’ttherootandputtingitinthebass.

Beginningwhereweleftoffinthelastexample:Am9becomesAm9/C,whichisCMaj7add13,orifyoulike,CMaj13(pickingupa9and11).

TritoneSubstitutionToperformatritonesubstitution,simplyreplaceadominantchordwiththesamechordatritoneaboveorbelowit.B7becomesF7.

ModalSubstitutionModal substitutioncanbea little tricky to figureout,butonceyoudo it is assimple as the rest. First, you pick a scale— in this case, we will assume ADorian.Then,youderiveachordfromthatscale—wemightpickD7sus4—andreplacesomechordintheprogressionwiththatone.AnaturalchoicemightbeD7,butitcanbeanyofthem,forinstance,theF#.

PolytonalSubstitutionWith polytonal substitution, we begin with the key of the song and then addanotherkey, takingsomeof thenotesof thatnewkeyandadding them to theprogression.

TakingEMinor as the key,we can add another key—GMinor— and addnotesfromthatkeytothechords:AmbecomesperhapsAmb9,ormaybeevenCm/Am,apolychord.

ChromaticsubstitutionTosubstituteusingall12tones, just takesomenotesfromoutsideof thescaleandaddthemtotheprogression.

GMaj7 becomesG#m9b5 (still containing, in this case, theB andD from theoriginalchord,butaddingG#andA#).

SeriesSubstitutionTo substitute with a series, replace perhaps the first ii-V7-I with some otherseries, maybe IV-V-I, iii-vi-ii-V-I, the Coltrane cycle, or some less commonseriessuchasiiim13-IV7b5-bii7-IMaj7.

ImprovisingOverChordProgressionsOnceyouunderstandhow to applyharmonic theory to extend andmanipulatetheharmony(thechordstructure)ofapiece,thenextstepistolearntousethoseharmonicmanipulations to generatemelody lines in and over that piece. Thiscanbedoneeithercompositionally,butthewayweareintroducingithereisthewaythatjazzimprovisersthinkabouttheissue.Wewilldiscussithereintermsofimprovisation,butknowthatitispossibletoapplyallofthesameprinciplestocomposition.

ChordTonesThe foundation of traditional jazz improvisation (think bebop) is chord tones.Chordtonesare,simply,thenotesofa7thchord.Eachdegreeofascalehasa7thchordattachedto it,andeach7thchordhas fourchord tones(thefournotesofthatchord).These4notes,whichwillchangedependingon thechordyouareplayingover,arethebasisforthemelodiesthatyoucreateoverthatchord.Inthecaseofa6thchord(oranyotherchordthatdoesn’tcontaina7thchord)thechordtonesaresimplythenotesofthatchord.

Chord tonesareused tocreate improvisedorcomposedmelodiesoverasetofchordchanges.Inpre-modaljazzinparticular,thelinesthatareplayedinasongaretieddirectlytothemovementofitschords—foreachnewchord,thereisanewsetofchordtones,andthosearethenotesthatareusedtocreatemelodies.Thisisakintoarpeggiatingthechordsofasongastheypassindifferentwaystocreatenovelmelodies.

JoePasswasknown tohave said“when thechordchanges,youchange,”andthat has always been the rule of (a certain kind of) jazz improvisation andcomposition,aswellasa techniqueusedbyclassicalcomposers, rockplayers,countryplayers,andvirtuallyallmodernwesternmusicians.

Arpeggiatingthechordsinaprogressionisthefoundationofmelodyaswenowknowitinthewest,anditisresponsibleforeverythingfromthemostcomplextonaljazzarrangementstothesimplest,catchiestpopsongs.

Playingthechordtonesof7thchordsisthewaythatjazzplayersunderstandtherootoftonalimprovisation.Itisnottheonlytechniquetheyuse,notatleastallbyitself,andcertainlynotinmodernjazz(afterMilesDavis),butitaccountsforthebasicunderstandingofsingle-noteharmonyinjazz.

ExtensionsYoumaybethinkingthatchord-tone-basedmelodiesseemtooeasyandsimple,even to thepointofbeingreductive.Youmayhearwhat, for instance,CharlieParkerdid,andknowthathewasn’tjustfocusingallofhisenergyonfourtonesforeachchord.Thisisofcoursetrue.Therearemanywaysgreatplayersachievecolor and variation, even if they are using the traditional method ofimprovisation that tells them to focus on chord tones. One of them is chordsubstitutions,whichwewilldiscussagainnext.Anotherischromaticism,whichwillbediscussedlaterinthischapter.

But maybe the simplest thing improvisers can do is play the extensions ofwhatever chord they are playing over. When you’re assembling a chord, anextensionis,asyoulikelyknow,anyofthenotesbeyondthe7ththatyougettobyascendingsomescalein3rds.Inotherwords,theyarethe9th,the11th,the13th,andtheiralterations.

Byplayinganextension,youareplayinganotethatisn’tachordtonebutthatisa tone in a chord of that same root that contains those chord tones. In otherwords, you areplaying anote that is in an extended chordbasedon the samenotethatthe7thchordyouareplayingoverisbasedon.Therearemultiplewaysofdoingthis,eachwithdifferenteffects,butthegeneralideaisthesame—byopeninguptheextensionsofachordyouallowyourselfmoremelodicfreedomand open the door to subtler and complex harmonic colors. If you have everlistenedtoBillEvans,hewasamasterofthis.

Oneway of playing extensions is to use them to get from one chord tone toanother.This isamore traditionalway,and itwasused in jazzasearlyas thebop years. Thisway of using extensions treats them as tones to pass throughratherthantolandon,andsoitstilltreatsthechordtonesasprimitive.Theotherwayofseeingandplayingextensionsistoopenthemupfully,allowingyourselftobeginandendphrasesonextensions.

Thisisawayofdoingawaywiththeoldmethodoftreatingchordtonesastheessential buildingblocksof allmelody, and it is decidedlymodern (hitting itsstrideinthelate50s).OpeningchordtonesupcompletelywasinmanywaysaninventionofJohnColtrane,anditledhiminsomerespectstohismodalandfreejazzperiods.

UsingSubstitutionsinSingle-NoteLinesChord substitutions (subs for short) are a time-honored way of generatingmelodic variation.By reharmonizing a set of changes, the lead player has theabilitytoplaynewmelodicideasnotallowedbytheoldchords.If,forinstance,aCMaj7issubstitutedforanAm7,thenaplayercanchoosetoplaythechordtones of the new C chord. In this case, this gives them a B which was notavailableasachordtoneoftheAm7chord.

Thisisoneofthewaystouseachordsub—asameansofextendingthechordtonesthatyouareallowedtoplay.Anotherwayofusingachordsubinsingle-noteplaying is toassignsomescale to thenewchordand thenplay that scale(seechordscalesbelow).Forinstance,ifyousubstituteanF7foraB7,thenyoucanplayanFMixolydian(sincethenotesoftheF7chordareallfoundinthatscale).

Chordsubstitutionsareonewayofbreakingoutof thebindofmerelyplayingchord tones. They are not, however, the only way. Even in standard tonalharmony,thereareotherdevicesforachievingvariation.Butchordsubsremainperhaps themostwidely-used formof harmonic variation. They are simple innature, though not always in concept— by reharmonizing a progression, weachievewhatiseffectivelyanewprogressionaltogether,whichthenallowsustoplay in newways by playing over the new progression as though it were theoriginalone.

Thismustbedonetastefully,andit is importantheretochooseyoursubswell(since thewrong one can sound quite clanky over the rhythm section of yourband),butwhenitisdonewellitdoesamazingwork.Withchordssubsyoucanbegin to sound like a professional improviser, straight away, right out of thegate.

Another lovely feature of substitutions is that the effect they have is hugelyvariabledependingonwhatsubyouchoose.Ifyouchoosesomethingveryclose

to the original chord or very consonant within the key of the song, then theresulting melody will be very consonant. If, however, you choose a sub thatcreatesmoretensionormuddiesuptheharmonicwaters,thenthatwillbeyourresult.

Everyplayerdecideswhichsubstouseandwhen,andthatispartofwhatmakesthemsouseful—chordsubsarehighlypersonalandbecomeapartofyourstylejust as a particular tone or technique might. You can even begin to seesubstitutions as harmonic techniques, some of which you have mastered and,likealltechniques,haveaddedtoyourbagoftools.

Chord-ScalesWhenyouaretryingtomovebeyondchordtonesandintoavaster,morewideopen, even more ambiguous harmonic space, there are two basic ways ofproceeding.

Aswehaveseen,youcan:

1. Playextensionsof thechordsintheprogression,allowingyoutomovebeyondthe(usually)fourchordtonesforeachchord.

2. Youcansubstitutechords,allowingyou toopennewchord tones (andextensions)thatwerepreviouslyunavailable.

Bothofthesemethods,however,evenwhentheyarecombined,representonlyonewayofthinkingaboutmovingbeyondchordtones.Theyarebothchordalinnature,bywhichImeantheyarebothtreatingthechordsoftheprogressionasisolable, fundamental, immutable units, which can be altered, extended, andeven substituted for, butwhich are still the sole foundations for yourmelodicimprovisationorcomposition.

Thiswayofthinkingaboutachordprogressionisold(hundredsofyearsoldinclassicalmusicandasoldastheearliestbebopinjazz)anditisthereforetime-tested.Butitislimiting.Atitscore,itconsistsoftheideathattoplayoverasetof chords means basically arpeggiating those chords (playing chord tones) ortheir substitutions and extensions. And that is more or less the foundation ofwhatwethinkofasmelody,oratleastithasbeenformostofthemodernera.

Thereis,however,anotherwayofseeingthings.Ratherthantreatingachordasanimmutableobject, it ispossibletoseethatchordasamemberofsomethinglarger.Inmodalmusic,thismeansseeingitasnothingbutacuttingofalargerscale, and so often times the chord indicates nothing but a particular scale ormodetobeplayed(payingnoattentiontospecificchordtones).

Wewill havemore to say about puremodal harmony later, but even in tonalharmony (chord-based harmony) it is possible to move in this direction. It ispossibletoseeascaleaspartofachordthatisbeingwrittendownorplayed.Touseascaleinthiswaymeansgettingpastseeingachordasamapthatyouhavetofollowandbeginningtoseeitasanindicatorofalargerharmonicstructure.

Enter chord-scales.A chord-scale is a scale that ismapped to a chord (and achordthatisthenmappedtoascale).Playingachordscaleisawayofplayingachordbyplayingalargerharmonicstructure(ascale,usuallyconsistingofsevennotes), and that means that it extends the harmony of the chord, but withoutthinkingaboutanextensionandnotnecessarilythinkingaboutasubstitution.

Achord-scaleextends theharmonyofachord inanynumberofdirectionsbyfinding a scale that includes all of the notes of the notated chord and thenmappingthatscaleontothechord,givingtheplayerorcomposerallofthenotesofthescaletoworkwith.Thechordisnolongerthoughtofinisolation,butisnow part of something larger. The harmonic landscape is freer than in strictchordalharmony,sincetherearemorenotestochoosefromatanygiventime.This allows formoremelodic variation. Since there aremultiple chord-scalesavailable formost chords (due to the fact thatmost chords can “fit” into thenotesofmorethanonescale),thereisevenmorevariety.

Here’showitworks:

Youcometoachord—anFMaj7forinstance.Ratherthanseeingthefournotesofthatchord(F,A,C,E)asthefoundationforyourmelodyline,yougoinsearchofachord-scale.Youfindascale(orscales)thatcontainsFMaj7.EvenifwelimitourselvestoscaleswhoserootisF,thereismorethanoneoption.Forinstance,FIoniancontainsthosenotes. FLydian also contains them.The 7thmode of the harmonicminor scale, FLydian#2,alsocontainsthosenotes.Youcanalsoproduceanynumberof synthetic scalesby takingoneof those threescales and altering the second, fourth, or sixth notes of them. You are left withmultiplescalestochoosefrom.Youwill,dependingonhowlongyouhavetositonthisonechord,potentiallyplay

more thanoneof them.Assuming thatyouonlyhaveabeator two,however,youwilllikelychooseoneofthosescalesanduseittocreateamelody.

Bydoingthat,youwillhavechosenachord-scale,aunitformedbythemappingof,for instance,anFLydianscaleontoanFMaj7chord.WhileyouareontheFMaj7chord,youcanthenplayanyofthenotesoftheFLydianscale—F,G,A,B,C,D,E.Andthat’showitworks.

Themagicofchord-scalesismostevidentintwocases:

1. When the chords aremoving quickly and thinking about chord tones, extensions,leading tones, and substitutions is made difficult (or impossible). In these cases,havingmemoriesafewchordscalesforeachcommonchordmakesplayingthroughthechangesbreezy.

2. Whenthechordsaremovingslowlyenoughthatitispossibletousemorethanonechord-scale over a single chord. In these cases, a tremendous amount of tonalvariation can be achieved without ever having to do very much in the way ofcalculation.

Ingeneral, chord-scales areusedon a chord-by-chordbasis.Themotto is still“whenthechordchanges,youchange”,andthat’swhyitisn’tmodal(it’sstillatonalharmonictechnique).Itsjobistoassembletonestogetherthatdefineandextend a tonal point of gravity (the root of a chord), which along with otherpointsofgravitydefinesatonalcenterandsoakey(justthesamewayachordprogressiondoes).Inthisway,chord-scaleplayingisclosertobopharmonythanitistowhatcameafterit,butitisamodernwayofthinkingaboutthatkindofharmony.

Though chord-scales are generally played chord-by-chord, it is possible tocombinethemwithtechniquessuchasmodalsubstitutionandmodalreduction,which results in a harmonic space that ismore ambiguous. In general, chord-scales play well with substitutions across the board, so it is a great idea tosubstituteachordand thenfindachord-scale togoalongwith thenewchord.When you do thiswith something likemodal reduction, you can end upwithfewerchordsandmoretimetoplaywiththescalesyouaremappingontothosechords,whichcanbegintosoundandfeelmorelikemodalmusic.

ChromaticismWhen you have moved beyond pure chordal harmony and into the world ofscales,thereisasenseofgreatfreedom.Itisasthoughyoucanopenyourlungswide and take in the air.Butyou are still verymuch inside.There is awholeworldoutsideyourdoor that is available toyou.Chromaticism is thewayoutthatdoor.

Chromaticism, at its most basic, is simply the use of any of the notes in thechromaticscale.Ingeneral,itrefersto:

1. Usingthe12-tonechromaticscaletoalterachordorascaletoachievesomekindofvariation.

2. It can also mean discarding chords and scales altogether to play as outside aspossible.

Thefirstofthesetwousesiscommonintonalmusic,andthesecondiscommonin atonal music. Tonal chromaticism is in some sense less pure form ofchromaticismthanatonalchromaticism— in theway that it is still tied to achord or scale that ismore restrictive than the 12 tone scale.But that doesn’tmeanitisn’tapowerfultool.

A rather conservative way to use chromaticism in tonal music is the waychromaticswereused inbop. In theheydayofbebop, itwasquitecommon touseachromatic run toget fromoneplace toanother, inbetweenarpeggiosofchords. In a similar vein, a chromatic addition can be used as a passing orleadingtonebeforeorinbetweennotesofanarpeggioorchord.Thisamountstoaddinganoteaboveorbelow(byahalf-step)anoteinthescaleorchordyouareusing.

Bop players alsomade synthetic scales consisting ofmore than 7 notes, nowcalled bebop scales. These scales were designed to allow the player to playascendingordescendingandendupplayingachordtoneoneverystrongbeatwhile playing other notes, sometimes chromatic notes, in between them.Theywould often begin with a diatonic scale, such as a major scale, and add onechromatic note in between two of the existing notes of that scale, such asbetweenthemajor6thandmajor7th,orbetweenthemajor2ndandmajor3rd.

It ispossible tousesomeof thesebeboptechniques toachievemore“outside”harmoniceffects.Beginningwithachordsub,forinstance,thatalreadycontains

non-diatonic notes, and then altering or adding to that chord or its extensionschromatically,allowsyou toendupwithanarpeggio that is far-from-intuitivebutthatmaystillsoundgreat.

It is also a commonpractice tobeginwith a commonchord-scale (aC IonianmappedontoaCMajchord for instance)and thenadd toandalter thatchord-scalechromatically(perhapsflatteningthe9thandaddinganotebetweenthe5thand6thnotesofthescale,endingupwithasyntheticscalethat“works”withaCMajchordbutsoundsquiteexotic).

Ingeneral,fewthingsinmusicaremorepowerfulthanthechromaticscale.Itissopowerfulthatwehaveinventedseven-notescalestorestrainusandreigninthechromaticscale,inaway.Itwouldbeeasyenoughtosay“playoneofthese12notes”ateverypoint in time,butmostofuswouldbeentirely lostby this.However, the judicious use of chromaticism to alter, add to, and eventemporarilyreplaceachordorchord-scalecanbethedifferencebetweenstayingindoorsandfeelingthefreshbreeze.

PolytonalityAconclusionwhichwecandrawsofaristhatTonalharmonyitselfcanbe:

1. Chordal2. Scalar3. Chromaticinnature

However,Tonalharmonyislimitedbyonefoundationalprinciple:thereisone,andonlyone, tonal center at anygiven time.Themusic canmove, andmovequickly,fromcenterofgravitytocenterofgravity,butatanyonemomentthereisonepoint inharmonicspace thatcommandsyourattention.Thatmeans thatanynote,andchord,anyscaleyouplayatthattimewillhavemoreorlessonesetofdefiningcharacteristics(relativetowhateverthetonalcenteris).

Thisisthecasewithallpurelytonalmusic,andithasbeenthecasewiththevastmajority of music in general in the west for hundreds of years. This is notnecessarily a bad thing. But in the last 100 or so years, composers began toexperiment with ways of moving outside of this one-key-at-a-time structure.

Andimprovisers,particularlyinjazz,begantodothesamethingaroundthelate50s.Thisresultsinwhatiscalled“polytonality”,whichisawayofsayingthatthere ismore than one, sometimesmany, tonal centers happening at the sametime.Thisiswhenitgetsveryadvanced.

Inpolytonalmusic,asinglenotehasmorethanonefunctionatthesametime.Achordorscale is thenaquitecomplicatedmatter. Ifyouareplaying inbothAminorandCminor,thenaCisbothaminor3rdandaroot.AnAmchordisbotha iminor (inAminor)chordandaviminorchord (inCminor).AnAminorscalecontainsbothdiatonicallyconsonanttones(inAmin)anddissonanttones(inCmin).Navigating sucha spacecanbedifficult, but it can result in someincrediblesubtleandbeautifulmusic.

In order to achieve polytonality, sometimes a piece of music is written withchordsbeingborrowedfrommore thanonekey.But ifyouareplayingoverastandardtonalpieceofmusic,andyouwanttoplaypolytonally,thenthereareafewthingsyoucando.

First,youcansubstituteslashchordsforsomeoralloftheoriginalchords.Asyoudothis,besuretochoosesometriadsfromanentirelydifferentkey.Whenyouplayover your subs, you can choose to arpeggiate the chord from theoriginal key, thechordfromthenewkey,ortheentireslashchord.Youcan also choose a chord-scale that suits eitherorof those chords (oryou canmovebetweenchordscalesthatsuiteachofthem).Whereyouchoosetoplayyouremphasis will determine how “out” the music sounds. If you lean heavily on theoriginalkey,thenthemusicwillsoundmoreconsonant.Ifyouleanawayfromit,itwillsoundmoredissonant.Youcanalsosimplyselectchord-scalesfromchordsthataren’tinthekeyyoursongis written in. This is achieved by subbing in a chord that has a root that isn’tcontained in thekeyof the song, and thenchoosing somechord-scaleon that rootthat contains multiple non-key tones. By moving between this chord-scale and amorestandardchord-scale(thatisinorclosetointhekeyofthesong),orevenbychoosing more than two such scales and moving between them all, you achievepolytonality.

Polytonalityisdifficulttounderstand,especiallyifyouareimprovisingandhavetowrapyourheadaround itquickly,but it canbepracticed.Youcanpracticeinjecting chords and scales from some second or third or fourth key into themelody you play over a chord progression. Begin slowly and with simpleprogressions thatmaintain theirkeycenter (suchasa slowversionofAutumnLeaves).Eventually,youwillbeusedtothewayitsoundsandyouwillbeginto

add second (and more) key scales and chords without having to think aboutprecisely which keys you are borrowing from. At that point it is a matter ofhearingandfeelingthemovementofthemusicandknowingwhentodoit(andwhennotto).

ModalHarmony(Miles,Debussy,Pre-Common-EraMusic)Mostof themusicwenowlisten to,andhavelistenedtosince themodernerabeganintheWest,hasonethingincommon—tonality.Thismusicistonalinnature— from classical to romantic, from rock to pop, from blues to jazz tocountry, and even including rap, hip hop, and R&B.We have seenwhat itmeans to be tonal: a particular tone (or sometimes set of tones) acts as theweighty center of the music. All of the chords and scales and notes that areplayedorwritteninthatpiecetaketheirharmonicfunctionfromthatcenter,andall of them can be seen as either moving away from or moving toward thatweight.

Thisisnot,however,theonlywayforharmonytobeorganized.Inmodalmusic,thecenterofgravitythatwasasinglenote(atonalcenter)isnowreplacedwithanetworkofnotes—amodeorscale.Therearethen,generally,sevennotes,allactingastheweightycenter(takentogether)ofthemusic.Thereisakey,andinsome respects it can be said to center (on a scale), but there is no one notearoundwhichtheharmonyofthepiececongeals.

Thenotesofthescaleusedastheharmonicfoundationarealltreatedequally—oneisnotseenasthetonic,withtheothersservingtobuildorreleasetensionvisavisthattonic.Nowthereareinsomesenseseventonics,andtherelationshipsbetween them emerge out of the specific intervals — the chords and themelodies—thatthecomposerorimprovisercreateswithinthatscale(oroutsideofit).Thesongissaidtohaveakey,butthekeyiswrittenassomethinglike“ADorian”ratherthan“Aminor,”with“A”inthemodalsenseonlybeingtheretoindicatethescalebeingplayedandnotnecessarilythetonalrootofthepiece.

Thisisthebasicideaofmodalharmony,anditisasoldaspre-modernEuropeanmusic (prior to theBaroqueperiod andgoingback as far asGreekmusic andGregorianchants)andmuchofthemusicthathashistoricallycomeoutofAsiaandAfrica.Modal harmonywas revitalized at the turn of the 20thCenturybyFrenchcomposerssuchasDebussyandRavel,andinjazzitwaschampionedinthe mid-to-late 50s by Miles Davis, John Coltrane, and Bill Evans (amongothers).Sincetheinventionofmodaljazz,modalharmonyhasbeenaubiquitouspartofrock,fusion,country,freeandavant-gardemusic,andithasalwaysbeena feature of the blues. Few things inmusic are as powerful or as adaptable ismodalharmony.

ModalSubstitutionsWehavealreadymentionedmodalsubstitutions.Thesearepartof theheartofmodal music. When there is a chord progression, the traditional method forharmonicsubstitutionistoalter,addto,andinverttheexistingchords,resultinginnewchordsthatshareimportantchordtoneswiththeoldones.Inthisway,weare sure toendupwitha setof changes that functions in the sameway,or inmuch the sameway, as theoldone— functions, that is, tonally.Thatwayofsubstitutingchordsisbasedonthefunctionofachordwithintonalharmony(visavisatonalcenter).Theideaisthatthenewchordhasasimilarfunctionastheoldone.

There is, however, anotherway of going about substituting a chord. If, ratherthan seeing each chord ashaving aparticular functionwith respect to a tonic,andeachnoteofeachchordhavingaparticularfunctionwithrespecttoaroot,weseeinsteadallofthenotesasbeinginside(oroutside)ofsomescaleorseriesofscales, then thegame isdifferent.Wecannow,since thechordsaresimplycuttingsofalargerscaleormode,replacethatchordwithanyotherchordthatisalsoacutting fromthatsamescaleormode. IfweseeanAm7chord,andweassumeforthetimebeingthatitispartofaGDorianscale(orAPhrygian)thenwecanreplaceitwithanychordalsocontainedinthatGDorianscale(suchas,forinstance,aGm13sus4chord.

Theartistryofthissortofsubstitutionisintwothings:

1. The choice of modal center (the scale being used). At any given time, there aremultiplescales that include thechordwrittendown,either in isolationor including

thechordsaroundit in theprogression,andsodecidingwhichscales touseat thatpointintheprogressionisamatteroftaste.

2. Thechoiceofachordtobeusedwithinthatscale.Ichose,intheexampleabove,aGm13sus4chord,butIcouldhavejustaseasilychosenanFMaj11chord,oranyoneof a number of other chords. Deciding which one to use is a matter of overallharmoniccolor,andisoftendonebylisteningtothemelodiccontentofthemusicasonechordmovestothenextone.

ModalInterchangeModal substitution is the way that a modal player or composer opens theharmony of a song to allow for maximum harmonic freedom (and melodicvariation).Playingsinglenotelinesovermodalchordsisaseasyasplayinganyof the notes in the scale you have chosen at that time (and again involves acertain amount of artistry inmaking judicious decisions aboutwhich notes toselect — Miles Davis was the master of this). But sometimes a player orcomposerwantsevenmoreflexibility.Entermodalinterchange.

Modal interchange is a kind of substitution whereby the scale being used isswappedoutforanotherscale—anyotherscale—ofthesameroot.Andsinceevery seven-note scale has sevenmodes, eachwith their own roots, there aretheoretically seven different notes for each scale that can be used to anchor anewsetofscales.Allyouneedtodoispickoneofthoserootsandplayascale—anyscaleyouchoose—beginningwiththatnote.Then,newchordscanbeintroducedbasedonthatnewscale(anditsavailablemodes).ModalinterchangewasusedtogreateffectbyJohnColtraneonthealbum“ALoveSupreme”.

ChromaticSlidingMiles Davis was known for a particular kind of scalar substitution in modalmusic.Thetechniqueiscalled“sliding,”anditinvolvesplayingtheexactscaleyouareusingcurrently,onlyonehalf-stepupordown,andthenreturningtothescaleyouwereusing.Itisausefultechniqueforgeneratingtensionandcreatingnovelmelodicideas.

PolymodalityWhat polytonalmusic is to tonalmusic, polymodalmusic is tomodalmusic.Polymodality is theuseofmore thanonescaleat thesame time toanchor theharmonyofthepiece.OneexamplecomesfromJohnColtrane:ascale(Fmajorfor instance) is used as themodal center of an improvisation, but at the verysametime,twootherscalesamajor3rdaboveandbelowthatscalearealsoused(inthiscase,AmajorandC#major).Thescalesareallusedtocreatemelodies,sometimesoneafteranotherandsometimeswithinthesamephrase.Chordsareborrowedfromallofthescales,resultinginaharmonicnetworkthatiscomplexandambiguous.

AtonalityFinally, we arrive at atonal music. Atonal music can be seen as one of twothings:

1. Thenaturalextensionoftonalharmony,inwhichpolytonalityistakentoitslimit;2. The most complete version of modal harmony, in which the 12-tone scale is the

“mode”beingused.

Inthefirstwayoflookingatit,atonalityisthedenialoftonalitybywayofitsmultiplication. “Atonal”means “without a key center,” but it is impossible toconceive ofmusic that iswithout harmonic organization in the strictest sense.The limit of polytonality, however, approaches the lack of a key center byestablishingsomanysmallcentersthatthemusicneverhasachangetocongealaroundasingletonic(orevenasetoftonics).

Thesecondwayofseeingatonalityissimpler—itismodalmusicinwhichall12tonesareusedtodefinethescalebeingused.Onthismodel,atonalharmonysimply treatsall12 tonesequallyanddemocratically,allowingrelationships toemergebetweenthemasthemusicprogresses.

It is important tonotethatatonaldoesnotmeanwithoutrules.Thereissuchathing as free music (to be discussed briefly) but, for instance, the through-composedatonalmusicoftheearly-to-mid20thCentury(oftencalled“serialism”

andpioneeredbySchoenbergandWeber,amongothers)wasarule-governedasBaroquemusic(andperhapsasmathematicalaswell!).

ChromaticPlayingTheeasiestwayformostpeopletoapproachatonalplayingandcomposingistothink of it through the chromatic scale. Seeing the chromatic scale as thefoundationofthemusic(ratherthanany5or7-notescale)isawayoftreatingall12tonesdemocratically.Whatemergesoutofaspacesuchasthisisverymanysmallerrelationshipsbetweennotesandchords—relationshipsthatcanbeseeneitheraspolytonalorasmodalinthemostabsolutesense.

Itisworthpracticingthiskindofplaying,inwhichtheharmonyofthemusicisrestrainedonlybyonescaleandincludesallofthenotesofWesternharmony.Itsoundsasthoughthissortofmusiciseasiertocomposeorimprovise,butdoingsowith any kind of lyricism requires great skill (and an impressive ear), anddemandspractice.

OrnetteColeman–HarmelodicsOrnetteColemanpioneeredawayofplayingchromaticallythatendurestothisday. All 12 tones are treated equally, but rather than attempting to createharmonicstructuresoutofthose12tonesinvariouscombinations,theharmonyisleftentirelyuptothemelody.Thisiscalledharmelodics,andwhatitmeansisthat themelodic function of a note or chord is what determines its value (itsharmonicvalue)ratherthan,forinstanceitsrelationshipwithinachordorscale.

Ratherthanseeingharmonyassomethingfrozenintime(arelationshipbetweentonesinabstractcollectionsofnotes),harmelodicsseestherelationshipbetweennotes in time, as they move up and down and are held for longer or shorteramountsoftime,aspartofthosenotes’harmonyfunction.Colemanwasafanofsayingthatharmelodicswasallabouttreatingthemelody,harmony,andrhythmequally(ratherthanprivilegingharmony).

FreeHarmonyInfreemusic,thingsareunlikeanywhereelse.Wehavealreadysaidthatatonalmusicdoesnotmeanmusicwithoutrules,butinfreemusicthat’sexactlywhatitmeans.Thereare,infact,norulesatallinfreeharmony.

Every musical structure — from the Moonlight sonata to the sounds of atrainyard—areallowedin.Inaslightlymorerestrictedversion,freeharmonymeans that any of the 12 notes can be played at any timewithout necessarilybeingconcernedatallabouttheirharmoniccontent.

Freemusic is so far removed from traditional notions of harmony that in factmostfreemusiciansdistancethemselvesfromthe“jazz”nametag,insistingonbeing called “free improvisers” instead. This is an extension beyond even thelatemodalmusicofColtraneandthefreejazzofColeman.Itisofteninfluencedbythosethings(aswellasbylateMilesDavisand20thcenturyclassicalmusic)but it isnot identicalwithanyof them.Mostpractitionersof freemusic in itspurestsensearealsoplayersofsomeothermoretraditionalmusic,suchasjazz,rock, or classical, but in the space of free improvisation those names meanrelativelylittle(intheory).

BeyondHarmony,Melody,andRhythmFree music establishes a space in which traditional musical structures are nolonger dominant. The composer or performer is allowed to move beyondharmony, melody, and rhythm and into other sonic territories. These includetimbre,tone,volume,andmusicaldensity.

It is not uncommon for a free player (or any avant-garde or experimentalmusician who embraces this music space) to think and feel those musicalpropertiesratherthanconcerningthemselvesatallwiththetraditionalstructuresweareused to.Thismoves suchcomposersandperformerseven further fromthetraditionsofrock,jazz,andclassicalmusicandintonewareas,whichmanylisteners find difficult to encounter but some players find exceptionallyrewarding.

SpiritualityandMusicTheoryIt may seem strange to move beyond tonality, and even beyond harmonyaltogether.But there is a long tradition in avant-garde, experimental, and freemusicof lofty reasons fordoing so. In theexperimental classical tradition, forinstance,asinmuchofthefreeimprovisationsincethe70s,musictheoryistieddirectlytophilosophy.Thinkingaboutthemetaphysicalandotherphilosophicalramifications of playing music takes the place of thinking about harmony ormelody,withsomeoftheseplayersandcomposerssuchasJohnCageandDerekBailey even publishing philosophical books and essays linking their work todeepphilosophicalthemes.

Thereisanothertradition,closelyrelated,comingoutof60sjazz(fromOrnetteColeman, SunRa,Cecil Taylor, JohnColtrane, Pharaoh Saunders, andAlbertAyler).This traditionreplacesmusic theoryas ithasbeenknownforcenturieswithspiritualreflectionandreligiouscommitment.

Theseplayers,someofthematleast,werewell-knownforseeingtheirmusicasdirect lines to divinity, much the same way that music functions in somemystical traditions outside of themodernWest.Contemporary spiritual atonaland free musicians have continued this tradition, often linking philosophy,spirituality,religion,andevenscholarshipdirectlytothepracticeandtheoryoftheir music. This means that for these players the new music theory isintellectualandspiritualinnature(ratherthanmathematical).

Theorynolongerappearsonthepage,anditnolongerconcernsitselfwiththesorts of things we have become accustomed to thinking about. This sort oftheoryisboundless,andpointstowardafutureinwhichmusicwillnotliveonlyonthepage(diditever?).

ANotefromtheAuthor

Thank you for reading this book. I hope you enjoyed reading it asmuch as Ienjoyedputtingittogether.

I have only one request; if you feel like this book helped you in anyway, itwouldbegreatlyappreciatedifyoucouldtakeamomenttowriteaquickhonestreview on Amazon. Reviews are immensely important to independent self-publishedauthorsandgreatlyhelpusgetmorebooksinfrontofmorereaders.Ifyoudidn’t like it, that’s fine too. Just leave anhonest review, that’s all I ask.DropmeareviewonAmazon.com.

This will not only help others find and benefit from this book, but it is alsoextremely helpful and rewarding to me to know how much this book hasbenefitedothers,aswellastolearnanywaysIcanimprove.

Also,ifyouwishtostayintouchyoucanvisitmywebsiteat:www.guitaryourday.comandsubscribetomyemaillist.Iveryrarelysendoutemails,butwhenIdoit’sonlybecauseIhavesomethingcooltoshare.

Remember to keep practicing and be disciplined, always work on expandingyourknowledgeandbecoming thebetteryou.Learn to enjoy theprocess, andeverythingthatyoudo,eventhesimplest,smallestthings.Thiswillgiveyoutheresultsyouwantanditwillleadtosomethingtrulygreat.

Wishyouloveandjoy,

Nicolas

OtherBooksbyNicolas

HowtoReadMusic

ASimpleandEffectiveGuidetoUnderstandingandReadingMusicwithEase

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ACompleteStep-By-StepGuidetoLearningGuitarforBeginners

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ACompleteBeginner’sGuideToUnderstandingGuitarEffectsAndTheGearUsedForElectricGuitarPlaying&HowToMasterYourToneOnGuitar

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KaizenTheArtofContinuousLifeImprovement,HowtoCreateaLastingChangeOneStepataTime

Asthetitlesuggests,thisbookisallaboutthewaysyoucantheartofKaizentoimproveyoureverydaylifeandachievesignificantgoals.

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CheatSheet

MajorScaleinAllKeys

MastertheIntervalsE->C(ascending)—minor6th

E->C(descending)—Major3rd

D->A#(ascending)—minor6th

D->Bb(descending)—Major3rd

Gb->Ab—minor7th

PMSExercise1.GDorian–PMSisFMajor

2.F#Mixolydian–PMSisBMajor

3.EPhrygian–PMSisCMajor

4.A#Aeolian–PMSisC#Major

5.GLydian–PMSisDMajor

6.DLocrian–PMSisEbMajor

7.BIonian–PMSisBMajor

8.DbMixolydian–PMSisGbMajor

4-BarSequenceExercise1Bar1

1and2eand(a)3eand(a)4e(and)a;

8th–8th–16th–16th–8th–16th–16th–8th–16th–8th–16th

Notesthatfalloneachbeat(1234)arebolded.

Bar2

1and2eanda3eand(a)4(e)anda;

8th–8th–16th–16th–16th–16th–16th–16th–8th–8th–16th–16th;

Bar3

1triplet2triplet3eand(a)4(e)anda;

8thTriplets–8thTriplets–16th–16th–8th–8th–16th–16th;

Bar4

1eand(a)2(e)anda3e(and)(a)4e(and)(a);

16th—16th–8th–8th–16th–16th–16th–8th.—16th–8th.;

4-BarSequenceExercise2Bar1

|1||e||and|a|2||e|anda|3|triplet|4||e|anda;

8threst.–16th–8threst–16th–16th–8thsync.triplets–8threst–16th–16th;

Bar2

|1|and|2|eanda|3|eand(a)|4||e|anda;

8threst–8th–16threst–16th–16th–16th–16threst–16th–8th–8threst–16th–16th;

Bar3

|1|triplet|2|triplet|3|eand(a)|4||e|anda;

8thsync.triplets–8thsync.triplets–16threst–16th–8th–8threst–16th–16th;

Bar4

|1|eand(a)|2||e|anda|3||e|and(a)|4|e(and)(a);

16threst–16th–8th–8threst–16th–16th–8threst–8th–16threst–8th