THEEVERYTHING®MUSICTHEORYBOOKAcompleteguidetotakingyourunderstandingofmusictothe

nextlevelMarcSchonbrun

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The MusicTheoryBookDearReader,Assomeonewhohasbeenanacademicmusicstudent,acomposer,andaprofessionalmusicianinallareasofmusic,Iseeclearlythedividethat

hasmadetheorysuchahardtopictoteach.Ilovemusictheorybecauseit fascinates me. But at the same time, I understand that it serves apurposeandthatpurposeisdifferentforeachreader.Totrytotacklethis,Ioptedforafewuniquethings.First,theexamplesinthebookrangefromclassicalmusictopopandjazzinanefforttoreachasmanyreadersaspossible.Also, thenotation ispresentedforsingle-lineinstruments,mainlypianoandguitar.Thisisalsomeanttomotivateyoutoplaytheexamplesbecausetheorydoesnotliveonpaper.Musicisnotatheory;itisarealthingthatIwantallofyoutoexperienceinfull.Ihope no matter who you are, you leave this book with a deeperunderstandingofsomethingthatyouandIlovesomuch:music.Best,

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INTIMEAquickspotofmusichistory

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Contents

Introduction

1

ReviewoftheBasicsInsandOutsNotesClefsTimeBasicRhythmsRestsMeter

2

IntervalsGotheDistanceIntervalsfromScalesTheSimpleIntervalsAdvancedIntervalsInvertedandExtendedIntervals

3

TheMajorScaleScalesDefinedSpellingScalesScaleTonesHowScalesAreUsedinMusic

4

TheMinorScaleMinorColorsTheDefinitiveApproachTheDerivativeApproachDegreesinMinorScalesMultipleScales—ScaleClarityVariantVariables

5

MusicalKeysandKeySignaturesMusicalOrganizationTheSystemofKeySignaturesRelativeMinorKeysMinorKeysonPaperKeysChange

6

ModesandOtherScalesModes—TheOtherSideofScalesSevenModalScalesLookingatModesonTheirOwnOtherImportantScalesTimeforEtudes

7

EtudeOne:ScalesandKeys

8

ChordsWhatIsaChord?BuildingChordsMinorTriads/ChordsDiminishedTriadsAugmentedTriadsChordsinScalesDiatonicChordsMinorScaleHarmony

9

SeventhChordsandChordInversionsSeventhChordsSeventhChordConstructionSeventhChordRecapInvertedChordsQuickStudy:BachPreludeinC

10

Movements:ChordProgressionsWhatIsaChordProgression?ProgressionsinTimeDiatonicProgressionsandSolarHarmonySolarHarmonyandtheChordLadder

11

MoreChordProgressionsTonicandDominantRelationshipsUsingDominantChordsinMinorKeysHarmonicRhythmVoiceLeading

12

MelodicHarmonizationWhatIsMelody?ChordTonesandPassingTonesTrueMelodicHarmonizationSingleLineHarmonyDealingwithAccidentals

13

EtudeTwo:ChordsandHarmony

14

AdvancedHarmonyBeyondDiatonicModalMixtureModulation

15

JazzHarmonyWhatIsJazz?JazzHarmonyJazzProgressionsBluesForms

16

TranspositionandInstrumentationWhatIsTransposing?TransposingChant

BbInstrumentsEbInstrumentsFInstrumentsOctaveTransposesAnalyzingScoresInstrumentRanges

17

EtudeThree:AdvancedHarmony,JazzHarmony,andTranspositionAppendixA:GlossaryAppendixB:AdditionalResources

Acknowledgments

Thanks to my family: Mom, Dad, Bill, Trish, Joshua, and David. ManythanksagaintoJoeMooneyforhistime,alsotoDr.PaulSiskindforhisguidance.ThankstoErnieJacksonfortheformativeideas.TotheCraneSchoolofMusicformyeducation,andDr.DougRubioformystart!ToKarla,lifeisajourneyandit'sbetterwithyouasapartnerontheroad.

Introduction

MUSICIANSOFTEN START at an early age with study in school thattypicallyincludeslearninghowtoreadmusicnotation.Manyofyouwhoplay traditional instruments got your start in public schools. Traditionalinstruments include band and orchestral instruments like flute, clarinet,violin,andcello.Ifyouwereabletostudyinschool,youprobablygotagood foundation of practical work on your own instrument, includingreadingmusic and performance.Many schools only offer instruction inband and orchestral instruments, although that is starting to change. Ifyou studied a nontraditional instrument, such as guitar, bass, or piano,chancesarethatyoudidn'tdosoinschool.Youprobablydidittotallyonyour own, either teaching yourself or through private instruction.Depending on the instrument you chose, youmay or may not have astrong background in readingmusic. Pianists typically are grounded inreading,whilemanyguitarists'learningrarelyincludesreading.Whenyoustudyamusical instrument,youtypicallyworkinstages.Thefirststageislearningthebasicsofyourinstrument.Youcandevoteyearstolearningaboutthetechniquesandpracticesthatmakeyourinstrumentwork.Afteryouhaveattainedsomemasteryofyourindividualinstrument,thingsstart tochange,andtheinstrumentbecomessimplyavehicleformusicalexpression.Asamusician,youbegintolookatthelargerpictureofwhatmakesmusicworkandholdtogether.Theword theory is almostalways thrownaroundasanelusivesecondstep toward understanding music. Many musicians view the study ofmusictheoryasachore,akinto“Ihavetopaintthehouse”oranyothertedioustask.Butmusictheoryisnotatask.Itisaneducatedlookbackatwhat happened throughoutmusic history.Music has undergone a slowevolution,and theory looksbackatwhat'shappenedand tries tomakesense of it. Theorywill put words to concepts that you hear and haveunderstoodallofyourlife.Studyingmusictheorywon'tnecessarilymakeyouabetterplayer,butitcould.Inasense,achievinganunderstandingofmusictheoryisverymuchlikebuyinganewinstrument:Inthehandsofaskilledplayer,itcanbeapowerfultoolforself-improvement.This book is a follow-up toTheEverything®ReadingMusicBook. Thepurposeofthatbookwastogivealogicalwayforallplayerstolearnto

readmusicalnotation.Understandingmusicalnotationisacriticalstepintheprocessofreadingmusic,andifyouarenotcomfortablewithit,youshouldcheckoutthatbookaswell.Thisbookwillreviewbasicconceptsofreadingmusicalnotationinthefirstchapter,butmusicreadingwillnotbecovered indepthandyouwill needknowledgeof notation.Youcanlearntheorywithoutstrongmusic-readingskills,butstrongreadingskillswillmakeeverything,ateverystep,easier.Thisbookisdifferentfrommanyothertheorybooks.Manytheorybookssimply start off too hard for many people. They presuppose toomuchinformationand typically put the reader off to the ideaofmusic theory.They often cater to college-level music-theory topics. Rarely are theysuitable forself-study.Theotherproblemofmany theorybooks is theirfailuretospeaktoalargecrosssectionofreaders, includingarangeofinstrumentsplayed,abilities,andstylesofmusic.Manytextsfocussolelyon classical music, using examples from the canon of classical musiconly—totallyignoringpopularmusic.Thisbookwillremedythatsoyoucan get the most out of your experience. If your goal is to be on anadvancedtracktomusictheory,thisbookwillgiveyouthefoundationyouwillneedtogofurther,andyouwillbeabletotackleamuchharderbookwithease.

1

ReviewoftheBasics

Everyone needs a good review! You might not know everything youneed,orevenhavereadanyothermusic-theorybooksinyourlife,sothepurposeofthischapteristogiveyouaverybriefoverviewofsomeofthevisualconceptsofmusic,suchasnotes,clefs,andrhythms,sothatyoucanlookattheforthcomingexamplesinthebookanddecipherthemwithease.

InsandOuts

Since youwill see the language ofwrittenmusic throughout this book,youmustmakesurethatyouwillbeabletoreadit.ManyoftheconceptswillreinforcethemselvesthroughtheuseoftheaccompanyingaudioCD,but there is noway around an inability to read notation. Youmight besittingtheresaying,“Icanread just fine,”but therealquestion is,“Howwelldoyoureadinotherclefs?”

INTIME

In Europe, musical tradition began with the simple monophonic (onevoice)chantsoftheearlyChristianera.Thiswasthemostcommontypeofmusic during theEarlyMiddleAges (fromabout a. d. 350 to 1050).Polyphonicliturgicalmusic,composedofmorecomplexcompositionwithmultiplemelodies,developed in theHighMiddleAges(fromabouta.d.1050to1300).Music theory isall about lookingatwhat'sbeendone,and through thestudyofothermusic,youcancometoagreaterunderstandingofwhat'sup.Youwillneed toknowhow to read inmultipleclefs, sincestandardnotationusestrebleandbassclefataminimum,andoftenthrowsinaltoclef, too. In order to seewhat's goingon, youneed to beable to readthose clefs as well! Here is some basic review so that you canmakesenseofwhatyouarereading.Thereisalsoareviewofrhythmsinsomedetailasrhythmcanbeaconceptthatisverydifficulttounderstand,andeven ifyouknowhowtodecipher thenotesonastaff,youstillmaybeuneasy with the counting aspect. If this chapter is already scaring theheckoutofyou,trypickingupTheEverything®ReadingMusicBookandkeeping that around, as it will help you greatly in understanding thismaterial!

Notes

Whatbetterplacetostartthannotes?Here'sashortsampleofmusic;trytodissectwhat'sgoingonandseeifyouhaveallyouneedtoknow.

AsyoucanseefromFIGURE1.1,thisisashortexcerptfromapieceofsolopianomusic.Hereiswhatyouareseeing:

1. Therearenotesplacedontwomusicalstaffs:onetreblestaffandonebassstaff.

2. Thestaffsarefurtherdefinedbytheirclefs.

3. Thenotes are identifiedonlybyuseof a clef; otherwise, theyare simplydotssittingonlinesandspaces.

Ifyouwanttotalkaboutthenotes,youhavetotalkaboutclefsbecauseclefsactuallydefinethenameofthenotesinastaff.

Clefs

Aclef isasymbol thatsitsat thebeginningofeverystaffofmusic thatyoulookat.Astaffcontainsfivelinesandfourspaces.Howdoyouknowwhere thenoteAor thenoteC is?Themissingelementneeded is theclef.Theclefdefineswhatnotesgowhere,functioningalot likeamap.Placingatrebleclefatthestartofthestaffdefinesthelinesandspaceswithnotenames.FIGURE1.2showsthenotesofatreblestaff.

ThetrebleclefcirclesaroundthenoteG.Thisiswhyit'scommonlycalledtheG clef. As for the notes, there is an important pattern. Look at thelowest line,which is designatedE. Follow themusical alphabet to findwherethenextnoteis.TheFisinthespacejustabovetheE.Thestaffascends in this fashion — line, then space, then line — as it cyclesthroughthemusicalalphabet(A–B–C–D–E–F–G).

ExtraCredit

Eventhoughyoumayunderstandthenotesonbothclefs,theonlywaytogetproficientistoreadotherclefsasoftenasyoucan.Setasideafewminutesadaytolookatotherclefssoyoucaneasilyidentifytheirnotes.Since clefs definenotes, you canalmost thinkof beingable to read inmanyclefsasakindofmusicalliteracy.The bass clef is a different clef than the treble and identifies not onlydifferentnotenames,butalsonotesindifferentranges.Thebassclefisused for instruments that have a lower pitch, like a bass guitar. Eventhough the bass clef sits on the same five-line staff, it defines verydifferentnotenames.Manymusicians read trebleclefbecause it is themostcommonclef.Becauseofthis,toomanymusicianshaveagreaterdifficulty readingbassclef than reading trebleclef. Inorder toprogressyour understanding of theory, you will need to be adept at reading allclefs.FIGURE1.3showsthenotesofabassclefstaff.

GrandStaffandMiddleCWhen thebassclef and the treble clef aregrouped together, it createssomethingcalledthegrandstaff.Thegrandstaffisusedinpianowriting.Tomakeagrandstaff,allyouhavetodoisconnectatrebleandabassstaff,orclef,withabrace,whichisshowninFIGURE1.4.

Whatagrandstaffshowsisaveryimportantnote:middleC.FIGURE1.5showsamiddleC.

WhenyoulookatFIGURE1.5,canyoutellwhetherthenotebelongstothebassclef,orthetrebleclef?Actually,itbelongsequallytoboth.Ifyoutracedownfromthetrebleclef,oneledgerlinebelowthestaff isaC.Ifyoulookatthebassclefnotes,oneledgerlineabovethestaff isalsoaC.Theyare,infact,thesamepitchonthepiano.ThisiscalledmiddleCbecause it's right in the middle of everything. Middle C will come upthroughoutthisbook,sokeeptrackofit!Moveable“C”ClefsThe last type of clef is called the C clef. Typically, you see this clefassociatedwith theviolabecause it's themostcommoninstrument thatreads in thatclef;however,more instruments than just theviolaread it.WhentheCclefisusedwiththeviola,itiscalledthealtoclef.Thankfully,thisclef isveryeasytoreadbecausethesymbolfortheCclefhastwosemicircles that curve into themiddle of the staff and basically “point”toward themiddle line, which is aC. It's not just anyC, it'smiddleC.FIGURE1.6showsthenotesforaltoclef.

Sincethisisamovableclef,youcanplacetheclefanywhereyouwant,andwhatever lines its twosemicirclespoint tobecomemiddleC.SomeveryoldchoralmusicusesadifferentmovableCclefforeachpart(tenorclef,altoclef,andsopranoclef).Justas longasyouknowthat theclefalwayspointstowardmiddleC,youwillbeabletodecipherthenotesinthisclef.Asalittleexercise,hereareafewlinesofmusic,eachinadifferentclef.Belowthemusic, there isspace foryou towrite thenotenames in.Goaheadanddosorightinthebook.

Noticeanythingaboutyouranswersfromthefourexamples?Ifyoudiditcorrectly,youshouldhavecomeupwiththeexactsameanswerforeachline.Thiswas intentional!Lookathowdifferenteach line looks.At firstglance,youneverwouldhave thought that theywere thesame!This isthepowerofclefsandwhyit'ssoimportanttobeabletoreadwellinallclefs—sometimesitlooksmuchmoredifficultthanitreallyis!

PointtoConsider

Whennotes use ledger lines that are extremely high or extremely low,theycanbedifficulttoread;it'smucheasiertoreadnotesthatsitinthestaff you are reading. Using different clefs allows you to move thelocationofmiddleCinsuchawaythatthemajorityofyournotesareinandaroundthestaff.

Time

Even though this is in the “review” section of this book, time is afundamentalaspectofmusictheorythatisoftenleftoutofformalmusic-theorystudy.Timehasmoretoitthanjustcountingbeatsandbars.Timecandictatethefeelandflowofapiece,andevenharmonyhasarhythmto it,aptlycalled“harmonicrhythm.”You'llstartwith timesignatures,astheyarethefirsttime-relatedaspectyouwanttounderstandindetail.TimeSignaturesMusicisdividedintobars,alsocalledmeasures,forreadingconvenienceand for musical purposes. Most music adheres to a meter, and thataffects thephrasingof themelody. Ifyoudon'thavea lotofexperiencewithreading,rhythmcanbeaverydifficultconcepttograsp.The most standard time signature is 4 4 time, which is also called“commontime”andisabbreviatedbythissymbolc.Commontimelookslikea fractionand itsignifies two things.First, the topnumber4meansthat every measure will have four beats in it. The bottom number 4indicateswhatnotevaluewillreceivethebeat;inthiscase,4standsforaquarter note ( ). So common time breaks up each measure into fourbeats,asaquarternote receivesonebeat.Youcan,of course, furtherdivide themeasure intoasmanysmallpartsasyou feel like,but in theend,itmustadduptofourbeats.Rhythm

Music iscomposedofpitchand rhythm.While thereare finerelementsthat come into play later on, such as dynamics and expression,musiccanbemadebyknowingsimplythis:whichnoteandhowlongtoholdit.Withoutrhythm,peoplecouldn'tfullyreadmusic.Rhythm is music's way of setting the duration of a note. Musicaccomplishesthistaskbyvaryingtheappearanceofthenotesthatsitonthestaff.Differentrhythms indicatedifferentnote lengths.Togetrolling,youneedtohearaboutanessentialconcept:beat.Haveyoueverbeentoaconcertandclappedalongwith30,000other fans?Haveyouevernoticedhoweveryoneclaps together inasteadypattern?Didyoueverwonder how 30,000 people could possibly agree on anything? If youhavebeentoadanceclub,youmayhavenoticedthatthereisalwaysasteadydrumbeatorbassline,usuallyup-tempo,todrivethemusicalong.Those are examples of pulse and beat in music. Rhythm is a primalelementandpulseandbeatareuniversalconcepts.

BasicRhythms

Inmusic,changingtheappearanceofthenotesindicatestherhythm.Asyouwill remember, the locationof thenotes is fixedon thestaff,whichwill never change. The appearance of the note varies, indicating howlongthatnoteshouldbeheld.Now,you'llgothroughallthebasicmusicalsymbolsforrhythm.QuarterNotesA quarter note ( ), which is signified with a filled-in black circle (alsocalled a notehead) and a stem, is the simplest rhythm to talk about.Quarternotesreceiveonecount;theirdurationisonebeat(seeFIGURE1.8).

HalfNotesThenextinourseriesofsimplerhythmsisthehalfnote:(h).Asyoucansee, the half note looks similar to the quarter note, except the circle isopenandnotfilledin.Likeaquarternote,italsohasasinglestemthatpointseitherupordown.Thehalfnotereceivestwocounts;itsdurationistwobeats.Inrelationtothequarternote,thehalfnoteistwiceaslong

becauseitreceivestwocounts(seeFIGURE1.9).

WholeNotesAwholenoteisarhythmthatreceivesfourbeats.It'stwiceaslongasahalfnoteand four timesas longasaquarternote—count toyourself:one,two,three,four.It isrepresentedasanopencirclewithoutastem.Thewholenoteisprobablythesinglelongestrhythmicvaluethatyouwillcomeacross.Wholenotesareeasy to spotbecause theyare theonlynotesthatlackastem(seeFIGURE1.10).

EighthNotesThesmallest rhythmyouhaveencounteredthusfar is thequarternote,which lasts for one beat. Chopping up this beat into smaller divisionsallows musicians to explore faster rhythms and faster passages.Choppingthequarternoteinhalfgivesustheeighthnote,whichreceiveshalfofonebeat(seeFIGURE1.11).

SixteenthNotesThebeat can be broken downeven smaller for the faster note values.Thenextrhythmiscalledthesixteenthnote.Asixteenthnotebreaksthequarternoteintofourequalpartsandtheeighthnoteintotwoequalparts(FIGURE1.12).

FasterNoteValuesIt'spossibletokeepchoppingthebeatupintosmallerandsmallerparts.Thenextstepbeyondsixteenthnotes is thethirty-secondnote.Athirty-second note breaks one beat into eight equal parts. Just like thetransition from eighth to sixteenth notes, going from sixteenth to thirty-secondnoteswilladdanother flagorbeamto thenotes.Youcankeepaddinganotherflaganditwillsimplymakethenotevaluehalfthelengthofthepreviousnote.FIGURE1.13showsfasternotevalues.

AugmentationDots

Youhave focusedonmaking note values smaller and smaller, but youcan make them larger by using what's called an augmentation dot.Placingasmalldotdirectlytotherightofanynoteincreasesthedurationof that note by one half. For example, placing a dot after a half notemakesthedottedhalflastforthreebeats.Theoriginalhalfnotereceivestwo beats and the dot adds half the value of the original note (a halfnote):Thedotaddsoneextrabeat(aquarternote),bringingthetotaluptothreebeats.Anynotecanbedotted.FIGURE1.14isachartofdottedrhythmsandtheirduration.

PointtoConsider

Adotextendsthevalueofanote.Atiealsoextendsnotes.Bothdothesame thing but they do it differently visually. A dot added to a noterequiresthatyoufigureoutwhathalfofthenotevalueisandcountit.Atieissometimeseasiertoreadasthenotesarevisually“glued”together.TupletsUptothispoint,rhythmshavebeenbasedonequaldivisionsoftwo.Forexample,breakingawholenote inhalf results in twohalfnotes. In thesameway,dividingahalfnote in twopartsresults in twoquarternotes.As the divisions get smaller, going through eighth and sixteenth notes,the notes are continuously broken in half equally. However, beats canalsobebroken intoother groupings,most importantly groupingsbasedon odd numbers such as three. Such odd groupings are commonlyreferredtoastuplets.Whenyoubreakabeatintothreeparts,yougivebirthtoa“triplet.”Themostbasictriplettolookatistheeighth-notetriplet.Aneighth-notetripletissimplythreeeighthnotesthatequallydivideonebeatintothreeparts(seeFIGURE 1.15). You could also look at it like a ratio: three notesequally divided in the same space as one beat. Since there are threenotes ineachbeat,eighth-note tripletsare faster than twoeighthnotestaking up the same beat. The more notes per beat, the faster theyprogress.

Tuplets don't have to be in threes, although that is the most commontupletinmusic.Youcanhavetupletsthatdivideabeatintoanynumberof parts: five, seven, even eleven. The number above the grouping ofnotesindicateshowit'ssupposedtobedivided.

Rests

Allthistalkaboutnotesandrhythmswouldn'tbecompletewithoutsomediscussion about rests. The best news of the day is that everythingyou'velearnedaboutrhythmsalsoappliestorests.Theonlydifferenceisthataresttellsyounottodoanything!Atlast,yougetabreak.Every pitch needs duration.Rhythm defines how long notes should besustained.Music isn't always about sound— rests are as common aspitches.Restsindicateaspotinthemusicwhereyoudon'tplayasound.Since a rest does not have a pitch associated with it, it requires adifferent symbol. Here's a chart of the rests (FIGURE 1.16) and theirassociatednotes.

Meter

The last thing tobrieflyexplain ismeter.Youencounteredonemeteratthebeginningof thischapter: common time,or44,meter.Now takealittlebitoftimeandlookatthedifferentmeters.SimpleMeter

Asimplemeterisanymeterthatbreaksthebeatupintoevendivisions.Thismeansthatwhateverthebeatis,whetherit's44,34,or24,eachbeat(whichisaquarternote)isequallydivided.Thebeatisbrokenintoeven divisions of two (eighth notes), four (sixteenth notes), or eight(thirty-second)notes.

What sets simplemeter apart from othermeters is how the beats aregroupedtogether.Theclearestwaytoseehowbeatsaregroupedistheuseof eighthand sixteenthnotes.Since the flags joinandare visuallygroupedtogether,youcanclearlyseehowthenotesandthebeatsbreakdown. Inasimplemeter,youplaceslightnaturalaccentson thestrongbeats, which are always on the first note of any rhythmic grouping.Whenever you see notes grouped together in twos or fours, you knowthatyouareinsimpletime.Since44,34,and24arethemostcommonmetersandallareinsimpletime,youwillbecomeaproatsimplemetersinshortorder!CompoundMeterSimple meters have one important feature: groupings of two or fournotes.Thenextmetersarecompoundmeters.Acompoundmeterbreaksitself intogroupsof three.This iswhatmakes compound timedifferentfromsimpletime.Commoncompoundmetersare .Compoundmeters usually have an 8 in the lower part of the meter because themeterisbasedoneighthnotesreceivingthebeat.

PointtoConsider

Compound time relies on groupings of three notes; you need to adjusthowyouviewbeatdurations.Aclickonthemetronomedoesnotalwayssignifyaquarternote.Whatitdoessignifyisthe“pulse”ofthemusic.Incommon time, that click could be a dotted quarter note, so keep yourconceptoftimeelastic.

AsyoucanseeinFIGURE1.18,compoundmetersvisuallygroupsetsofthreenotes.That is,38simplycontainsonegroupingof three,68 twogroupingsof three,andsoon.Counting in44andothersimplemetershasn'tbeensuchabigdeal.Yousimplysetyourmetronomeortapyourfootalongwiththequarternotes.Incompoundtime,yourbeatbecomesagroupingofthreenotes—morespecifically,agroupingofthreeeighthnotes(althoughifyouwerein316, threesixteenthnoteswouldget thebeat,butsincetimeisallrelative,itallworksoutthesame).OtherMetersInmusic, thecombinationof simpleandcompound timesignatureswillget you through the majority of the music you'll encounter. Even so,composers and musicians love to stretch the boundaries. All of themeters you've learned about so far have been divided into easy

groupings.Othermusicexistsinunusualgroupings,calledoddtime.Oddtimeandoddmeterissimplyameterthatisasymmetric,orameterthathasunevengroupings.Oddtimecanbeexpressedanytimethat5,7,10,11,13,and15are the topvalue ina timesignature.Thebottomofthe signature can be any rhythmic value; it's the top number thatdetermines if it's symmetric (simple) or asymmetric (odd) time. Take alookatabasicoddmeterlike54(seeFIGURE1.19).

2

Intervals

The most elemental part of music theory is understanding therelationshipsbetweensinglenotes.Thedistancebetweenthosenotesisaninterval,whichwillserveasthefoundationforpracticallyeverysingleconcept that you will explore throughout this book. Understandingintervalsisextremelyimportant.

GotheDistance

Anintervalisdefinedasthedistancefromonenotetoanother.Intervalsare going to provide the basic framework for everything else inmusic.Not only is knowledge of intervals as a subject itself important, butintervals areusedeverywhere.Small intervals combine to formscales.Larger intervals combine to form chords. Intervalswill aid you in voiceleading, composition, and transposition. There are virtually no musicalsituations where intervals aren't used (barring snare drum solos), andeveninsomeoftheextremelydissonantmusicofthetwentiethcentury,intervalsarestillthebasisformostcompositionandanalysis.Therearefivedifferenttypesofintervals:

MajorintervalsMinorintervalsPerfectintervalsAugmentedintervalsDiminishedintervals

You will learn all about the five types of intervals in this chapter, butbefore you go any further, you must have a visual helper, kind of amusicalsliderule:thepianokeyboard.Intervalscanseemlikeanabstractconcept,butwhenyouhavesomevisual relationships to reference, theabstractconceptbecomessomethingmoreconcreteandeasiertograsp.FIGURE2.1showsthepiano.

Thisimagewillrepeatatdifferenttimesthroughoutthisbook,butyoucanearmarkthispageforreferenceasyou'regoingtoneedit.Thekeyboardshowsyouwhereallthenotesarewithinonefulloctaveonapiano.Italsoshowsyouallthesharpsandflatsontheblackkeys.

PointtoConsider

NoticehowC#andDboccupy thesamekey.Thissituation,whereonekey can have more than one name, is called an enharmonic. Thishappensonalloftheblackkeysonthekeyboard.Thewhitekeyshaveonlyonenamewhereastheblackkeysalwayshaveasecondpossibility.Thiswillbeexplainedfurtheralonginthisbook.HalfStepsThefirstintervaltolookatisthehalfstep;it isthesmallestintervalthatWestern music uses (Eastern music uses quarter tones, which aresmallerthanahalfstep),andit'sthesmallestintervalyoucanplayonthemajorityofmusicalinstruments.Howfarisahalfstep?Well, ifyoulookatapieceofmusic,agreatexampleofahalfstepisthedistancefromCtoC#orDb—remember thatC#andDbare thesamething.FIGURE2.2showsthehalfstepinatreblestaff.

Nowthatyouhavebeengivenaveryrudimentaryexplanationofwhatahalfstep is,gobackto thepiano.Statedsimply, thepiano is laidout insuccessivehalfstepsstarting fromC.Toget to thenextavailablenote,yousimplyprogresstothenextavailablekey.Ifyouareonawhitekey,likeC, forexample, thenextnote is theblackkeyofC#/Db.Youhavemovedahalf step.Move from theblackkey to thewhitekeyofDandyou'vemovedanotherhalfstep.Whenyou'vedonethistwelvetimes,youhavecomebackaroundtoCandcompletedanoctave,whichisanotherinterval.Now,thisisnotalwaysasteadfastrule.Itisnotalwaysthecasethatyouwillmovefromawhitekeytoablackkey,orvice-versa,inordertomoveahalfstep.FIGURE2.3willillustrateanexampleofthis.Asyoucanseefromthefigure,themovementbetweenEandFandthemovementbetweenBandCarebothcarriedoutfromwhitekeytowhitekey,withnoblackkeybetween them.Thismeans thatBandC,andE

andF,areahalfstepapart.This iscalleda“natural”halfstep,andit isthe only exception to our half-step logic. The good news is that if youkeep this in the front of yourmind, all intervalswill bemuch easier todefine,notjusthalfsteps.

WhyisthereahalfstepbetweenBandCandEandFwheneverywhereelseittakesawholesteptogettothenextlettername?Theanswerissimplerthanyouthink.ThesoundoftheCmajorscale(C–D–E–F–G–A–B–C)camefirst.ThescalehappenedtohaveahalfstepbetweenEandFandBandC.Whenthesystemofmusicwasbrokendownandactuallydefined,thatscalewaslaidoutinwhitekeysandhadtofittheotherhalfsteps between the other notes. It really is an arbitrary thingmore thananything else. It's another argument for the fact that sounds come firstandthenyoufigureoutawaytoname/explainthem.WholeStepsA whole step is simply the distance of two half steps combined.MovementsfromCtoDorF#toG#areexamplesofwholesteps.Ifyouaregettingthehangofbothwholeandhalfsteps,youcanactuallytakethisinformationquiteabitfurther.Youcouldskiptoscales,whichwould,inturn,leadyoutochords.The intervalsbetweenEandFandBandCarestillnaturalhalfsteps.LookatFIGURE2.4toseeanexample.WholeStepIntervals

Awhole step fromE ends up on F# because you have to go two halfstepstogettoF#,passingrightbyFnatural.ThesameholdstrueforBbtoC.Now it's time for you to put this information to work.FIGURE2.5 is aworksheet for half and whole steps. You'll be asked to name someintervalsbylookingatthemandalsowriteanintervalfromasinglenote.Thereareafewdifferentclefs,tomakethisexercisefunandchallenging.Feelfreetowriteinyourbook,butuseapencil!

Nowthatyouhavegonethroughhalfandwholesteps,thenextstepisalookat theCmajorscale, toget tosomeof theother typesof intervals

outthere.

IntervalsfromScales

Now, you may be wondering why a discussion of the C major scaleappearshere in the intervalchapter,when,according to theplanof thebook, scalesappear in thenext chapter.Simply, onceyou knowwholeandhalfsteps,youcanspellanyscale,butmore importantly, theotherintervalsaremucheasiertoseeandlearnthroughtheuseofascale.

PointtoConsider

Whenmanymusiciansnamealargeintervaltheyusuallydon'tcountthenumbersofhalfstepsthattheyneedtofigureouttheanswer.Typically,mostmusiciansaresofamiliarwithscalesthattheyusethatinformationtosolvetheirpuzzle.Scalesaresuchusefulbitsofinformation,andtheyare,ofcourse,madeupofsimpleintervals!This will become clearer as the book progresses, so consider this asneakpeekatscales;youwillgetthefullscoopinthenextchapter.IntervalsintheCMajorScaleFormingaCmajorscale isprettysimple:YoustartandendonC,useeverynoteinthemusicalalphabet,andusenosharpsorflats.BecausetheCmajorscalecontainsnosharpsorflats,it'sveryeasytospellandunderstand.It'sthescaleyougetifyouplayfromCtoConjustthewhitekeysofapiano.So,hereisthescalespelledout.

Ifyoulookatthedistancebetweenanytwoadjacentnotesinthescale,youwillseethatthisissimplyacollectionofhalfandwholesteps.Nowtryskippingaroundthescaleandseewhat intervalsyoucomeupwith.StartwithCasabasis foryourwork fornow.Every intervalwillbe thedistancefromCtosomeothernoteintheCscale.Tostartsimply,measure thedistancewhere there isnodistanceatall.Anintervalofnodistanceiscalledunison.

Unisonismoreimportantthanyouthink.Whileyouwon'tseeitinasolopianoscore—youcouldn'tplaythesamekeytwiceatthesametime—whenyou learn toanalyzea full scoreofmusic, it's reallyhandy tobeabletotellwheninstrumentsareplayingexactlythesamenotesandnototherintervals,likeoctavesandsuch.The movement from C to D is a whole step, but the interval is moreformallycalledamajorsecond.Everymajorsecondcomprises twohalfsteps'distance.

ThenextintervalwouldbefromCtoE,whichisfourhalfsteps'distanceandmoreformallycalledamajorthird.

Next up is the distance from C to F, which is five half steps, and isformallycalledaperfectfourth.

Perfectfourth?Areyouconfusedyetwiththenamingoftheseintervals?Hanginthere!Beforeyougettothewhyandthelogicbehindthis,finishthescale.Youhaveonlybeguntochipawayatintervals.Thenext interval is thedistancefromCtoG,which issevenhalfstepsandisformallycalledaperfectfifth.

The interval fromC to A, which is nine half steps, is formally called amajorsixth.

Thenextinterval,fromCtoB,iselevenhalfstepsandisformallycalleda

majorseventh.

To complete this scale, the last interval will be C to C, a distance oftwelvehalfsteps,oranoctave.

IntervalsintheCMinorScaleNowthatyou'veseentheintervalsintheCmajorscale,hereisthewholeCminorscaleandallofitsintervals.

Whatdoyouseehere?Forstartersthethird,sixth,andseventhintervalsarenowminor.ThatmakessensebecausethosearethethreenotesthataredifferentifyoudirectlycompareaCmajorandaCminorscalesidebyside,asinFIGURE2.16.

The intervals that were “perfect” in the major scale remain the samebetween both scales. However, the second note of the scale (C to D)remains the same in both scales, yet that interval is called a “majorsecond.”Whyarescalessoimportantwhendealingwithintervals?Aren'tintervalssomethingthatyoucanmeasureontheirown,separatelyfromascale?Yes,ofcourse,that'sright,butmostmusiciansgetverycomfortablewithscales and they use them to figure intervals out because scales are apointofreference.IfyouaskamusicianwhattheintervalisbetweenAandF,it'slikelythatheorshewillthinkofanAmajorscalefirstandtrytoseeifF#isintheAscale.SinceF#is,heorshewillquicklylowertheF#fromamajorsixthdowntoaminorsixthandthat'stheanswer.Otherwise,halfstepswouldhave to be counted, which is tedious, or every possible intervalcombinationinmusicwouldhavetobememorized,andthathasit'sownobvious disadvantages. (It might happen naturally over time, but itcertainly wouldn't happen overnight.) Certain intervals are easy tomemorize,andyoudo learn tomemorizesomeof them,butscalesstillremaininmostmusicians'headssincetheyknowthemsowell.What you don't see in either themajor orminor scale is diminished oraugmentedintervals.That'snottosaytheyaren'tthere;italldependson

howyoulookatit.Sufficeittosaythatmajor,minor,andperfectintervalsare the most basic intervals, and they are the easiest to spell andunderstandastheynaturallyoccurinthemajorandminorscalesthatyouplaysomuch.Augmentedanddiminishedintervalsarelesscommonbutareequallyimportanttoknowandunderstand.

PointtoConsider

Whenmeasuring musical intervals, always count the first note as onestep.Forexample,CtoGisafifthbecauseyouhavetocountCasone.This is the most common mistake that students make when they areworkingwithmusical intervals, theyoftencomeuponeshortof therealanswerbecausetheysimplyforgettocountthestartingspotasone!QualityandDistanceIntervals have two distinct parts: quality and distance.Quality refers tothefirstpartofan interval,eitherbeing“major”or“perfect,”asyousawfromtheCmajorscaleintervals.Now,thesearenottheonlyintervalsinmusic,thesearejusttheintervalsintheCscale;youwillseetherestoftheintervalsshortly.Distanceisthesimplestpart—designationssuchassecond, third, fourth, and so on refer to the absolute distance of theletters.Forexample,CtoEwillalwaysbea“third”apart,becausetherearethreeletters(C,D,andE)fromCtoE.Thenumericaldistanceistheeasiestpartofintervals:Yousimplycounttheletters!Determiningthequalityofanintervalisadifferentstory.IntheCmajor scale, there are two different qualities of intervals: major andperfect.Whyweresomeof themmajorandwhat'ssoperfectabout thefourthandthefifth?Atfirst,learningalloftheserulescanbeachallenge,butwhenyouunderstandthebasics,youcandosomuch.Asforintervalquality,it'sonlywhenyouunderstandallofthedifferentqualitiesthatyoucannameanyinterval.EnharmonicsAnintervalhastodeterminethedistancefromanynotetoanothernote.AsyoucanseeaboveintheCmajorscale,everyintervalhasadistanceandaquality to it.Where therealconfusioncomes in is thatnotescanhave more than one name. You might recall enharmonics, mentionedearlier, where C# and Db sound the same yet are different notes onpaper.When you analyze writtenmusic, you have to deal with what you are

given.Whenyoulistentoanyinterval,youdon'tlistentothespelling,youhearthesound,sothedistancefromCtoD#willsoundjustlikeCtoEb.Whatyouhearisthesoundofthosenotesringingtogether,butifyouhadtoanalyzeitonpaper,you'dbelookingattwodifferentintervals(oneisaminor third and the other is an augmented second), with two differentnames. This is exactly why the system of intervals has evolvedsomewhat strangely and with a certain amount of ambiguity, becausewrittenmusichastheenharmonicissuebuiltin.

INTIME

Many modern theorists and composers don't use the traditional inter-vallicsystem. Instead, theybasetheir intervallicmeasurementsonpuredistance-basedrelationshipsinhalfsteps.Thissolvestheambiguitywithenharmonicintervalscompletely.So,insteadofamajorthird,itwouldbea“five.”Thismorenumericallybasedsystemoforganizationformusiciscalled“set”or“settheory.”

TheSimpleIntervals

Aspreviouslymentioned,therearefivedistincttypesofintervalqualitiesto deal with: major, minor, perfect, diminished, and augmented. The“distance”ofanintervalwillalwaysconsistofthequalityfirst,followedbythe numerical measure of how many notes you are traveling, forexample,“majorsixth.”Gothroughthe“simple”intervals—major,minor,and perfect — first, and you'll deal with diminished and augmentedintervalsinthenextsection.MajorIntervalsMajorintervalscanapplyonlytodistancesofseconds,thirds,sixths,andsevenths.Aquicktricktospellanymajorintervalwouldbetolooktothemajorscaleyouareworkingwith.Forexample,ifyouwantedtofindoutwhat amajor thirdwas from thenoteE, you could spell the scale andsimplynamethethirdnoteoftheEmajorscaleandthatwouldbeyouranswer.Manymusiciansusethismethodtospellintervalsandscales.Theotherwaytolookattheseintervalsistolookatthedistanceinhalfsteps(orwholesteps).Thisisanotherwaytofigureoutaninterval,anditprecludesknowingthescale(whichthisbookdoesn'tofficiallygettountilnextchapter).Hereisatableofallthemajorintervalsandtheirintervallicdistance.

TableofMajorIntervals

Type Distanceinhalfsteps DistanceinwholestepsMajorSecond two oneMajorThird four twoMajorSixth nine fourandonehalfMajorSeventh eleven fiveandonehalfThat's all there is tomajor intervals!FIGURE2.17 is a short quiz thatasksyoutonameabunchofmajorintervals.Usewhatevermethodyouare familiar and comfortable with to name these, either using scales ifyou know them already or simply counting the steps. Just remember,there are no trick questions here — all of these intervals are majorintervals:seconds,thirds,sixths,orsevenths.Writeyouranswersbelowtheintervals.

MinorIntervalsMinor intervals are next up, and they are closely related to majorintervals,astheybothonlyexistasseconds,thirds,sixths,andsevenths.So,what'sthedifferencebetweenamajorandaminorinterval?Simply,aminorintervalisexactlyonehalfstepsmallerthanamajorinterval.Takealookatthetablebelowandcompareittothetablepresentedaboveforthemajorintervals.

TableofMinorIntervals

Type Distanceinhalfsteps DistanceinwholestepsMinorSecond one onehalfMinorThird three oneandahalfMinorSixth eight four

MinorSeventh ten fiveWith themajor intervals,youare luckyenough tobeable tonameanymajorintervalsimplybylookingatamajorscaleandcounting.Thissortofworksfortheminorscale,butit'snotperfect.Ifyouspellouttheminorscale,youdo,infact,gettheminorthird,minorsixth,andminorseventh,butbewareofthesecond.Aminorscale'ssecondnoteisamajorsecondfromtheroot.Ifyouneedtomeasureaminorsecond,justrememberthataminorsecondisthesmallestintervalinmusic,thehalfstep.Whatyourealizeabouttheminorintervalsisthattheyarealwaysexactlyonehalfsteplowerthantheirmajorcounterparts.So,ifyouhavetonameaminorintervalandyou'resuperfastatthemajorintervals,simplyloweranymajor intervalexactlyonehalf stepandyouwillbe there.FIGURE2.18showshowthisworks.

See,that isn'tsobad!Justrememberthatmajor intervalsarethelargerofthetwointervalswhenyoucomparemajorandminorintervals.

ExtraCredit

Strengthen your vocabulary! Instead of talking about half and wholesteps,callthembytheirpropernames.Ahalfstepisaminorsecondandawholestepisamajorsecond.PerfectIntervalsSo far, the logic to naming interval quality has made sense: Majorintervals come frommajor scales, andminor intervals (all except one)comefromtheminorscale.Nowyoucometoperfectintervals,andyoumaybewonderingwhat isso“perfect”about them.Here isaverybriefhistory lesson. As music was evolving, most music was monophonic,meaningthatyousungorplayedonlyonelineatatime.Oncetheygotdaringenoughtoaddasecondlineofmusic,onlycertainintervalswereconsidered “consonant” and could be used. In the early days ofpolyphony,fourthsandfifthswerecommonlyused,soperfectseemedtofittheirnameastheyalmostneversoundedbad.Tomodernears,fourthsandfifthsdon'talwayssoundasniceasthirdsorsixthsdo,butthat'sjustamatteroftaste.Backtotheintervals!Perfect intervalsencompassthefollowingdistances:unison(nodistanceatall),fourth,fifth,andoctave.Perfect intervalsarefairlyeasytospellbecauseall theperfect intervalsappearinboththemajorandtheminorscales,sonomatterwhatyouaremorecomfortablespellingin,you'llfindallyourperfectintervalsthere.Ifyou'reupforcountinginsteps,hereisanothertable!

TableofPerfectIntervals

Type Distanceinhalfsteps DistanceinwholestepsUnison n/a n/a

PerfectFourth five twoandahalfPerfectFifth seven threeandahalfPerfectOctave twelve sixIn contrast tomajor intervals that can bemade intominor intervals by

simplyloweringthemahalfstep,theperfectintervalsarestuck.Ifyoudoanything to a perfect interval (flat or sharp one of the notes), you arechanging interval type away from being perfect. It always becomessomethingelse.Whatitactuallybecomesissomethingdiscussedinthenext section. Before you move on to the more advanced intervals,practice spelling some perfect intervals. FIGURE 2.19 will help youpracticeidentifyingperfectintervals.

See,thisisn'tthatbad.Intervalsareafairlyconcretethingthathaveanabsolutedistanceandyoucannamethembasedonthoseparameters.Butasstatedbefore,naminganintervalcomprisestwoparts:qualityanddistance. You have two more qualities to explore: augmented anddiminished.

INTIME

Thetermoctavehastherootoctlikeoctagondoes.Oct,ofcourse,istheprefix indicating eight, and an octave is the distance spanning eightnotes.Moreimportantly,anoctaveisthesameletternamerepeatedatahigherpartofthemusicalspectrum.

AdvancedIntervals

Thebasicintervalsofmusicaremajor,minor,andperfect.Ifyoustoppedthere, you would have more than just a cursory understanding ofintervals; you could domore than just get by. However, there are twomoretypesofintervals,whichdealwiththeissueofenharmonicspellingsofnotesandothersuchanomalies:augmentedanddiminishedintervals.Asyouknow,theintervalofCtoEbandthatofCtoD#soundexactlythesame.Theonlythingthat'sdifferentisthespellingoftheD#andtheEb.Ifyouremember,that'scalledanenharmonic.Now, thespellingof those intervalswillchangeas thenotechanges itsname — this is regardless of whether or not those intervals “sound”exactly the same. For example, if the interval is spelled C to Eb, theintervaliscalledaminorthird.IftheintervalisspelledCtoD#,youcan'tcall itaminorthirdanymore.Thirdintervalsarereservedforintervalsofthreenotes(CtoE).SincethisintervalisfromCtoD,itmustbecalledasecond of some sort. In this case, the correct name is an augmentedsecond. Enharmonic spellings give birth to the need for terms likeaugmentedanddiminishedintervals.AugmentedIntervalsAnaugmentedintervalisanyintervalthatislargerthanamajororperfectinterval.FIGURE2.20showsafewexamplesofaugmentedintervals.

Traditionally, you can only augment second, third, fourth, fifth, or sixthintervals. Use augmented intervals when the notes are spelled in anunusualwayandyouhavetoadheretotheruleof“it'sthreenotesapart,soImustcallitsomesortofthird,butit'slargerthanamajorthird.”Thedecidingfactorinallofthisishowtheintervalisspelledonpaper.Lookfor the distance between the notes and use that as your guide.Again,augmented intervalsareusedwhenan interval is too largetobecalledmajororperfect.DiminishedIntervalsDiminished intervalsaremorespecialized.Adiminished intervalnamesan interval that has been made smaller. Typically, diminished intervalsareusedonlytomaketheperfectintervalssmaller.Inreality,thisisjustanother spelling conventionmore than anything else. You canmake afourth or a fifth diminishedby loweringanyof theperfect intervals onehalf step. You can also make a minor interval diminished by simplylowering aminor interval one half step down. The interval ofC toEbbwould be a diminished third. The interval of a diminished fifth iscommonlycalledatritonebecause,atsixhalfsteps, itsplits theoctaveevenlyinhalf(twelvehalfstepsinanoctave).

INTIME

Both the diminished fifth and the augmented fourth are consideredtritones—thespelling isnot important,onlythedistance.Thetritoneissuch a dissonant interval it was called diablo en music (“the devil inmusic”)duringtheMiddleAges,andwassomethingtoavoidatallcosts.Thingshavechanged,andyoudoheartritoneintervalsinmodernmusic,buttheystillsounddissonant.ChromaticIntervalsThechromaticscaleincludesalltwelvetones(includingallthehalftones)intheoctave.Thus,chromaticintervalsareasemitoneapart.FIGURE 2.21 provides a full chart of every possible interval andenharmonic spelling in one octave to show you how all this lays out.Notice how the number of half steps an interval has is not always thedeciding factor in itsname.Becauseofenharmonicspellings, therearepluralitiestodealwith.Alwaysremembertolookatthedistancebetweenthewrittennotesandthenlookforthequality.Hereisanotherwaytounderstandintervals.Ifthetopnoteoftheintervalexists in the major scale of the bottom note, the interval is major orperfect.Ifnot, it'sminor,diminished,oraugmented.Hereisalittlechartto help you. An arrow in either direction indicatesmovement of a halfstep.Diminished←Minor←Major→AugmentedDiminished←Perfect→Augmented

InvertedandExtendedIntervals

How far is it fromC toG?Youmight say a perfect fifth.Youmight beright.However,whatiftheintervalwentdown?WhatiftheCwerewrittenhigher on the staff than theG?Would it still be a perfect fifth? In thiscase,itwouldactuallybeaperfectfourth.So far, this text has dealt with ascending intervals. But what happenswhenyoureadanintervaldown?Whenyounameanyinterval,suchasCtoG,youmustspecifyifit'sanascendingintervalorifit'sdescending.If the interval ascends, no worries, you've been trained to handle thatwithout a problem.On the other hand, if the interval descends, it's notspelledthesameway.Afifth interval,whenflippedaround, isnotafifthanymore.Thisisbecausethemusicalscaleisnotsymmetric.IntervalInversionAnyintervalthatascendscanbeinverted(flippedupsidedown).FIGURE2.22looksattheexampleofCtoGfromthelastsection.Whenyouflip

theperfectfifth, itbecomesaperfectfourth.Wouldn't itbegreatiftherewereasystem tohelpyou invertany interval?Thankfully, there is.Youaregoingtolearntousetheruleofninetoinvertanyintervalwithease.

TheRuleofNineThe rule of nine is defined as such:When any interval is inverted, thesum of the ascending and descending intervals must add up to nine.Using the first example, the interval fromC toG is a perfect fifth. TheintervalfromGtoCisaperfectfourth.Whenyouaddup5and4,youget9.Test thisout ina fewnotationexamples inFIGURE2.23.What's theinversionofathird?It'sasixth,because3and6addupto9.Thisworksonanyinterval.

InvertedQualitiesWhenusingtheruleofnine,it'seasytofliptheintervalsoverandgetthecorrect inversion.But the typeof interval,orqualityof the interval,alsochanges as you invert it. The rule of nine tells you the name of theintervalnumerically,butthetypeofintervalthatitbecomes(major,minor,perfect) will change as intervals are flipped over. The answer to thisproblemhasasimplesolution.Hereiswhathappenstointervalqualitieswhentheintervalsinvert.

Iftheintervalwasmajor,itbecomesminorwheninverted.Iftheintervalwasminor,itbecomesmajorwheninverted.

Iftheintervalwasperfect,itremainsperfectwheninverted.

Thisiseasytoremember.Majorbecomesminor,minorbecomesmajor,andperfectstaysperfect.Asyoucansee,byusingtheruleofnineandchanging the typeof intervalaccordingly,youcan invert intervals likeapro!

3

TheMajorScale

Themajor scale is one of the first structural elements that you shouldlookatinmusic.Asimpleformationofnotescanbringyouintothemindof the composer, allowing you to see what elements are used incomposition. Major scales are multifaceted and are used for melodiesandharmonies.Anyoneinterestedinlearningaboutmusictheoryshouldknowasmuchaspossibleaboutthemajorscale.

ScalesDefined

You'veheardthetermmajorscalemanytimesbefore.Manyofyouplayscalesinsomeshapeorformanddon'tevenknowit.Scaleshavebeenmentionedalreadyinthisbook.Nowit'stimetolookmorecloselyatwhatmakesthemtick.Forstarters,here'sabasicdefinitionofwhatascaleis:A scale is a grouping of notes together thatmakes a key.Most of thescalesthatyouwillencounterhavesevendifferentpitches(butatotalofeight notes, including the repeated octave) in them. Some scales thatyou'll learnabout later in thebookcontainmore thansevennotes,andsomecontainless.Thebread-and-butterdefinitionofascaleisthatit'saseriesofeightnotes (sevendifferentpitches) thatstartandendon thesamenote,whichisalsocalledtheroot.Therootnamesthescale.IfascalestartsandendsonC,theroot isCandthescale'snameistheCsomething(major,minor,etc.)scale.Whatthatsomethingisdependsonitsintervallicformula.Thankfully,youknowathingortwoaboutintervals.Sincethischapterfocusesonmajorscales,lookataverybasicCmajorscaleinFIGURE3.1.

Asyoucansee,thescalestartsandendsonCandprogressesupeverynoteinorder.SinceCmajorcontainsnosharpsandnoflats,it'saneasyscaletounderstandandremember.Onthepiano,it'ssimplyallthewhitenotes.TheCscalecontainssevendifferentnotes:C,D,E,F,G,A,andB.ThelastCisn'tcounted,asit'sjustarepeatednote.Themajorscalehaseightnotesintotal,though.WhatmakesthisamajorscaleisnotthefactthatitusesthenotesC–D–E– F–G–A–B–C. That only tells you that it's one particular key. Musictheory looks for larger scale ideasand tries to tie them together.Whatmakes that scale amajor scale are the intervals between the notes. Ifyousimply lookat thedistancefromeachnote in thescale to thenext,youseeapatternofhalforwholesteps inaseries.Thisseries,whichyoucanalsocallaformula,isexactlywhatyouaregoingtolearnaboutnow.FIGURE3.2showstheCmajorscalewiththeintervalsdefined.

What you come up with is the interval series of Whole, Whole, Half,Whole,Whole,Whole,Half, orWWHWWWH for short.This is theonlythingthatmakesanyscaledifferentfromanyotherscale:theformulaoftheintervals.Aslongasthatintervalformulaispresent,youhaveamajorscale. It's an absolutely perfect system, because you can start on anynoteyoufeel like(anyof thetwelvechromaticnotes, that is)andfollowthesesimplerules:

1. Pickarootnote.

2. Progressupsevennotesuntilyoureachtheoctave.

3. Use the formulaofWWHWWWHbetweenyournotes toensure thatyouhavethecorrectspelling.

4. Makesurethatyouuseanyletteronlyoncebeforetheoctave.

Ifyoucanfollowthoserules,youcanspellanyscale.Here'show.

SpellingScales

FIGURE3.7 will be an exercise where you will be given four differentnotestostarton,andyouwillbeaskedtofillinthecorrectnotestospellthemajor scales.To seehow it's going towork, tryonenow.Start outwitha root note,which in thisexamplewill beAb,as seen inFIGURE3.3.

Next,placetherestofthenotesonthestaff.Now,don'tbetooconcernedaboutwhetheryouhavethecorrectintervalsoreventherightspellings,youjustneedtohaveoneofeachlettername,inorder,uptotheoctave.SosimplyaddaB–C–D–E–F–GandAtoFIGURE3.4.

Nowthatyouhavetherawnotesin,youneedtoaddtheintervals.Theformula isWWHWWWH,soyouaddthe intervalsbetweenthenotesofthescale,asseeninFIGURE3.5.

You'renearlydone.Allyouhavetodoisactually“engage”the intervalsandmakesureyourscaleisspelledcorrectly.Followthisprocess:

YouneedawholestepfromAb.AwholestepawaywouldbeBb.AddaBb

tothescale.YouneedawholestepfromBb.AwholestepawaywouldbeC,whichyoualreadyhavewrittendown,soyoudon'thavetochangeanything.YouneedahalfstepfromC.AhalfstepawaywouldbeDb,soyouputaflatinfrontoftheDtomakeitDb.YouneedawholestepfromDb.AwholestepawayisEb,somaketheEanEb.YouneedawholestepfromEb.AwholestepawayisF,whichyoualreadyhave,sonochangeisneeded.You need awhole step fromF.Awhole step away isG,which you alsoalreadyhave,sonochangeisneeded.YouneedahalfstepfromG.AhalfstepawayisAb.ChangetheAtoAb.(Coincidentally,sincethisisabscale,everyAinthisscaleisflat,soyoucouldhavejustmadeitflat.)

Now,lookatFIGURE3.6.

That's it! You have a scale that ascends up using every letter of themusical alphabet once. The scale follows the pattern ofWWHWWWH,whichallmajorscales follow.Play itonyour instrument just tobesure,andthatfamiliarsoundwilltellyouthatyou'recorrect.FIGURE3.7 is practice time. Start on each note and spell yourmajorscales. You can use the method above or go your own way. Justremember that you have to use the WWHWWWH interval pattern,otherwisetheywon'tbemajorscales.

SomeThoughtsWehavenowseena total of sixmajor scales: the twoyouhavebeenshowninfull(CandAb)andthefouryouhavejustdone.Thisisagoodtimetopauseandpointoutsomeveryinterestingthingsthatyoushouldnotice.First, eachof the scales is totally unique.What does thatmean?Well,eachof themhasdifferentpitches.Notwoscales lookthesameonthesurface. While it's true that each of the scales uses the exact sameintervalpattern,thatfactisnotclearuntilyouanalyzethescale.Thefactthat each scale uses a unique set of pitches is whatmakes each one

unique,andthatissomethingthatyoucanclearlysee.

INTIME

LudwigvanBeethoven(1770–1827)composedinalmosteverygenreofmusicduringhis lifetime, includingpianosonatas,chambermusic,ninesymphonies,andanopera.AlthoughborninBonn,Germany,hemovedtoVienna,Austria,asayoungman,and itwas there thathewrotehismostcelebratedworks,includingthefamous“OdetoJoy.”Scales are a bit likeDNA in that each one is unique. This factmakesthemprettyeasytospotifyouknowwhatyou'relookingfor.Second, did you notice that the scales that contain sharps use onlysharpsandneverthrowinaflatortwo?Also,thescalesthatcontainflatsuseonly flatsandneversharps?That's right,whenyouspell scalesoranalyze inmusic,youwillnotice thatscaleshaveeither flatsorsharps;yourarelyseebothsharpsandflatsinthesamescale(seeChapter4fortherareexceptionstothisrule,posedbytheharmonicandmelodicminorscales).Thesetwopointswillhelpyouunderstandscalessomuchbetterandmakeyourlifeinmusictheorysomucheasier.Atthispoint,youmightwanttoseeallthescales,justforreference.Hereareallofthechromaticmajorscales,startingoneverypossiblechromaticnote,includingtheenharmonics(FIGURE3.8).Noticethatbasedonwhichchromaticnoteyoustartyourscaleon,youmay get a scale that spells pretty easily. On the other hand, certainscales contain double flats or double sharps in order to keep theWWHWWWHpatterngoingandutilizeoneofeachnoteinthealphabet.Somespelleasilyandothersareapain.Becauseofthat,youdon'tseeall the chromatic major scales often; you typically see about scales,whicharetheonesthatspellwithoutconstantuseofdoublesharpsanddoubleflats.Becauseofenharmonicnotes,you'regoingtohavescalesthathavetheexactsamesoundbutarespelleddifferently.AgoodexampleisAbandG#.ThekeyofAbhasfourflatsandisn'ttoohardtospelland/orreadin.The key of G# has six sharps and a double sharp. Which would you

rather read in if both scales actually sounded the same?Even thoughthere are twenty-four possible scales, there are only twelve chromaticnotesinthescale,andyouwillfindyourselfreadingintheeasiesttwelvekeys.Remember,musicisn'tjustforthecomposer;italsohastosuittheplayeraswell.

PointtoConsider

Nowthatyouknowthatflatsandsharpsaremutuallyexclusiveitemsinscales, thisshouldhelpyouspellyourscalesmoreaccurately. Ifyou'reworking on spelling a scale and you're seeing a mixture of flats andsharps,youdidsomethingwrong.Ifyouseemostlyflatsandonesharp,you did somethingwrong. Scaleswill simply always look cohesive thisway,andthatwillmakeyourjobabiteasier.

ScaleTones

Eachscalehasseventones(eight ifyouincludetheoctave).Therearetwowaystotalkaboutnotesinthescales:bynumberandbydegree.ScaleTonesbyNumberIn a C major scale, the note C would be considered “one” becausenaturally, it's the first note of the scale. A different note can then beassignedtoeachofthescaletones,onethroughseven.Thisisusefulforafewreasons.Firstofall,regardingintervals,thedistanceofanintervalismeasuredwithanumber,which isoften taken fromascale.Second,sinceallmajorscalesaremadeof thesamepattern, theoryonceagainlookstoa“universal”systemfornamingthesescales.Ifapieceissaidtostartonthethirdnoteofascale,youcanlatertakethatideaanduseitinanykey. Ifyousimplysay,“ItstartsonE,”you losethecontextofwhatscale/keyyouareinandneedextrainformationinordertoworkwiththeidea. Using numbers is a handy way to think about scales and scaletones.It'salsogoingtocomeinhandyaschordsandchordprogressionsarediscussed,aschordprogressionsarelabeledwithRomannumeralsexclusivelyinmusictheory.

INTIME

Originating in the thirteenthcentury, themotet (derived fromtheFrenchmot, meaning “word”) is an early example of polyphonic (multivoice)music. Motets were generally liturgical choral compositions written formultiple voices. Johann Sebastian Bach wrote many motets, seven ofwhichstillexisttoday.ScaleTonesbyDegreeTheotherway thatyoucandescribe the tonesof themajorscale isbygiving a distinct name to each degree, instead of a number. This istraditionallyusedinclassical/academicmusictheorycontexts,butsomeofthetermshavebecomeuniversalandyoushouldatleastbeawareofthem.Youmighthaveseenthetermtonicusedtorefertotherootofanyscale, and that is an example of the names given to each note in themajorscale.Thechartbelowwillshowyouhowtonameeachnoteinthemajorscale.

NamesofNotesintheMajorScale

ScaleDegree NameFirst TonicSecond SupertonicThird MediantFourth SubdominantFifth DominantSixth SubmediantorSuperdominantSeventh LeadingTone

Eighth(theOctave) TonicThese names are also used when talking about chords and chordprogressions, so knowing them will aid you in understandingprogressions.Whilethesetermsaren'tthrownaroundnearlyasmuchasthe numerical names for the tones, certain names such as the tonic,

dominant, and leading tone are used in the everyday vernacular ofmusiciansdespitethefactthatnumericalnamingismorewidespreadandeasiertouse.Ifyoufindyourselfinaformaltheorysituation,youwillfindthese names of scale degrees used, and luckily, now you'll knowwhattheymean!

HowScalesAreUsedinMusic

Scalesareeverything.That's a huge statement, but as you're going tosee, scales are going to spin off into all sorts of directions.By itself, ascale is an organization of pitches, which are called sounds. Thisorganization makes scales more than just a set of random pitches; itmakesthemintoasetofsoundsthatmusiciansandtheoristscallakey.Akeyisaconceptyouwillseeinmuchmoredetailthroughoutthisbook.To understand the concept, consider that a key is like a family:Everyone's related in someway.When you use a scale to compose amelody, those notes sound like they belong together. When you stayexclusively in a scale, or a key, you get a very regular and expectedsound. Composers use scales to construct melodies. Because keysalready have the built-in feeling of “belonging together” or, better yet,“sounding together,” it isn't hard to take a scale and make it into amemorablemelody.Literallyhundredsofmelodies thateveryoneknowsandcanhumat thedropofahat come fromascaleof somesort.Sothink of a scale as a vocabulary formusical phrases,much like lettersformwordsthat,inturn,formsentences—seetheparallels?Whenyouplayascaleonenoteatatime,yougetamelody.Whenyoutakesnotesfromscalesandcombinethembyplayingthemtogether,yougetharmony.Thisissomethingthatyouwilllookatinmoredepthlaterinthis book. For now, just accept that you can break the vastmajority ofmusic down intomelody and harmony.Now that you know that scalescan give us melodies and harmonies, you start to understand theimportanceofscales.Majorscalesarenottheonlyscales inthemusicaluniverse.Themajorscale is very important, but a true understanding of music would beincomplete without a look at the minor scale, the other basic scale ofmusic.Nowit'stimeforsomeminorexploration.

4

TheMinorScale

Thenextstoponyourjourneyintomusicalunderstandingisacloserlookattheminorscale.Minorscaleshavetheirowndistinctpatternand,moreimportantly,theirownsound.Incontrastwithmajorscales,minorscaleshaveadarkerandheaviersound.They,too,havetheirownconstructionand order.Major andminormake up the two fundamental elements ofmusicalscales thatarecommonlyusedandpracticed inmusical theoryandwritingandperformance.

MinorColors

By thispoint, youhave learneda lot about themajor scale.Themajorscale is an essential, commonly used musical scale. It represents acertain “color” or type of sound. Theminor scale is a different color, adarkersound.It'salsotheothermainmusicalscale.Asamusician,you'llencountertheminorscaleoften.Theminorscale isanalternative to themajorscale,yieldingadifferentmusical color than themajor scale. Certain pieces can conveymoodsandfeelingsbasedonthekeyandtypeofscalethey'rewrittenin.Majorscalesdefinitelyhaveabrightandcheerysoundtothem.Sincemusicisall about contrast, theminor scale and its darker sound are needed tojuxtaposewiththemajorscale.Thinkofitasanotherflavorinyourspicerack.There are a few ways to look at the minor scale. One is a definitiveapproachand theother is thederivativeapproach.Youwillexplore thederivative approach later. For now, treat the minor scale as a veryseparateentity thathas itsownformula, intervals,andusage.Lateron,you can take a look at the bigger picture and make some fun

connections.

TheDefinitiveApproach

InChapter2,intheexplanationofintervals,theexampleoftheCminorscaleillustratedsomeminorintervalsandalsoshowedacontrastagainstCmajor.FIGURE4.1showstheCminorscale.

Bynow,youshouldhaveinyourheadthatCmajorhasnosharpsorflats—that'swhatmakesitsuchaneasykeytoworkwith.Now,ifyoutakeapeekatFIGURE4.1again,youwillnotice that it'sdifferent.Sure, it'sadifferentscale,eventhoughithasthesamerootofC.YoulearnedaboutthedifferencesintheintervalspresentinthisscaleinChapter2,butyouneedtolearntheunderpinningsoftheintervalsbetweenthenotessoyoucan come to a formula that enables you to spell any minor scale youneed to.Remember that theory is an attempt to find universal parts ofmusic, elements that apply over the entire range of music. SimplyknowingthataCminorscaleisspelledC–D–Eb–F–G–Ab–Bbgivesyoutheabilitytorecognize,spell,andworkwithonlyonekey.However,ifyoulookat thescalefor its intervalliccontent,youcantakethat informationandapplyitanywhere.Timetobreakthescaleintopieces.FIGURE4.2showsthepatternofhalfandwholestepsthatarepresentintheCminorscale.

Not surprisingly, there is a different interval pattern than in the major

scale. It is WHWWHWW. You can use that interval pattern as aconstructionblueprintandspellanyscaleyouneedto.Nowtakeastep-by-steplookathowtocreateanyminorscale.Firststartoutwitharootnote,suchasC,asseeninFIGURE4.3.

Thenextthingyouwanttodoisplacetherestofthenotesonthestaff.Now,don'tbeconcernedwithwhetheryouhave thecorrect intervalsoreventherightspellings.Youjustneedtohaveoneofeachlettername,inorder,uptotheoctave.SosimplyaddaD–E–F–G–AandBtoFIGURE4.4.

Nowthatyouhavetherawnotesin,youneedtoaddtheintervals.Theformula isWHWWHWW,soadd the intervalsbetween thenotesof thescale,asseeninFIGURE4.5.

You'renearlydone.Allyouhavetodoisactually“engage”the intervalsandmakesureyourscaleisspelledcorrectly.Here'stheprocess:

YouneedawholestepfromC.AwholestepawaywouldbeD,whichyoualreadyhave.YouneedahalfstepfromD.AhalfstepawaywouldbeEb,soyouaddaflatbeforetheE.YouneedawholestepfromEb.AwholestepawaywouldbeF,whichyoualreadyhave.

You need awhole step fromF.Awhole step away isG,which you alsoalreadyhave.You need a half step fromG.A half step away isAb, so you add a flatbeforetheA.YouneedawholestepfromAb.AwholestepawayisBb,soyouplaceaflatbeforeB.YouneedawholestepfromBb.AwholestepawayisC.

Nowtoseeyourfullscale,lookatFIGURE4.6.

That'sit!Younowhaveascalethatascendsupusingeveryletterofthemusical alphabetonce.Your scale follows thepatternofWHWWHWW,whichallminorscalesfollow.Now try another one:FIGURE4.7 is your practice time. Start on eachnoteandspellyourminorscales.Youcanusethemethodaboveorgoyour ownway. Just remember that you have to use theWHWWHWWintervalpattern,otherwisetheywon'tbeminorscales.

Usingthespaceprovided,spelltheF,D,AandG#Minorscales.UsetheWHWWHWWintervalpatterntospellthescaletones.

TheDerivativeApproach

Being able to form scales from pure intervals is a common and usefulway tospell scales.Anotherconvenientway tospellminorscales is toderivethemfrommajorscales.Manystudentsbecomecomfortablewithspellingmajorscalesandfinditeasytorecallthosescales.Ifyoulookat

thedifferencebetweenamajor scaleandaminor scalewith thesameroot,youcanformanotherwaytospellminorscales:derivingthemfrommodificationstothemajorscales.FIGURE4.8showsaCmajorscaleonthetoplineandaCminorscaleonthebottomline.

TheHighlightedNotesAreTheOnlyChangesBetweenCMajorandCMinorWhatyouseeisthatthescalesareverysimilar.ThenotesC,D,F,andGstaythesame.Whatischangingisthatthethird,sixth,andseventhnotearechangingfromthemajorscaletotheminorscale.Morespecifically,thethird,sixth,andseventhscaledegreesare loweredexactlyonehalfstepdownfromtheirspellinginthemajorscaletomaketheminorscale.Sinceyouhavedealtwith intervals indetail, takeacloser lookatwhathappened when you went from the major scale to the minor scale.Simply, the intervals of themajor third,major sixth, andmajor seventh(whenmeasuredfromtherootofC)areallchangedfrommajorintervalstominorintervalsbysimplyloweringeachoftheintervalsonehalfstep.Ifyou remember from our discussion of intervals, the only differencebetweenamajorintervalandaminorintervalisthattheminorintervalisonehalfstepsmallerthanthemajorinterval,orviceversa.So,whatthismeansisthatyoucantakeanymajorscaleandmakeitintoa minor scale by simply lowering the third, sixth, and seventh scaledegreesonehalfstep.Doingthis,youarederivingtheminorscalefromthespellingof themajorscale—usingthederivativeapproach.This isone more way to look at spelling the minor scale, and you should becomfortablewithallthedifferentwaystospellscalesasyouneverknowwhichonewillworkthebestforyou!

DegreesinMinorScales

Asexplained inthepreviouschapteronmajorscales,minorscalescanhave scale degrees. Also, as with major scales, you can refer to thetonesintheminorscalenumerically,justlikeyoudidwhenlookingatthederivative approach for spelling minor scales (talking about the third,sixth,andseventhscaledegrees). Incaseyouskipped themajorscalechapter,hereisanexplanationofscaledegrees.Theotherwaytodescribethetonesoftheminorscaleistogiveadistinctname insteadof anumber toeachdegree.This is traditionally used inclassical/academicmusic theory contexts, but some of the terms havebecomeuniversal,andyoushouldat leastbeawareof them.The termtonic,usedtorefertotherootofanyscale,isanexampleofthenamesgiventoeachnoteintheminorscale.Thetablebelowwillshowyouhowtonameeachnoteintheminorscale.NamesofNotesintheMinorScale

ScaleDegree NameFirst TonicSecond SupertonicThird MediantFourth SubdominantFifth DominantSixth SubmediantorSuperdominantSeventh LeadingTone

Eighth(theOctave) TonicThese names are also used when talking about chords and chordprogressions, so knowing them will aid you in understandingprogressions.Whilethesetermsaren'tthrownaroundnearlyasmuchasthe numerical names for the tones, certain names such as the tonic,dominant, and leading tone are used in the everyday vernacular ofmusicians despite the numerical naming being more widespread andeasiertouse.Ifyoufindyourselfinaformaltheorysituation,youwillfindthese names of scale degrees used, and luckily, now you'll knowwhattheymean!

MultipleScales—ScaleClarity

Incontrasttothemajorscale,whichcomesinonlyonevariety,theminorscalecomesinafewdifferentforms.Whatyouhavebeguntoexploreisthenaturalminorscale.Whenpeople talkaboutminorscales, theyaretypically talkingabout thenaturalminorscale,whichhas the formulaofWHWWHWW.However,therearetwootherminorscalesthatyouneedto know about, which have different interval patterns than the naturalminorscale:harmonicandmelodicminor.

PointtoConsider

Thenaturalminorscaleiscallednaturalbecauseit'sanaturallyoccurringextension of the major scale, also called a related or relative minor.Relativeminorswill bediscussed inChapter5.Theotherminorscalesarederivativesofthenaturalminorscalesandaremadebymodifyingtheoriginalnaturalminorscale.Harmonicandmelodicminorscaleshaveaslightlycontroversialstanceintraditionalmusictheory.Sometheoristsarguethattheyarenot“true”scales because they are not naturally occurring patterns. But musictheoryisabout identifyingwhatyouseeandhear inmusicandwhetherornotyoubelievethatthescalesshouldhavetheirownnames,theyarefound inmusicoftenenoughthatyouneedtoknowabout them. Inanycase,harmonicandmelodicminor scalesarepart of thebasic level oftheoryknowledge,andyousimplyhavetoknowwhattheyare.HarmonicMinorHarmonicminoristhefirstvariationoftheminorscaleyoushouldknow.It's a simple change of the natural minor scale. To form the harmonicminorscale,simplytakeaminorscaleandraisetheseventhnoteuponehalfstep.Whatyouaredoingiscreatingwhatiscalledaleadingtonetothescale.Itsimplygivesaverystrongpullfromthelastnoteofthescalebacktothetonic.Allmajorscalesalreadyhavetheleadingtonebuiltin,butnaturalminorscalesdonot;theyhaveawholestepbetweenthesixthand seventh tones. Interestingly, this is not why composers use theharmonic minor scale. If you look at the name of the scale, you gainsomeinsightintowhythescaleexists.Simply,theraisingoftheseventhtonegivescomposersaslightlybetterharmonicpalettetoworkwith—itgivesusbetterchords.Theharmonicminorscaleprovidesamajorchordon the dominant degree and a diminished chord on the leading tonedegree.Bothofthesechordsareextremelyimportanttocomposersandmusicians and are used so frequently that the harmonic minor scaleactuallybecamea“scale.”

HereistheDharmonicminorscale.

Theformulaofthescaleisinterestinginthatyounolongerstrictlykeeptowholeandhalfsteps.Infact,betweenthesixthandseventhtone,youhaveastepandahalf (anaugmentedsecond tobemoreexact).Thatlargeleapbetweenthesixthandseventhtoneisawkwardmelodically.Ifyouplaythescalebyitself,youmayconjureupimagesoftheMiddleEastand the traditionalmelodiesof theJewishreligion,whichuses theharmonicminorscaleasmaterialformelodies.It'shardtousethescalebyitselfandnothaveitsound“ethnic.”Melodically, you are left with an awkward scale to work with. To workaroundthis,composerscreatedyetanotherscaletosolvethisdilemma:themelodicminorscale.MelodicMinorTo fix the strange sound that the harmonic minor scale makes, themelodic minor scale was born. The melodic minor scale is made byraisingthesixthandseventhtonesofanaturalminorscaleonehalfstepeach.The whole point of the melodic minor scale is to smooth out the skipbetween the sixth and the seventh tones in the harmonicminor scale.The raised seventh tone in harmonic minor is crucial to minor scaleharmony,butthescalewhenplayedalonesoundsstrange.Byraisingthesixth as well, the melodic minor scale works better for melodies andharmonies.You lose thataugmentedsecond interval between thesixthandseventhtoneandyougetbacktousingwholeandhalfsteps.Because the change in the scale makes it melodically smoother, it'scalled the melodic minor scale. Both the harmonic and melodic minorscalesfallundertheumbrellaofbasicmusictheory,whichisimportanttounderstandtomakesenseofreadingmusic.HereisthemelodicminorscaleinthekeyofDminor.

ClassicalMelodicMinorVersusJazzMelodicMinorHereisabitofveryspecificinformationforyou.Themelodicminorscalewhen used and practiced in a classical setting has some odd usagerules.The rule is thatwhenyouplay thescaleandascendwith it, yousharp the sixth and seventh tones, just like in the construction of themelodicminorscale.Theoddpart is,whenyougo todescendwith thesamescale,youreturnthesixthandseventhtonesbacktotheirnaturalminor spellings. This is something that is taught in classical musictraditions, and if you study an instrument with a classical teacher, youmaypracticeyourscales thatway:ascendingonewayanddescendinganotherway.FIGURE4.11iswhatthatscalewouldlooklike:

Nowadays,andespecially in jazzcircles, themelodicminorscale isnotaltereddependingon itsdirection; it is theexact samescalenomatterwhich direction it's played in (the sixth and seventh remain raised thewholetime).

PointtoConsider

Ratherthandoallyourpracticeinthisbook,considerkeepingaseparatenotebook of staff paper in which to practice spelling scales and otherconceptsandtojotdownnotes.Doasmuchasyoucantoreinforcethematerial presented here, to accelerate your learning and mastery ofmusictheory.

VariantVariables

Oneofthepointsmadeaboutscalesearlierinthisbookisthattheyarecomposedofhalfandwholestep intervals.Harmonicminorhasprovedthatscalesdon'talwayshavetohavethat intervalpattern.Theadditionof the augmented second (a step and a half) breaks that pattern.Alsoworthmentioningisthatalthoughitwasearlierstatedthatallscalesuseeither flatsorsharpsbutnotboth, in thecaseof theharmonicand themelodicminorscales, that rule is thrownout thewindow(not forall thescales, but for some of them). On a positive note, anomalies like thismakethescaleseasiertospotwhenyouanalyzemusic,asmixturesofsharpsandflatscanbethecallingcardsofthesescales.Takethetimeonyourowninstrumenttoplaythroughallofthesescalesonaregularbasis.Beingabletoplaythesescalesandrecognizethemvisuallyandaurallywillhelpyouunderstandthemonadeeperlevel.Foryour reference, all of the chromatic minor scales are on the followingpages.

5

MusicalKeysandKeySignatures

Asyoulearnedearlierinthisbook,intervalsarethesmallestelementofmusic.Intervalscombinetoformscales.Scales,inturn,makeupmelodyandharmony, the lifebloodofmusic.Thekey is thenextmajor leveloforganizationinmusicandoneofthemajorelementsofmusicalanalysis.Inthischapter,youwilllearnwhatmakesakey,howtoidentifyakey,andwhyyoushouldcareaboutthemusicalkey.

MusicalOrganization

Nowthatyouhaveexploredtheprincipalscalesthatmakeupmusic,it'stimetoexploretheideaofwhatakeyactuallyis.Akeyisthefirstleveloforganizationintonalmusic.Anoversimplifieddefinitionoftonalmusicismusicthatiscomposedofkeys,chords,andscales.Ofcourse,thereareforms of music that do not rely on keys, such as modern and atonalmusic.Forthepurposeofthisbook,tonalmusicmakesupthemajorityofmusic from the “commonpractice”period (circa1685–1900)and is stillverymuchinusetoday.Whenyoustudytheory,youstartinthecommonpracticeperiodandmoveforward.Ifyouwanttostudytonalmusic,keysaregoingtobeveryimportanttoyou!Theconceptofmusicalkeysisverycloselytiedtoscales,bothmajorandminor.Thesimplestdefinitionofamusicalkeyis:Akeydefinesthebasicpitches for a piece ofmusic. A key does not have to use those notesexclusively,butthemajorityofthenoteswillcomefromthescaleofthatkey. You know from studying the major and minor scales that no twoscales are ever spelled alike. Because each scale/key is unique, it isfairly easy to spot them inmusic and understand some of themusicalstructureinvolved.Morethananythingelse,keysaretheDNAofmusic.

PointtoConsider

Key signatures correspondwithmajor andminor scales. Since a greatdealofwrittenmusicadherestomajorandminorscales,keysignaturesare a convenient way to indicate keys and scales that are frequentlyused.Keysignaturescanalsovisuallytellyouwhatkeyapiecemaybein,simplyfromlookingatit.Akeyisaslightlyabstractconcept,whichcanbeachallengetodescribe.A key defineswhat notes can be used to create an “expected” sound,suchas consonant andnot dissonant.As youprogressasamusician,keys and key signatureswill becomemore important than just definingwhat notes to play. Keys can give you a glimpse into themind of thecomposerandhelpyouunravelhowmusic is composed. Inanyevent,youneedtoknowalotaboutkeysandtheirkeysignaturesifyouwanttobeacompetentmusictheorist.WhatIsaKeySignature?You know all about sharps and flats now. You can comfortably spellscalesinanykey.Thatknowledgeisonestepremovedfromrealmusicand how it functions. Observe the spelling of the A major scale inFIGURE5.1versusFIGURE5.2. Insteadofhavingeachsharpand flatspelledout,youcanuseakeysignaturetosimplymakeall theFs,Cs,andGssharp.MostmusicianswouldratherreadFIGURE5.2anydayoftheweek.

Simply,akeysignatureisusedtoindicatethatacertainnoteornotesis

goingtobesharporflatfortheentirepiece.Itcleansupthewrittenmusicforthereaderandeliminatestheneedforthesharpandflatsymbolsthatwould otherwise appear throughout. A good reader will be used toreadinginkeysignaturesandpreferthem.TheKeySignaturesInChapters3and4,yousaweverypossiblescaleinexistence,eventhereally odd enharmonic keys like Fb major that you rarely see. Keysignatures apply to the common keys/scales and rarely deal with theenharmonicones.Oneofthemostcommonthingsstudentsencounteristhe “circle of keys,” a graphic representation of all the keys that youtypicallysee.Sinceeverykeyorscalehasitsownuniquespelling,eachofthekeyslooksdifferentaswell.Eachsinglekeysignaturecorrespondstoonesinglemajorkey.Hereisthecircleofkeys(FIGURE5.3).

TheSystemofKeySignatures

Keysignaturesuseaspecificsystem.Notjustanynotecanappearinakeysignature.Thereisanorderandalogictokeysignaturesthatmakesthemunderstandable.Keysignaturesappearintwovarieties:sharpkeysignatures and flat key signatures (excluding C major, which has no

sharpsor flats).Akeysignaturewillalwaysdisplayonlysharpsoronlyflats. You will never see both in the same key signature. Within thegroupings of “sharp keys” or “flat keys,” there is an order to howindividualnotesappear.Takealookatsharpsandflatsseparately.Just like proper scale spellings will result in either sharps or flats, keysignatures follow theexact same rule.Theydosobecausescalesandkey signaturesare showing you the same information,which is exactlywhytheyhelpyouunderstandmoreaboutthemusic.Sharpsappearinkeysignaturesinaspecificorder.Hereistheorderofsharpsastheyappearinkeysignatures:F#,C#,G#,D#,A#,E#,B#.Thesharpsalwaysfollowthatorder.Alsoimportanttonoteisthatsharpsappearinthesameorder.Ifthekeyhasonesharp,itwillbeanF#.Ifthekeyhastwosharps,itwillhaveF#andC#.Italwaysworksthroughthepatternthatway.Agreatwaytoremembertheorderofsharpsistousealittlemnemonicdevice:FatherCharlesGoesDownAndEndsBattle.Thefirst letter of eachword corresponds to the sharps as they appear. It'ssilly,butitmightjusthelpyouremember.

PointtoConsider

Even though key signatures may appear confusing at first, mostmusicianswouldhaveahard time readingwithout them.Constant flatsand sharps placed throughout music can bemore challenging to readthanasinglekeysignature.Just like sharps, flats appear in a specific order as well. Also just likesharps, theorderof flatswillalsoappear in thesameorderevery time.Hereistheorderofflatsastheyappear:Bb,Eb,Ab,Db,Gb,Cb,andFb.Thereisalsoaneasywaytohelpyouremembertheorderofflats:Justreverse the saying for sharps! Battle Ends And Down Goes Charles'Father.Onesayinggetsyoubothsharpsandflats—prettyconvenient!LearningtheKeyNamesIfyoustareatthecircleofkeyslongenough,youmightmemorizewhateachkeyrepresents.Thereareafewtricksthatcanhelpyouout.Ontheflatside, thefirstkey isF,whichstartswiththesameletterasthewordflat.Afterthat,BEADthenamesofthenextfourflatkeys.That'sahandyway to learn some of the keys. The sharp side is a bit harder. BEADappearsagainon the rightside.However, thereare two little tricksyoucanlearnforinstantlynamingakeyjustbylookingatit.TheSharpKeyTrickFor any key that has a sharp in it, naming the key is as simple asfollowingtwoeasysteps.First,findthelastsharp(theoneallthewaytotheright).Onceyou'vefoundandnamedthenotethatcorrespondstothesame line or space the sharp is on, go one note higher, and you'venamed the key. LookatFIGURE5.4. The last sharp in this key isA#.Going one note above this is the note B. Five sharps is, indeed, thecorrect key signature for the key of Bmajor. You can check the trustycirclejusttomakesure.

Thegoodnewsisthatthisworksoneverykeythathasasharpinit.To

findthenameofasharpkey:

1. 1.Namethelastsharp,theoneallthewaytotheright.

2. 2.Goonenotehigherthanthelastsharp,andthat'sthename!

Easyenough!Unfortunately,itworksonlywhenyou'relookingatakey.Ifsomeoneasksyou, “Howmanysharpsare in thekeyofEmajor?” thislittletrickwon'tgetyouveryfar.Foreverythingelse,refertothecircleofkeysandtheorderofsharpsandflats.TheFlatKeyTrickTheflatkeyshave theirown,different trick fornaming them.Whenyouseeapieceofmusicthathasflats,findthesecond-to-lastflat.Thenameof that flat is the name of your key! This is an easy one. Look at theexampleinFIGURE5.5.Thiskeyhastwoflatsandthesecond-to-lastflatisBb.ThenameofthekeywithtwoflatsisBb!Thisoneisaneasytrick.

There is oneexception, however: the keywith one flat, Fmajor.Sincethis key has only one flat, you can't find the second-to-last flat. In thiscase, you'll just have to memorize that F has one flat (which is Bb).Shouldn'tbetoohard!Tofindthenameofaflatkey:

1. 1.Findthesecond-to-lastflat(fromtheright).

2. 2.Thenameoftheflatnoteyoufindisthenameofthekey.

Just remember the exception— the key of F major has one flat andthereforetheruledoesnotworkforit.Fortheotherkeys,itworkslikeacharm!TheCircleMovesinFourthsandFifthsThenameofthissectionsaysitall!Thecircleofkeysisoftenreferredtoasthe“circleoffifths”orthe“circleoffourths.”Thekeysarearrangedinthecircleinafairlylogicalway.ThekeyofC,withnosharpsorflats,sitssquarely in thecenter, and thesharpkeysmovearound the right side,eachkeyincreasingthenumberofsharpsbyone.Theflatkeysmoveto

theleft,increasingtheirflatsbyoneastheyprogress.

ExtraCredit

Even before you learn the entire circle of fifths by heart, you canconstructitusingintervals.DrawaCatthetopofapieceofpaper.Nowdrawafewfifthstotherighttonamethesharpkeys.Totheleft,drawafew fourths to get your basic flat keys.Across the bottomof the page,spelltheorderofsharpsfromF,infifths,andtheorderofflatsfromB,infourths.AsyoumoveawayfromthekeyofC,eachkeyincreasesbyoneflatorsharp(dependingonwhichdirectionyoumovein).Youcanmatchuptheflatsandsharpsfromthebottomofthepage.IfyoumovetotherightfromC,eachkeyisexactlyaperfectfifthapart!Not only that, but the order of sharps as they appear in the keysignaturesarealsoperfectfifthsstartingfromF#.IfyoumovetotheleftfromC,eachkeyisexactlyaperfectfourthapart!Conveniently, the flats as they appear in the key signature are also aperfectfourthapart,startingfromBb.Thinkaboutthesetwopoints:

Sharp keysmove in fifths around the circle, and the order of sharps arefifthsapart.Flat keys move in fourths around the circle, and the order of flats arefourthsapart.

Notethatwhenyoumoveinonedirectioninthekeycircle,youmoveinfifths,andwhenyoumoveintheoppositedirection,youmoveinfourths.Remember the explanation in Chapter 2 about interval inversion: Aperfect fifth becomes a perfect fourth when inverted. A fifth up is thesame as a fourth down. The same applies to the order of sharps andflats.ThesharpsarespacedafifthapartstartingfromF,andtheflatsarespacedafourthapartstartingfromB.Interestingly,whenyouspelloutallthesharpsandreadthembackward(backward= inverted= in fourths),

yougettheorderofflats.

RelativeMinorKeys

Uptothispoint,youhavelearnedsolelyaboutmajorkeysignaturesandtheir relatedmajor scales— thecircleof keysand those two tricks fornamingthekeyshaveallreferredtomajorkeys.Of course, you know aboutminor scales, andwhere there are scales,therearekeys.Thegoodnews is thatallof theminorscalesandkeyssharethesamekeysignatures,whichyoualreadyknow.Thebadnewsis that they aren't the same as the major keys! Never fear, there aresomeeasywaysforyoutolearntheminorkeysaswell.SharedSignaturesEverymajorkeyanditscorrespondingkeysignaturehasadualfunction.Notonlydoesitindicateamajorkey,butitalsoindicatesoneminorkeyaswell.Theconceptiscalledrelativekeysandrelatedminor.Simplyput,everymajor scale/key has aminor scale/key hiding inside it. For now,you'll learnhow to figureout thenameof theminor keys.FIGURE5.6showsthekeysignatureforEbmajor.TheexactsamekeysignaturecanalsosignifythekeyofCminor.

Howisthispossible?Well,simplyput,youcouldspelltheEbmajorscaleand the C minor scale and see that they share the exact same keysignature! The other thing that you are seeing is something called amode.Ifyou'veneverheardofmodesbefore,youjustlearnedyourfirstone:Theminorscaleisamodeofthemajorscale.Modescomeupinthenext chapter, sohold tight,but fornow, justunderstand that since theysharethesamepitches,andeveniftheyareinadifferentorder,theyarerelated.

PointtoConsider

Justlookingatakeysignaturewon'ttellyouwhetheryourpieceisinthemajoror theminorkey.Tofindoutforsure,youneedto investigatethepieceitself,notjustthesignature.NamingMinorKeysTonameaminorkeysignature,firstnamethemajorkey.Onceyouhavefoundthat,yousimplycountupsixnotes(upamajorsixth)ordownthree(downaminorthird).Eitherway,youarriveatthesamenote.InthecaseofCmajor,countingupsixnotesbringsyoutothenoteA.CmajorandAminor share the same key signature. They are referred to as “relatedkeys.”Whenyoulookatapiecewithnosharpsorflatsinthesignature,itmaynotnecessarilybe inCmajor, itcould justaseasilybe inAminor.Youwon'tknowforsurebyjustlookingatakeysignaturebecausemusicsimply isn't thateasy.To reallyget theanswer,youhave to lookat theharmonyofthepiece,andharmonyandchordscomelaterinthisbook.For now, just work on being able to nameminor keys frommajor keysignatures.Whennamingaminorkey,becarefultolookatthekeysignaturewhenyouaredoingso.Simplycountingupsixnotesordownthreenotesmaynotgiveyouthecorrectkey.Ifthenoteyoupickhasasharporaflatinthatkey,thenameoftheminorkeyneedstoreflectthat.Simply,you'renot justcountingupsix letters;youhave tomind thekeysignature. It'smucheasiertousetheintervalofamajorsixth,whichhasaclearname!LookatFIGURE5.7.Inthiscase,thesixthnotewasnotjustC,butC#,so the name of the key had to reflect that. The key of Emajor has arelativeminorofC#minor.

FIGURE5.8 is the full circleofkeyswithboth themajorand theminorkeyslisted.

DeterminingtheKeyWeknowthatyoucandeterminethekeybylookingatthesignatureandcheckingyourcircleofkeys.Doingsowillgiveyouatleasttwoanswers:

the major and the relative minor key. In a way, this is your first steptowardmusicalanalysis.Butmusicalanalysisismorethanjustlookingatakeysignature.Theanswerisrarelythatsimple.Orisn'tit?An old trick exists that suggests that you can look at the first and lastnotes of any piece to determine the key of a piece. Now, this rarelyworks,becausemusicinvolvessomanyvariables,butsometimesitdoeswork.Ifyoulookatakeysignatureandyourchoicesareeitheraminororamajorkey(CmajororAminor,forexample),youcouldscanthepieceforCsorAsandthatmayansweryourquestion.Thenagain,itmaynot.While it is true thatmanypiecesconcludeon the tonicnoteof thekey,that really gives you only the answer of where the piece ended andignoresthequestionofwhereitwentinthemiddle.

INTIME

Composer Antonio Vivaldi was born in Venice on March 4, 1678, anddied in Vienna on July 28, 1741. He was the son of a professionalviolinist,andwasalsoanaccomplishedviolinisthimself.Ordainedasapriestin1703,hesoonstoppedcelebratingMassonaccountofhispoorhealth. Today Vivaldi is most famous for his work Le Quattro Stagioni(TheFourSeasons).Simplyput, ifyouaretryingtodecipherwhatkeyyou'rein,thefirstandlastnote(orchord)maygiveyouabasicanswer.Theonlytrueanswerthatworks ineverypiececanbe foundonlyby lookingat thedetailsofthepiece—andthat involves lookingatnotonlythekeysignature,butalsotheharmonyandper-notechangesthatexist throughoutthepiece.Sinceyouknowaboutscales indetailnow,youcanworkononemoreaspectofkeysbasedonminorscalesandtheirtypicalvisualpatterns.

MinorKeysonPaper

Inagreatdealofmusic,yourarelyseethenaturalminorscale;whatyouseemoreoften is theharmonicormelodicminorscales.Whenyouarelookingatapieceofmusicandthekeysignaturetellsyoutwopossibleanswers,youcanlookinsidethemusicitselfforsomeclues.If thepiece is in themajorkey, itwon'tneedanyadditionalaccidentals(sharpsor flats) to function.That'snot tosay thatpieces inmajorkeysneverhaveaccidentals, far fromthat,butminorkeyshaveveryspecificaccidentalstolookfor.Ifyouknowwhattolookfor,youshouldhavenoproblemfindingouttheanswer.

PointtoConsider

Both the harmonic minor scale and the melodic minor scale havealterationsviaaccidentals.Foraminorscaletofunctioninthetraditionalsense,itwillneedthisalteration.Morespecifically,itwillneeditsleadingtone raised, and this will always cause a subsequent sharp, flat, ornaturalwhereitdoesn'tnormallybelong.Aleadingtoneistheseventhnoteofascale.Inthecaseoftheharmonicand melodic minor scale, it's raised one half step higher than in thenaturalminorscale.IfyoutakeAminorasanexample,theleadingtonein the natural scale is G, and if you raise it, it becomes a G#. Now,thinking back to what you know about key signatures, A minor and Cmajorshareakeysignaturethathasnosharpsorflats.So, you're looking at a piece with no key signature and scatteredthroughoutthepieceareabunchofG#s.ThefinalnoteofthepieceisA.ChancesarethatyouareinAminor,oratleastyouwereinAminorforapartofthatpieceandconcludedthere.Bythesametoken,ifyouseeapiecewithnokeysignatureandnothingbutG§s,youknowthatyou'reinCmajor,becausetheG#istheleadingtoneofAminor.Here is an example (FIGURE5.9); take a look and seewhat key youthinkitis.

Atfirstglance,thekeysignaturehasonesharp,soitcouldbeGmajororEMinor. The first thing youwant to do is look for accidentals.Do youhaveany?Yes,youdo,youhaveaD# throughout thepiece.Thenext

stepwouldbetodetermineifthatisjustanaccidentalorifitisaminor-scale leading tone. In the key of Eminor, the leading tone is a raisedseventhnote,whichhappenstobeD#.ThefactthatthepiecestartsandendsonEsurelydriveshomethepointthatyouareinthekeyofEminor!See,thatwasn'tsohard.Itdoesshowyouthatyoucannotjudgethekeybasedonthesignaturealone—youmustlookatthematerialwithinthepiece to be absolutely sure. Knowing what your leading tones are willmakeyour jobofunderstandingthedifferencesbetweenkeysignaturesandtheirrelativeminorscalesmucheasier.

ExtraCredit

Tofindtheleadingtonesforminorkeys,justfindtheseventhnoteofthescale.Rather thangosevennotesup,simplygoonenotedown.Thenmake sure it's a half step away. For example, the leading tone for Cminor is B§ because B and C are a half step apart. In D minor, theleadingtoneisC#.

KeysChange

Musicdoesnotneedtostayinonekey;keychangeshappenfrequentlyin pieces of music. The way that you will learn to change keys andidentify key changes will become much clearer when you understandharmonymore.Fornow,youcangobacktothecircleofkeysandsimplymakeafewassumptionsthatwillbeexplainedasthebookprogresses.Herearetherules:

Whenmusicchangeskeys,itdoessotoacloselyrelatedkey.Theclosestrelatedkeyistherelativeminor.Theotherclosekeysthatyoucanmodulatetoarenexttotheoriginalkeyonthekeycircle(eitheronekeytotheleftoronekeytotheright).Theothermodulationyoucanmakeisfromamajortoaparallelminor;forexample,CmajortoCminor.

Talking about “common” and “simple” ways to change keys does notmeanthat themoredifficultanduncommononesarenotused; just theopposite is true.Composers love tobreak the rulesand find interestingandmusicallycompellingwaystodoso.Partoflearningabouttheoryisunderstandingwhatthemajorityofmusicdidwhenitwaswritten—whatwere the norms of the times and why did the composers use them?There will always be musicians who push the boundaries of music,bringingmusictonewlevels.

Keysaremorethanjustscalesandkeysignatures,soyoureallyneedtokeepmovingon into the restof thescalesandchordsandharmony tofully graspwhat keysmean and how youwill use them. For now, youhave the basic groundwork that you need in order to name and spellkeys,whichwasyourgoalforthischapter.Thenextstepistolookatthelastgroupofscalesandmodesthatyouwilldealwith in thisbook,andthenontobiggerthings:chordsandharmony!

6

ModesandOtherScales

Itistruethatmajorandminorscalesmakeupthemajorityofthescalesthatyouencounterineverydaylife.However,bothtraditionalandmodernmusictheoryincludeotherscalesbesidesmajorandminor.Modesareaterm often thrown around as something to learn, and students rarelyunderstandwhatmodesactuallyare.Besidesmodes,otherscalesroundoutmusictheory:pentatonic,diminished,andwhole-tonescales.

Modes—TheOtherSideofScales

Thefirstplacetodeepenourunderstandingofscalesisrightbackatthemajor scale. As amusician, youmay ormay not have heard the termmodes.Manyclassicalmusiciansdon'tdealwithmodesearlyonintheirstudy. However, jazz and rock players are aware of modes early on.There are several reasons for this musical divide, which will becomeclearasyoulearnmoreaboutmodes.DefiningModesThesimplestdefinitionofamode isadisplacedmajorscale.First, youneedtoexaminewhatdisplacedmeans.TaketheFmajorscale:F–G–A–Bb–C–D–E–F.Asyouknow,whatmakes itanFmajorscale is that thenoteFhasthemostweight;thescalewantstostoponthehighFwhenyouplayit.YoucouldsaythatthenoteF(thetonicdegree)hasthemostweightwhenyouareinthekeyofFmajor.

PointtoConsider

Everheardthechildren'ssing-along“WhatDoWeDowiththeDrunkenSailor”?Thisfamiliaroldseachantey(asongsungbysailors)isactuallycomposed using a modal scale: the Dorian mode. Another famousexampleofmodesisthethemetoTheSimpsons,whichusestheLydianmodeforitsmaintheme.Modesareallaroundus;theyareoftenusedinfilmandTVsoundtracksaswell.Now,whatifyouweretousethesamevocabulary,thatis,usethesameF–G–A–Bb–C–D–E–Fpitches (theFmajor scale), but instead,makeadifferentnote theroot?What if thescale looked like this:D–E–F–G–A–Bb–C–D?If thescale looked like thatandDsounded like therootnote(which is based on the context of the piece), then you have an officialmode.Youhaveabitmorethanamode,actually.Ifyou reread the lastparagraph,you'llnotice thatanFscale isspelledfromD.IsthereaspecialrelationshipbetweenFandD?Well,theyareasixthapart.Hmm,sixthnoteofamajorscale,wherehaveyouheardthatbefore?InChapter5,undertheheadingNamingMinorKeys.Rememberthe trick you learned there, to find the relative minor by going up sixnotes.Usingtheexampleabove,youseethatyoucanspellanFmajorscalestartingfromD,itssixthnote,andit'scalledamode!It'sboththeDminorscaleandalsoamodeofFmajor.So,youseethatminorscalesarealsomodes.ThenotesD–E–F–G–A–Bb–C–D form a Dminor scale. Amode is formedwhen you call anyothernotebesidestheoriginalrootofthescaletheroot.Theminorscaleis just one example of a mode, one that you already know. But wait,there'smore!Becauseamajorscalehassevennotes, therearesevenmodes.ModalHistoryModes gained prominence during the golden age of Gregorian chant,circaA.D.900,whentheywereusedtocomposethemelodiesofvocalplainchant.Modes stayed in use throughoutmedieval timeswith some

modification.Thebaroqueandprebaroqueerasmadeuseofmajorandminorscalesexclusivelyinsteadofmodes.Forallintentsandpurposes,modes lay dormant throughout the baroque era, the classical era, andmost(butnotall)oftheromanticera.Eventhoughimpressionistcomposersrevivedmodes,itwasn'tuntiljazzmusicians started using modes in improvisation and composition thatmodes became a useful part of music curricula. Nowadays, all musicstudents learnaboutmodes,but it's therockandjazzplayerswhotendto utilize them more frequently than anyone else in improvisation andcomposition.

SevenModalScales

Eachandeverymajorscalecanbelookedatfromsevendifferentangles— one mode starting from each note in the scale. While modestheoreticallycomefrom“parent”majorscales,it'seasiesttothinkofthemastheirownentities.

INTIME

If you learn about modes in a classical music theory class, they arecommonlyreferredtoasthe“churchmodes”becauseofthewidespreaduse of modes in the sacred music that originated in the church —especiallyGregorian chant.Relegatingmodes to “historical” learning isdoing them a disservice! Modes are alive and well in modern music,especiallyjazz.IonianIonianisthefirstmodetolearnaboutand,thankfully,youalreadyknowit.TheIonianscaleissimplythemajorscale.ItfollowstheintervalpatternWWH-WWWH.FIGURE6.1showsanF Ionianmode.Since the Ionianmodeissimplythetraditionalmajorscale,thisexampleisjustadefinitionof the word Ionian. Think of Ionian as the “proper” name for a majorscale. It'sgreat toknowwhatthepropernameis,butyoudon'thavetobecaughtup in itsusageandrefer toeverymajorscaleasan“Ionian”mode;thetermsareinterchangeable.

DorianTheDorianmodeisthefirstofthedisplacedscales.Theeasiestwaytodefine Dorian is that a Dorian scale is a major scale played from itssecond note. If you continue to use F major as the parent scale, theDorianmode in this key starts from the noteGand progresses up thesamenotes.FIGURE6.2showstheGDorianscale.TheGDorianscaleusestheintervalpatternWHWWWHW.

There is a very important aspect to understandaboutmodes. It is truethattheGDorianscalecomesfromtheFmajorscaleandsharesallthesamenotes.This isan important learning tool.However,allmusiciansneed to learnthemodesas “theirown thing.”TheDorianmode isascaleunto itself,withitsowndistinctsound.IfyoulookatthenotesofGDorian(G–A–Bb–C–D–E–F–G), youmightnotice that theGDorianscale looksa lot likethetraditionalGminorscale(G–A–Bb–C–D–Eb–F–G).Andyou'reright;it looksawholelot likeit!TheonlydifferenceisthattheGDorianscalecontainsanE§andtheGminorscalecontainsanEb.YoucouldlookattheDorianscaleasaminor-typescale,withanalteredsixthnote. In thiscase, thesixthnote is raisedupahalf step. It'sverymuchlikea“flavored”minorscale.Thisishowmodesareusedtoday—to“spice”uptraditionalmajorandminorscalesthatmaysoundoverusedanddated.Asyou'llsee,alloftherestofthemodeswillcloselyresembleeitheratraditionalmajororatraditionalminorscale.

PointtoConsider

When you think of the parent scale relationship between each mode,don'tfall intothetrapofthinkingthateachmodehastoberelatedtoitsparentscale.Usingtheminorscaleasanexampleagain,youdon'thavetothinkaboutitsrelatedmajorscale,doyou?No,itcanstandonitsown.Thesameholdstrueforallofthemodes.Learntoseethemontheirownifyouplantousethemquickly.PhrygianPhrygian is the thirdmodeand is the result of forminga scale startingfromthethirdnoteoftheparentmajorscale.UsingFmajorastheparentscale, the Phrygian scale is an A Phrygian scale. It uses the intervalpatternHWWWH-WW(seeFIGURE6.3).PhrygianhasadistinctsoundandsometimesrecallsthemusicofSpain,asSpanishcomposersoftenusethisscale.

The A Phrygian scale (A–Bb–C–D–E–F–G–A) looks very much like atraditional A minor scale (A–B–C–D–E–F–G–A). The only difference isthattheAPhrygianscalelowersthesecondnoteahalfstepdown.YoucouldsaythatPhrygianisjustaminorscalewithaloweredsecondnote—andyou'dberight!LydianThe fourthmode of themajor scale is the Lydianmode.Using F as aparentscale,youcometotheBbLydianscale.LydianusestheintervalpatternWWWHWWH.SeeFIGURE6.4.

TheLydianmodeisastriking,beautiful,and“bright”sound.It'susedbyfilmcomposerstoconveyupliftingspiritandisafavoriteofjazzandrockcomposers.TheLydianscaleissobrightandhappy,it'snosurprisethatit'scloselyrelatedtothemajorscale.TheBbLydianscaleisspelledBb–C–D–E–F–G–A–Bb,whichresemblesatraditionalBbmajorscale(Bb–C–D–Eb–F–G–A–Bb). The only difference between Bb Lydian and BbmajoristhataLydianscaleraisesthefourthnoteofthemajorscaleupahalfstep.So,BbLydianisaBbmajorscalewitharaisedfourthnote.Theraised fourth tone results inabrightandunusualsoundandallows theplainmajorscaletohaveauniqueoveralleffect.MixolydianThe fifthmodeof themajorscale iscalled theMixolydianmode.Usingthe parent scale of F, our fifthmode is CMixolydian. CMixolydian, or“Mixo” as it's commonly abbreviated, uses the interval pattern ofWWHWWHW.SeeFIGURE6.5.TheMixolydianmode isamainstayofjazz,rock,andbluesmusic.

TheMixolydianmodeiscloselyrelatedtothemajorscalebut isslightlydarkersounding.TheCMixolydianscale(C–D–E–F–G–A–Bb–C)closelyresemblestheCmajorscale(C–D–E–F–G–A–B–C).TheonlydifferenceisthattheMixolydianscalelowerstheseventhnoteofthemajorscaleahalfstep.TheloweredseventhnotegivestheMixolydianmodeabluesy,darkcolor, leadingawayfromtheoverlypeppymajorscale.Becauseof

this,it'sastapleofblues,rock,andjazzplayerslookingtodarkenupthesoundofmajorscales.Italsocoincideswithoneoftheprincipalchordsof jazz, blues, and rockmusic: thedominant seventh chord (C7,whichyou'regoingtolearnallaboutinChapter9).AeolianThesixthmodeofthemajorscaleistheAeolianmode.Ifyourememberbacktothechapteronminorscalesearlierinthisbook,you'llrememberthatminorscalesarederivedfromthesixthnoteofamajorscale.That'sright, the Aeolian mode is the natural minor scale. Thankfully, this isanother mode that you already know. Aeolian is the proper name fornatural minor. Refer to it as “Aeolian” at parties tomake yourself looksmarter!UsingtheparentkeyofFmajor,oursixthmodebringsustoDAeolian.You'llalsorememberthatthekeysofFmajorandDminorarerelatedkeys—FIonianandDAeolianarerelatedmodesfromthesameparent scale. The D Aeolian scale uses the interval formulaWHWWHWW.SeeFIGURE6.6.

Since the Aeolian scale is an exact minor scale, no comparison toanothermajororminorscaleisneeded.Evenwiththat,someplayersaremorecomfortablewithmajorscales;Aeoliancanbelookedatasamajorscalewithaloweredthird,sixth,andseventhnote.Thiswayoflookingatminorscalesisusefultosome.LocrianThe seventh and finalmode is called the Locrianmode. In our parentscaleofFmajor, theseventhmode isELocrian.ELocrianmodeusesthe intervalpatternHWWHWWW.SeeFIGURE6.7.TheLocrianmodehasaverydistinctsound.You'renotgoingtoencounterthismodeoften.Actually, youmaygoyourwhole lifewithouteverhearing it or using it.Nevertheless, it completes your knowledge of modes, so it's good toknowit.

TheELocrianscale(E–F–G–A–Bb–C–D–E) looksa lot likeanEminorscale (E–F#–G–A–B–C–D–E). The only difference between the twoscalesisthattheLocrianscalehasaloweredsecondandaloweredfifthnote.

LookingatModesonTheirOwn

The modes that you know, you know in relation to a parent scale. IfsomeoneweretoaskyoutospellaC#Lydianscale,youmighthavetogo throughquiteanordeal.First,youhave to rememberwhichnumbermodeitis,thenyouhavetobacktrackandfindtheparentscale,andthenyoucanspell thescale correctly. It'smuchmoreconvenient to thinkofthemodeson theirown,which ishow theyareusuallyused. It'smucheasier tomake an effort to understandmodes than to always have totake several steps to puzzle them out. Looking at modes as “almost”majororminorscaleswillhelpyouunderstandthem.Here isarecapof themodes, their interval formulas,andeasywaystorelatethescales:

Modes,Scales,andIntervalFormulas

Mode Scale IntervalFormula Description

Mode1 Ionian (WWHWWWH) lonianisthemajorscale.

Mode2 Dorian (WHWWWHW) Dorianisaminorscalewitharaisedsixth

note.Mode3 Phrygian (HWWWHWW) Phrygianisaminorscalewithalowered

secondnote.

Mode4

Lydian (WWWHWWH) Lydianisamajorscalewitharaisedfourthnote.

Mode5 Mixolydian (WWHWWHW) Mixolydianisamajorscalewithalowered

seventhnote.Mode6 Aeolian (WHWWHWW) Aeolianistheminorscale.

Mode7 Locrian (HWWHWWW) Locrianisaminorscalewithlowered

secondandfifthnotes.Bylearningtheseformulas,youwillbeabletolearnmodesastheirownscalesandspellandrelate themquicklyandeasily.Here iseachmodespelled from the same root (goodoldC,which is soeasy to thinkandworkwith)soyoucanseehoweachmodediffersfromeachother.

ModalPracticeHere's some practice spelling some modal scales. In the followingexample,usethisprocess:

Ifyourmodeisamajor-typemode,spellthemajorscalefirst.Ifyourscaleisaminor-typemode,spelltheminorscalefirst.Alterthescaleasprescribedinthelistformodalformulas.

Ifyouworkthisway,youwon'tneedtofigureouttheparentscale,anditwillfurtherreinforceyourknowledgeofcommonmajorandminorscales.Seethenexttwofiguresforreference.

OtherImportantScales

Major scales, minor scales, and modes make up the majority of thescales encountered inWestern music. However, they are not the onlyimportant scales; scales come in many different shapes and sizes,especiallyasyoumovethroughouthistory.MajorPentatonicPentatonic scales differ from traditionalmajor andminor scales in thattheycontainonly fivenotesperoctaveasopposed tomajorandminorscales,whichcontainseven.Thenamepentatonicreflectsthisdistinctionas the prefix of pentatonic is penta, Greek for “five” — tonic means“tones” or “notes.” The pentatonic scales are widely used in folk,liturgical,rock,and jazzmusic.Pentatonicscalescomeintwovarieties:majorandminor.Themajorpentatonic isa five-notescale that isderived from themajorscale.Itsimplyomitstwonotes—thefourthandseventhtones—fromthemajorscale.InthekeyofG,themajorpentatonicscaleisG–A–B–D–E.Statedanotherway,theGmajorpentatonicisthefirst,second,third,fifth,andsixthnotesofamajorscale.

INTIME

The major pentatonic is a mainstay of folk, blues, rock, and countrymusic.Famousmelodiessuchas“MaryHadaLittleLamb”and“LondonBridge”were composed solely using themajor pentatonic scale. If youlike to improvise solos, the major pentatonic is a basic and essentialscalefor improvisationovermajortonalitiesfoundinmusicgenressuchasrock,jazz,andblues.MinorPentatonicLikeitsrelativethemajorpentatonicscale,theminorpentatonicscaleisalso derived from a scale with two notes omitted (just not the sameones).Toformaminorpentatonicscale,simplyleaveoutthesecondandsixthtonesfromanatural(ormoreformally,Aeolian)minorscale.InthekeyofD,aminorpentatonicscaleis(D–F–G–A–C).Youcouldalsosaythatthescaleisthefirst,third,fourth,fifth,andseventhnotesofanaturalminorscale.

WholeToneThe whole tone scale is a particular type of scale called a symmetricscale.Thewholetonescaleisbuiltentirelywithwholesteps.Becauseitusesthesameintervals,thewholetonescaleisconsideredasymmetricscale.Usingwhole steps fromC,aCwhole tonescale isC–D–E–F#–G#–A#.It'sveryimportanttonotethatthewholetonescaleisasix-notescale.Notfivenoteslikeourpentatonicscales,orsevennoteslikemajorandminorscales,butsix!

Of particular interest is that there are only two different whole tonescales.FormingwholetonescalesfromanywhereotherthanCorDbwillyield theexact samenotesas theCorDbwhole tone scales.See foryourself:

NoticehowboththeCandDwholetonescalescontaintheexactsamenotes.Thismakesthemveryeasytolearnandplay.Youseewholetonescalesinromanticmusicandjazzmusic.

INTIME

JazzpianistTheloniousMonk loved thewhole tonescale,andyoucanfinditinvirtuallyallofhisrecordedimprovisedjazzsolos.Thewholetonescalewasatrademarkforhim.Hewasn'tthefirsttouseit,butboy,didhelikeit!Diminished/OctatonicScalesThe last scale is another symmetric scale and is built using repeatingintervals. The diminished scale is based on repeating intervals, alwayshalfstepsandwholesteps.Therearetwovarietiesofdiminishedscales:onethatstartswiththepatternofwholestep,halfstepintervals,andonethatusesahalfstep,wholestepintervalpattern.FIGURE6.15showsthetwovarietiesofdiminishedscales,bothstartingfromC.Theothernamethatdiminishedscalesgoby isoctatonic,which isGreekfor“eight-notescale.”Thisisthefirstscalethatexceedssevenindividualnotes.

Another interesting fact is that there are only three unique diminishedscales. Diminished scales spelled from C, C#, and D are the onlydiminished scales that utilize unique tone sets. Spelling diminishedscalesfromotherrootswillyieldrepeatingscales,withtheidenticaltonesfromC,C#,orDdiminished.Composers,theorists,andjazzplayersusediminishedscalesprimarily.

TimeforEtudes

Next,youwillstartauniquepartof thisbook: theetudes.Etudecomesfrom the French termmeaning “to study.” The etude is a widely usedmonikerforpiecesthatyoumightlearnasastudentofaninstrument.Forexample,Chopin's piano etudes are famous not only for their teachingability,but for theirmusicalcontentaswell. In thisbook, theetudeswillgiveyouaspacenotonlytopracticewhatyouhavelearnedsofar,butmoreimportantly,toputittomusicalusebycomposingsomemusicwithwhat you have learned. You will encounter two other etude chapterswhereyouwillbeabletoturnthisinformationfrom“theory”intomusic—andisn'tthatthewholepointofthis?Indeeditis.

7

EtudeOne:ScalesandKeys

NametheFollowingIntervals

WritetheFollowingIntervals(Ascending)

WritetheFollowingIntervals(Descending)

WriteMajorScalesfromtheFollowingNotes

WriteMinorScalesfromtheFollowingNotes

NametheFollowingScales(MajororMinor)

NametheFollowingScales(MajororMinor)

NameTheFollowingKeySignatures(MajorandRelativeMinor)

WriteModalScalesFromTheFollowingNotes

WriteModalScalesfromtheFollowingNotes

Write“Special”ScalesfromtheFollowingNotes

8

Chords

Thus far, you have dealtwith, atmaximum, two notes at a time,whenworking with intervals. You have learned all about scales and keysignatures,which give you all the possible arrangements of notes in aline, but you have been waiting for one more piece to complete yourknowledge.Thenextstepistolookatchordsandthebasicfoundationsofharmony. Intervalscombine intochords,andharmoniesemergefromthosechords,providingthefoundationoftonality,whichisthelanguagespokenbythemusicyouhear.

WhatIsaChord?

What'sachord?Tostart,achordisessentiallydefinedasthreeormorenotes sounded simultaneously. Chords can, of course, be a whole lotmore than three notes, so a few things need to be clarified. First, thesimplest kind of chord is a triad, which begins with the prefix of tri,meaning“three.”Atriadisathree-notechord,andtheintervalsbetweenthe notes (as you will get into soon) are always thirds apart — yetanotheruseoftheprefixtri.Justlikeintervals,chordscomeindifferentqualities.Thequalityreferstothetypeofchorditis,whichisalwaysbasedonsomesortofconstructionrule. The basic chord qualities for triads aremajor, minor, augmented,and diminished. Those are the same qualities that the intervals had(excludingperfect).So to recap, a chordat its simplest is a three-notetriad with intervals that are thirds apart and notes that ring together.Beforeyougoanyfurther,hereiswhatasimpleCmajortriadlookslike.

That is the simplest way to look at a chord, essentially the model or“prototype” voicing, but rarely do you see chords in such clear order.Whatyoudoseearechordvoicings.You should think about triads as being “model” chords. They are theabsolutesimplestwayforyoutohaveachordspelledout.Unfortunately,rarelydoyoueverseesuchmodelsofperfectioninmusic.Whatyoudosee are chord voicings. What's a voicing? Simply, it's a sort ofrearrangement of thenotes of the triad in somewaywithout addingortakingawayfromtheessentialingredients(inthecaseofCmajor:C–E–G).

FIGURE8.2showswhataguitaristplayswhenaskedtoplayaCmajorchord.If you compare this with the “pure” triad inFIGURE8.1, you see thatwhiletheyappearvisuallydifferentonthepage,infact,theycontainthesamestuff.BothchordscontaintheprincipalnotesC,E,andG,buttheguitarvoicingrepeats thenotesCandEagain.Thissimply fillsout thechordandmakesitsoundmorefull.Eitherway,it'sstillC–E–Gnomatterhowyousliceit.Whenyouanalyzechords,youlookforthebasicnotesthat define it, and typically, youdon't see themall in a pretty little row,right in triadicorder;many timesyouhave tohuntaround,butyoucanaddress that during analysis later on. Now you need to define exactlywhatmakeseachofthechordswhattheyare.

INTIME

The son of a schoolmaster, Franz Schubert was born in Vienna onJanuary31,1797,anddiedinViennaonNovember19,1828,attheageof thirty-one. Even as a child he showed an extraordinary aptitude formusic and studied the violin as well as the piano. His fame increasedmarkedly after his death, and today he is perhaps most noted for hispianosonatas.

BuildingChords

If youunderstandyour intervalswell,buildingchords isnobigdeal.Ofthe four triadqualities (major,minor,diminished,andaugmented),eachhasitsowndistinctbuildingpatterns,muchlikeall thescalesdid:Onceyoulearnthem,it'sveryhardtogetthemconfusedastheyaredifferentfromoneanother.Startbydetailingthestructureofthefourbasictriadsinmusic,beginningwithmajor.MajorTriads/ChordsThe formations of each chord and triad are going to be describeddifferently than in the past. Previously, it was formula first and thenapplication. This time, you know enough to look at a chord first anddeducetheformula(withabitofguidance)afterward.StartbylookingataplainCmajortriad:

Here'swhatyouknowabout tri-ads:Theyare three-notechordsbuilt inthirds. So, you should look at the structure of the intervals (which youknowarethirds)betweenthenotesandfigureoutthepattern.FirstupistheintervalofCtoE,whichisamajorthird.NextupisEtoG,

whichisaminorthird.Youcannowformformulasformajortriads:Startwitharoot,anyrootyouwant,andaddamajorthirdfromtherootandaminorthirdfromtheresultantnote.Youcanthinkof itasmajor3/minor3for short, knowing that with triads, you are always dealing with thirdintervals,andthiswillgiveyouthefastwaytospellthistriad.AlternativeViewofMajorTriadsBesides lookingat the intervals in thirds, it is veryhelpful to seea fewotherrelationshipsthatarepresentinthesimpleCmajortriad.Firstthingtolookat:CtoE,whichisclearlyamajorthirdinterval.ButhowabouttheintervalfromCtoG?Intervalsmeasuredistance,andwhilethechordiscomposedofthirds,that's lookingattherelationshipfromonlyonenotetoitsadjacentnoteinthetriad.Whatifyoumeasuredeachintervalfromtherootofthechord?Well,ifyoudidthat,youwouldneedtolookatthedistancefromthefirstnote(C)tothelastnote(G).TheintervalfromCtoGisaperfectfifth.Toconstructtriadssolelyfromtheroot,youhavetodothefollowing:

1. Formamajorthirdintervalfromtherootofthechord.

2. Formaperfectfifthintervalfromtherootofthechord.

It's really important to know both ways to form your triads, but it'sbeneficialtolearnintervalsfromtherootbecauseitmakesyouawareofsomethingnew:Triadshaveroots,thirds,andfifths!

ExtraCredit

Justlikescaleshavetohavesevennotesandthosesevennoteshavetouse one letter from the musical alphabet each time they are spelled,triadsmustcontainaroot,athird,andafifth.AllofthebasictriadsfromCwillcontainsomeformofC–E–G(withdifferentaccidentals,ofcourse),but all C triads will have C–E–G. Knowing this makes spelling triadsmuch faster — especially when you learn the derivative approach toformingtriadsfromeachother(whichyouwillgettoverysoon).Theotherthingtoknowaboutmajortriadsisthatnotonlydotheyhavearoot,athird,andafifth,buttheyalsohavetherootthirdandfifthfromthemajorscalethattheycomefrom!Thisisgreattoknow.Ifyou'respellingaDmajorchord, just takethefirst, third,andfifthnotesfromtheDmajorscale (which you know how to spell so well now) — D–F#–A— andbingo,youhavean instantmajor triad.There'smuchmore to this,andyouwillgetintothewholerangeofwhatyoucandowithscalesandtheirrelations to chords in the section entitled Diatonic Chords later in thischapter.Now,ontominorchords!

MinorTriads/Chords

To further drive home the derivative approach, take a look at all thechords in the chapter from a C root. This way, you can look at eachpossible variant and learn the differences among them. Sometimes,learningwhatstaysthesameandwhatsmallelementschangehelpsyouacquiretheknowledgefaster.StartwithaCminortriad:

Basedonwhatyouknowabout intervals, lookat thedistancebetweeneachofthethirdintervalstodeduceaformulaforthistriad.StartwithCtoEb,which is an interval of aminor third.Eb toG is an interval of amajorthird.Sotheformulawouldgoasfollows:minorthird,majorthird.Ifyou compare thatwith the formula for amajor triad (major third,minorthird), you see that both the major triad and the minor triad contain amajor third and a minor third.What's unique is that both of the triadscontain one of each quality of third, but they are backward! Themajortriadismajor3/minor3whereastheminortriadisminor3/major3.

ExtraCredit

Here'sagreatwaytoremembertheorderofyourthirdsinsimplemajorandminortriads:Thenameofthetriadwilltellyouthequalityofthefirstthird.Majortriadsstartwithmajorthirds,andminortriadsstartwithminorthirds.Bothtriadsconcludewiththeoppositeinterval;thatis,majortriadsstart withmajor thirds but concludewithminor thirds, andminor triadsstartwithminorthirdsbutconcludewithmajorthirds.Memorizethis!AlternativeViewofMinorTriadsAswiththemajortriadsabove,youcanlookattheminortriadsinafewotherwaystoaidyourunderstanding.ThefirstwouldbetolookatalltheintervalsfromtherootofC.Lookatwhatyouget:

TheintervalfromCtoEbisaminorthird.TheintervalfromCtoGisaperfectfifth.

Ifyourememberfromthemajortriad,italsohadaperfectfifth!Thisisyetanother reason that it is calledaperfect interval.As for thedifferencesbetweenmajorandminor,sincethefifthsdon'tchange,youhavetolookatthethirds.Majortriadshavemajorthirds,andminortriadshaveminorthirds,andbothhaveperfectfifthsfromtheirroots.It'samazingthatthedifferencebetweenaCmajortriadandaCminortriadis justonenote,yet they sound so different. UseFIGURE8.5 as a sound example—changeonenoteandthewholegamechanges!

AnotherlookatthederivativeAnotherlookatthederivativeapproachtomusic:Ifyoucanspellanymajortriad,allyouhavetodotomakeitintoaminortriadissimplylowerthethirdofthemajortriadonehalfstepdown.It's a trick that always works!Many times, your speed at working withtheory can come from changing things you already know, and mostpeoplefindthatthemajorscaleandthemajortriadarememorizedearlyon,beforereallymemorizingtheotheraspectsoftheory.So,ifyouhavethose scales and triads memorized, changing one note to make themmajororminor isn'tsuchabigdeal.Withmusic theory,youhave tobeveryquick,andthesethingsenhanceyourspeed.

INTIME

Historically, themajor scalehasbeen thebasis formusic theory.Manyformulas and the entire idea of a derivative approach to theory existbecausetheoristsareconstantlyderivingmethodandrelationshipsfromthe major scale. As you will see as this book rolls on, just abouteverythingissomeformofanalteredmajorscale,orinthecaseofthischapter,amajorchord!Theotherwayto lookataminortriadistorelate it to itscorrespondingminor scale. Just like themajor triad took the first, third, and fifth notefromtheCmajorscale,theCminortriaddoesthesamething,justfromitscorrespondingminorscale.TospellaCminortriad,spelltheCminorscaleandselectitsfirst,third,andfifthnotes:C–Eb–G.Thismayormaynotbethefastestwayforyoutowork.

DiminishedTriads

Nextuponyourlookattriadsisthediminishedtriad.FIGURE8.6showsaCdiminishedtriad.

BreaktheintervalsintheCdiminishedchorddown.StartwiththeintervalfromCtoEb,whichisaminorthird.ThenextintervalisfromEbtoGb,which is also a minor third. The intervallic pattern of this triad isminor3/minor3. This is important to note, because both intervals are

minorthirds.Boththemajorandminortriadshavecontainedoneofeachthird(onemajorthird,oneminorthird),albeiteachtriadhadthethirdsindifferent order. In the diminished triad, you have the same thirds (bothminor).Thinkofitthisway:Eachtriadcontainstwothirds,andthereareonlymajorandminorthirdstochoosefrom.Youcanhavetwotriadsthatuseonemajorthirdandoneminorthird(inreverseorder),andthatgivesyou two possible triads (major and minor). If you use the same thirdtwice,youcangettwomoretriads.Inthecaseofusingtwominorthirds,yougetadiminishedtriad.Youwillseeshortlywhathappenswhenyouusetwomajorthirds.

INTIME

The diminished triad is used more in classical music than in popularmusic,although it is found incertainpopularsongs.Agreatexample is“Michelle”bytheBeatles,whichusesadiminishedchordinitsharmony(youshouldcheckoutthesheetmusictoseewhereitis).Ournaturallyoccurringscalesarethemajorandminorscales.Theotherscales you have learned are either “man-made” or outgrowths of themajorscale.Chordscanbeconstructedsolelyon intervals,or theycanberelatedtoscales,andasyouwillseeshortly,theyalsocanbederivedfromscales.Thethreetriadsyouhaveexploredthusfar—major,minor,and diminished— are all “natural” triads that occur naturally in musicbecauseoftheirrelationshiptoscales.Thefinaltriad,augmented,isnotanaturallyoccurringtriadfromanymajororminorscale.AlternativeViewforDiminishedTriadsStart off by looking at all the intervals in the C diminished triad allmeasuredfromC.

TheintervalfromCtoEbisaminorthird.TheintervalfromCtoGbisadiminishedfifth.

It's importanttonotethatthediminishedtriadisthefirst timeyouseeafifth inachord that isn'tperfect!Thatcouldexplainwhy thediminishedtriad has an unusual sound when compared to the major and minortriads.While there is a diminished scale, most musicians don't correlate thespellingofadiminishedtriadtothatofthediminishedscaleeventhoughyoucanstill takethefirst, third,andfifth tonesof thatscale to formthechord.Thereality isthatunlessyouareajazzimproviser,youprobablywon'tdealwiththediminishedscaleexceptintheoreticalunderstanding.Formost of us, the derivative approachmakes themost sense. If aC

majortriadisC–E–GandaCdiminishedchordisspelledC–Eb–Gb,thenyoucanderivethefollowingrule:Toturnanymajortriadintoadiminishedtriad,lowerthethirdandfifthonehalfstepdown.Youcouldalternativelyderivetheanswerfromtheminortriad(1,b3,5):Toturnanyminortriadintoadiminishedtriad,lowerthefifthonehalfstepdown.

AugmentedTriads

Thelasttriadtoexamineistheaugmentedtriad.Atthispoint,youhaveseen triads formed fromalmosteverypossiblecombinationof thirds—you're only missing one combination! A quick look atFIGURE8.7 willshowyoutheinterval-licformulaofaCaugmentedtriad:

IfyoubreakdownthechordbyIfyoubreakdownthechordby its thirdintervals,yougetfromCtoE,amajorthirdinterval,andfromEtoG#isamajor third.At last, youhaveeverypossiblecombinationof thirds!Thetablebelowwillexplainwhatyoucandowiththreenotesandtwothirds!

TableofTriadFormulas

Triad FormulaMajor Majorthird,MinorthirdMinor Minorthird,Majorthird

DiminishedMinorthird,MinorthirdAugmented Majorthird,MajorthirdAsyoucansee, that'sall thepossiblepermutationsof combinationsofmajorandminorthirdsinatriad;thosecombinationsyieldthefourtriadsthatmusicdealswith!

Symmetryrelatestointervalsbeingconsistentthroughoutamusicalideaor form.Diminishedandwhole tonescalesareconsideredsymmetricalbecausetheycontaineithertheexactsameintervals(wholetone)orthesame repeating interval pattern (diminished). With the introduction ofdiminished and augmented triads, you extend your understanding ofsymmetry to theworld of triads.Since diminished triads are composedsolelyofminor third intervals, theyaresymmetric triads.Also,sincetheaugmentedtriadiscomposedsolelyofmajorthirds,itisalsoconsideredasymmetrictriad.

PointtoConsider

Ifdiminishedtriadsarerareinpopularmusic,thenaugmentedtriadsareevenmoresparselyused!Butasalways,learnasmuchasyoucan,andhey,youjustmaybetheonetouseanaugmentedtriadinpopularmusic.(PinkFloydusesanaugmentedtriadin“UsandThem.”)AlternativeViewofAugmentedTriadsTake another look at the augmented triad, this time looking at all theintervalsfromtherootofC.TheintervalfromCtoEisamajorthird.TheintervalfromCtoG#isanaugmentedfifth.This is thesecondtriad thathasanonperfect fifth(theother was diminished). It's also not a coincidence that the fifth is anaugmentedfifthandthetriadiscalledanaugmentedtriad(thesamewiththediminishedchords,diminishedfifthinterval).Lookingat thederivativeapproach for formingaugmented triads, if youstart with the C major triad (C–E–G) and compare it with the Caugmented triad (C–E–G#), you come to the following conclusion: Tomakeanymajortriadintoanaugmentedtriad,simplyraisethefifthnoteonehalfstep.Now,here'sarecapofthederivativeapproachforallofthetriadssoyoucanbecomeatriadspellerinnotime!TheFullDerivativeApproachforFormingTriadsThederivativeapproachsimplypresupposesthatyoucanspellamajortriadeasily.Sincemajorscalesaresocommonlyusedandpracticed,it'sfairly easy to spell them. If you can't do that as easily as youwant to,workhardonmajorscalesbecausemuchofthetheoryremaininginthisbookwillderivefromthemajorscaleinsomeway;it'ssimplyanexcellentbasetostartwith.The first slight change you are going tomake is to use only numbersnow.So,insteadoftalkingabouttheroot,third,andfifth,youwillsimplysay1–3–5.

Hereisthefulllistingofallthetriadsandhowtheyderivefromthemajortriad:

Major 1–3–5Minor 1– 3–5

Diminished 1– 3– 5Augmented 1–3–#5Sincethisisamusicbook,takealookatallthetriadssidebysidesoyoucanseewhat'shappeningmusically.

Knowinghowtobuildtriadsonpureinterval,fromintervalsfromtheroot,andderivingthemfromthebasicmajortriadareallapproachesthatyoushouldbefamiliarwith.

ChordsinScales

Scalesarevery important.Thiscannotbeoverstated.Theyarenothingshort of musical DNA— an essential building block. Now, it's time torevisittheCmajortriad.

Thistriadcanbeconstructedafewdifferentways.Oneofthewaysistotake the first, third,and fifthnotesof theCmajorscaleandstack themtogether.Bydoingthis,youareabletobuildaquickCmajortriad.Thistrickworksineverymajorandminorscale,sointheory,youcouldbuildanymajororminorchordyouneedto.Sincechordsarebuilt fromthirdintervals,itwouldmakesensethatyoucoulddomorethanjuststackthefirst,third,andfifthnotestogether.Thereareawholebunchofpossiblethirdcombinations inascale ifyoustartoneachnote in thescaleandbuild triads. What would happen if you stacked these differentcombinations from each note? You'd get a whole bunch of differentchords,seventobeexact—onefromeachdegreeofthescale.YouaregoingtolearnhowtomaketriadsfromeverynoteinaCmajorscale. To do this, start outwith aCmajor scale and simply add triads(roots, thirds, and fifths) from each note in the scale.What you've justdone iscreatedallof thebasicharmonies(andchords) in thekeyofCmajorbycreatingtriadsoffofeachnote.

Don'tdownplaythesignificanceofthis.You'vejustlearnedthebasisforunderstandingharmonyandchordprogressions.Containedwithinthosetriads are seven different chords and endless possibilities for creatingmusic.Whenyoucreatetriadsfromascaleanduseonlythosenotestodo so, you use a technique called “diatonic” harmony. Diatonicmeansusingthenotesfromonlyonescale/keytomakechords.

DiatonicChords

In the last section, you tookaCmajor scaleandadded triads toeachnote inthescale,creatingsevendiatonictriads inthatkey.Nowlookatexactlywhatchordsarecreatedfrommakingthesetriads.

Youcanseefromtheexamplethatthereareavarietyoftriadscreated.Youseeamajorchord,minorchords,andadiminishedchord.Strangely,augmentedtriadsaremissing!TheOrderofTriadsThe order of triads in the scale is important. In amajor scale/key, thetriads always progress in this order: major, minor, minor, major, major,minor,anddiminished.Memorizethis;it'sgoingtoserveyouquitewellinthefuture.Andthebestpartisthatwhatyou'vejustdoneinthekeyofCmajor holds true in every major key. Since all major scales areconstructed in the exact same fashion, with the exact same intervals,whenyoustacktriadsinanymajorscale,youalwaysgetthesameorderof triads/chords.This isahugetime-saver!Theonly thingthatchangesarethenamesof thenotes themselves,asnotwokeyshavetheexactsamepitches.Thechordsandtheirorderwillalwaysbethesame.FIGURE8.12showsanexampleinthekeyofDmajor,Emajor,andBbmajor to showyou that nomatterwhat the scale is, the sameorderoftriads always exists. Just like major scales have formulas for theirconstruction that allow you to spell any scale easily, knowing that thetriadorderholdstruetoallthekeysissomethingyoucandependon!

ExtraCredit

Noticethatthenotesinthescalesareindifferentkeys,buttheorderofchords (major,minor,minor,major,major,minor, anddiminished) staysthesame.Thisholdstrueforeverymajorscale/key.RomanNumeralsTomusictheorists,thereisn'tanyrealdifferencebetweenanymajorkey.Unlessyoupossesstheabilityof“perfectpitch,”whereyoucannameanotejustbylisteningtoit,youwon'tbeabletohearadifferencebetweenCmajor andDmajor scales. Since there is such equality in the keys,musictheoryhasasystemofnamingchordsrelativetowhatnoteofthescale they are built from. If you were to number the notes and theircorrespondingtriadsfromtheGmajorscale,you'dendupwith:

Astriadsarebuiltoffofthenotes,theycannowbereferredtobynumberandorRomannumeral.Forexample,aonechordinthekeyofCmajoristhechordbuiltoffofthefirstnoteinthescale,whichisCmajor.Sinceeverymajor scale startswith amajor triad, you could say that the onechordinanymajorkeyismajor.

ExtraCredit

In Chapter 3, you learned the names of the scale degrees. Whendiscussing chords, the scale degree names are used as well. I (one)chordsarereferredtoastonicchords,whileV(five)chordsarereferredtoasdominantchordscorrespondingwiththeinformationinChapter3onthepropernamesforscaledegrees.Theonlylimitationwithusingnumbersthiswayisthatthereisnowaytoconveywhetherthatchordismajororminorsimplybyusingthenumber1,2,or3.MusiciansuseRomannumeralsinsteadofArabicnumbersforthis very reason. You may remember from math class that Romannumerals have lowercase equivalents. By using uppercase Romannumerals for major chords and lowercase Roman numerals for minorchords, musicians have a system that makes sense in every key andconveysalotofinformationaboutachord.FIGURE 8.14 shows the harmonized major scale with all of thecorresponding Roman numerals. You'll also notice that the diminishedchord is denoted by a lowercase Roman numeral and a small degreesymbolnexttoit.That'sthestandardwaytoindicatediminishedchords.

INTIME

Romannumeralsareastandardwayformusictheoristsnotonlytonamechords, but also to analyze choral structures in pre-existing music inorder togainsome insight intohowthemusicwasconstructed.Romannumerals are still a convention in classicalmusic. If you plan to studymusic formally, becoming more familiar with Roman numerals isessential.

MinorScaleHarmony

Theminorscalehasa fewpeculiarities.Theminorscalehas theexactsamenotes as themajor scale and accordingly should have the exactsameresultingchords, just inadifferentorder,but theminorscalehassome quirks when it comes to harmony. You may recall the harmonicminorscale,aminorscalewitha raisedseventh tone, fromChapter4.The harmonic minor scale exists solely to correct the harmony of theminor scale andmake itmore useful. Take a look at a “normal”minorscaleharmonizedwithtriadstoseewhatyouget.

By harmonizing the A natural minor scale like this, you get the samechordsasyoudidinCmajor,buttheyarejustinadifferentorder.Thereisnothingwrongwith thenaturalminorscale.However, in tonalmusic,

thatminorscaleisnotharmonized,becauseit'slackingwhatisknownasa proper dominant chord. You will get a chance to examine functionalchordprogressionsinChapter10toseehowtheminorscaleisactuallyusedinpractice.

9

SeventhChordsandChordInversions

Chords are more than just a collection of intervals! You know fromChapter 8 that chords have their origins in scales and melodies. Youneedto lookat twomoreaspects inordertounderstandchords intheirentirety: seventh chords and chord inversions. Seventh chords are thenextlogicalstepafteryouunderstandtriadsandareusedextensivelyinmusic throughout the ages. Inversions allow your chords to movesmoothlyandefficientlyfromonechordtothenext;thisisthefoundationforvoiceleading.

SeventhChords

A triad is a three-note chord; thismuch you know. Triads take care ofmostofthebasicharmony,butnotallofit!Youbuildallofyourchordsinthirds.Whenyouderiveddiatonicharmonyfrommajorandminorscales,yousimplystackedthirdsfromeachrootandcameupwithseventriads—allbuilt in thirds.Yourknowledgeof intervalsallowedyou todecodewhatthetriadswereandwhatordertheyappearin.

Now,whatwouldhappenifyouaddedanotherthirdtoyourtriads?Well,simply,you'dformseventhchords,whicharenamedsobecausethelastintervalyouaddissevennotesawayfromtheroot.Youcouldcallthemquad-ads,butitdoesn'thavethesameringtoitas“seventhchord”does—plusitsoundslikeaformofsit-ups!

INTIME

Themajorityoftheharmonyyoudealwithisbuiltinintervalsofthirds.This type of harmony is called tertian harmony and is the basis for“common practice” or “tonal” harmony that is studied and still utilizedtoday.DiatonicSeventhChordsRemember thetermdiatonic?Itmeans“fromthekey.”Youfirst learnedaboutdiatonicwhenyouformedsimpletriadswithinascale.DoitagaininFmajor!Now,tomakethemintoseventhchords,yousimplyneedtoaddanotherthirdontopofeachtriad,addinganintervalofaseventhifyoumeasurefromtheroot.RemembertouseonlythenotesfromtheFscale(F–G–A–Bb–C–D–E–F)whenadding your thirds to keep this examplediatonic.Doingsowillleaveyouwiththeseseventhchords:

From this listofchords,yousee fourdifferent typesofseventhchords:major seventh, minor seventh, dominant seventh, and half diminishedseventh.Notice that inFIGURE 9.2, the Roman numerals used to analyze thechords did not identify which kind of seventh chord you wereencountering.Theysimplyadded“7”nexttoeachRomannumeral.Theanswerhad tobespelledout.Becauseof this,youneedtounderstandwhat makes a major seventh different from a dominant seventh, eventhough both use uppercaseRoman numerals (signifyingmajor chords)withseventhsattachedtothem.

PointtoConsider

Typically, even if your experience with theory is limited, you've comeacross,played,orheardaboutaG7chord(oranyotherroot).Thatisonekindofseventhchord(asyouwilllearnabout).Thisbookusesthetermseventh chord as a broad category. Seventh chords come in manydifferenttypes,andG7issimplyonetype.Diatonicseventhchordsaredefinitelyuseful,andinChapter10,youwillsee justhowuseful theyare,when the focus isonchordprogressions.For now, you need to understand the structure of the seventh chords,becausetherearemorethanjustthefourdiatonicseventhchordsusedinmodernmusic!

SeventhChordConstruction

Here,youwillexploreallthedifferentseventhchordsthatareavailabletoyou.Youshouldbegintothinklikethis:Aseventhchordisnothingmorethan a triad with an added seventh interval (whenmeasured from theroot).Doingsowillgiveyouatleasteightseventhchords(fourpossibletriads and two sev-enths), although there is onemore that breaks therulesatouch(moreonthatsoon).Gothroughthemonebyonesoyoucanseehowtheyareputtogetherandhowtheyarenamed.MajorTriadswithSeventhsIfyoutakeamajortriadandmakeitintoaseventhchord,youcancomeupwithonlytwopossibilities:amajortriadwithamajorseventhontop,andamajortriadwithaminorseventhontop.StartwithFIGURE9.3.

Whenyoulookatthatchord,youcanlookattwothings:first,youhaveyourmajor triad,D (D–F#–A),andyouhaveanaddedC#.The intervalfrom the rootof thechord to theseventh (D toC#) isamajorseventh.Callthischordamajor/majorseventhchordforasecondbecauseittellsyou exactly what you have:amajor triad with a major seventh intervaladded. Now, the rest of the world will simply call this chord a majorseventh,as inDmajorseventh,orDmaj7 forshort.Many theoristswilluse “major/major seventh” to bemore specific, but if you say “Dmajor

seventh,”you'resayingexactlythesamething.Themajorseventhchordis found on the first (tonic) and fourth (subdominant) degrees of aharmonizedmajorscale.Youcouldthinkoftheformulaforamajorseventhchordasbeing:1,3,5,7(Thisisifyoutakethescaledegreesfromamajorscale.)

ExtraCredit

Themajor seventh chord is interesting for two reasons: First, you canspell it simply by choosing the first, third, fifth, and seventh notes fromany major scale. This is because a major seventh chord is the tonicseventhchordinamajorkey.It'salsointerestingthatitspropernameof“major/majorseventh”shortenstosimply“majorseventh.”

ThenextpossibleseventhchordwouldbeFIGURE9.4.Lookingat this chord, youseeanotherDmajor triad (D–F#–A)andanaddedseventhofC.The intervalbetweenDandC isaminorseventh.This chord is fully called a major/minor seventh chord. When it'sshortened,it'ssimplycalledaseventhchord,asinG7,orD7inthiscase.Sincethetermseventhchordisfartoogeneralformusictheory,theoristsandmanymusicianscall thischordadominantseventhchordbecause,as illustrated inFIGURE 9.1, this chord occurs only on the fifth scaledegree, which has the proper name of the dominant scale degree.Whichever you call it,G7 orG dominant seventh, both are acceptableandcorrect.Theformulaforadominantseventhchordis:1,3,5, 7(ifyoutakethescaledegreesfromthemajorscale).Dominantseventhchordsarereallyimportant!It'sawfullyhardtohaveharmonywithoutdominant(V)chords.MinorTriadswithSeventhsWhenitcomestominortriadswithsevenths,therearealsotwovarieties!StartwithFIGURE9.5.

StartwithaCminor triad(C–Eb–G)andaddthenoteBb.The intervalfromCtoBbisaminorseventh,sothischordiscalledaCminor/minorseventhchord.It'sshortenedtosimplyCminorseventhorCm7orC-7.Thisisthebasicminorseventhchordthatisfoundonthesecond,third,and sixth scale degrees of a harmonized major scale. Also worthmentioningisthatagain,justlikethemajorseventh,whenboththetriadand the seventh are the same (bothminor), the name of the chord issimplyminorseventh.Theminorseventhchordisalsothechordyoucanformbytakingthefirst,third,fifth,andseventhnotesfromapureminorscale(Aeolian).Ifyouwantedtorelatethescaletomajor,itsformulawouldbe:1,b3,5,b7(relatingthescaledegreestothemajorscale).Thenextseventhchordthatyoucometoisyourfirst“unnatural”seventhchordinthatit'snotformedinthediatonicmajororminorscales.TakealookatFIGURE9.6.

ThisCminortriadwithanaddedBnaturalgivesusaveryunusualsound—unnatural,even!TheintervalfromCtoBisamajorseventh,sothefullname for this chord would be a C minor/major seventh chord. Thereactually is no shortening for this chord; it is always referred to as aminor/major seventh chord. The only shorthand youmay see is in thechord symbols in popular music: Cm(maj7), C-(maj7) or Cmin(maj7).While these chords have an unusual sound, they can be quite strikingandbeautifulwhenusedinthepropercontext.Again,thistriaddoesnotoccuranywhereinthenaturalmajororminorscales.

PointtoConsider

If you were to harmonize the harmonic or melodic minor scales, youwould spell aminor/major seventh from the tonic scale degree. This iswheremoderntheoristsseethechordcomingfrom.Othersthinkthatitissimplythenaturalextensionoftryingaminortriadwithamajorseventhintervaladdedtoit.Eitherway,itexistsinjazzandpopularmusic,mostfamouslyin“UsandThem”byPinkFloyd,ontheir legendaryDarkSideoftheMoonalbum.Ifyouweretoderiveaformulaforaminor/majorseventhchord,itwouldappear as follows: 1, b3, 5, 7 (if you take the scalesdegrees from themajorscale).That's all you can do to minor triads and sevenths! That brings yourgrandtotaluptofourseventhchords,andyou'rethroughonlymajorandminor!Nextup:diminished.DiminishedTriadswithSeventhsDiminished chordsare a bit tricky, especiallywhen it comes to namingthem. Start with the diatonic diminished seventh chord, built from theleadingtoneofamajorscale.

WhatyouhaveisaBdiminishedtriadwithanaddedA.TheintervalfromBtoAisaminorseventh,sothefullnameforthischordisadimin-ished/minorseventh.However,here'swhereitgetstricky.Thischordiscalledahalfdiminishedchord.Halfdiminishedchordsusethissymbol:BØ7.Ifyouwantedtoderiveaformulaforthehalfdiminishedseventhchord,itwouldlooklikethis:1,b3,b5,b7(ifyoutakethesefromthemajorscale

degrees).This chord, while it may be the “diatonic” chord, is not the typicaldiminished seventh chord you see. Take a look at another diminishedseventhchord,whichwillexplainwhythatparticularchord iscalledhalfdiminished.

WestartwithadiminishedtriadandaddanAb.TheintervalfromBtoAbis a diminished seventh. The full name for this chord would be adiminished/diminishedseventh.Justlikemajorandminorseventhchordsthat share the same name and type of seventh, this is the diminishedseventh chord. It's also calleda fully diminishedseventh chord, but formost people, “diminished seventh” will do. The º symbol for a fullydiminishedseventhchordisBº7.If you wanted to derive a formula for the diminished seventh chord, itwould look like this: 1, b3, b5, bb7 (if you take these frommajor scaledegrees).Note:Thisisthefirsttimeyou'veseenadoubleflat inachordformula!That's because fully diminished seventh chords don't occur inmajor orminor scales naturally. They are the result of stacking of minor thirdintervals.Youcanalsoderive thischord ifyouharmonize theharmonicminorscaleattheleadingtonedegree.

HalfandWholeDiminished

It'sabit confusing—why isonediminishedchordhalfdiminishedandanother whole diminished? Well, for starters, part of this is simply aname. But there's more to it than that. The diminished triad is asymmetricchordinthatitusesallminorthirdintervals.Whenyouspelladiminishedseventhchord,youactuallyuseallminorthirdsagain(B–D–F–Ab). It iscalled “fully”diminishedbecause it follows thepatternofall

minor thirds and becomes perfectly symmetrical at that point. A halfdiminishedchord(B–D–F–A)hasamajorthirdbetweenthefifthandtheseventhandisn'tfullydiminishedbecauseitlosesthepatternofallminorthirds.That'swherethedifferencecomesfrom.Inmusic,whenyouseediminished chordswith sevenths, 90 percent of the time, they are fullydiminishedseventhchords.Youdoseehalfdiminishedchords,mostlyinjazzbutsometimesinclassicalandpopularmusicaswell.Since the diminished chord comes in two flavors — half and fulldiminished — modern musicians, especially jazz musicians, help todifferentiate these two chords. One way that they differentiate them issimplybynotcallingahalfdiminishedchordahalfdiminished!Ifyoulookatahalfdiminishedchord,youcouldlookatitasaminorseventhchordwithab5.Toavoidconfusion,mostmodernmusicusesmin7b5insteadofthehalfdiminishedsymbol(Ø)toavoidconfusion.Thisway,whenyousee a diminished symbol (º), you can infer that it's a fully diminishedchord.AugmentedTriadswithSeventhsAugmentedtriadsareweirdchordstobeginwith.Theyhaveaparticularsound that simply isn't used very much. Nonetheless, modern music,especiallyjazz,makesuseofaugmentedseventhchords,whichcomeintwovarieties.StartwithFIGURE9.9.

Start with the G augmented triad of (G–B–D#) and add an F#. TheintervalfromGtoF#isamajorseventh,sothischordwouldbecalledanaugmentedmajor seventh. For short, you see the symbolG+(maj7) orGaug(maj7).Ifyouwantedtoderiveaformulaforthischord,itwouldlooklikethis:1,3,#5,7(ifyouderivethisfromthedegreesofamajorscale).Thischorddoesnotoccurinnaturalmajororminorscales,butyoucan

finditonthethirddegree(submedi-an)oftheharmonizedharmonicandmelodicminor scales. It's a very strongmusical soundand it's used inmodern jazz quite a bit as well as late romantic and twentieth-centurymusic.TheotheraugmentedchordisshowninFIGURE9.10.We start again with the G augmented triad and add the note F. Theinterval fromG toF isaminorseventh, so the full name for thischordwould be an augmented minor seventh. Typically, you'll see thisshortened to G+7, Gaug7, or G7#5 — all are synonymous. The G+7chord is closely related to a G7 chord. The augmented nature of theraised fifth issimplyseenasanalteration.Typically,whenyousee thischord, it functionsmuch the sameway that a dominant V chord does.Moreinthenextchaptersonusage.

Ifyouwantedtoseetheformulaforthischord,itwouldlooklikethis:1,3,#5,b7(ifyouderivetheformulafrommajorscaledegrees).Well, as far as seventh chords go, that's all you have!As youwill seefrom themusic lookedat later in thebook,outof theeightchords,youtypically see four or five of these chords in everyday usage, but if youwant to understand everything there is to know about chords and howtheyareformed,thenyou'llwanttoatleastunderstandhowtoformthemfromtheirintervallicrelationships.

SeventhChordRecap

Youjustspentafairamountoftimegoingoveralleightseventhchords,soitwouldbeagoodideatocodifyallthatinformationintoonesectionwhereyoucanseeall thechords from thesame rootand,also,all theformulassidebyside.Firstupisachartofeverypossibleseventhchord

fromtherootofCinnotation.

Now,lookatalltheformulasasderivedfromamajorscale.FormulasDerivedfromaMajorScaleMajorSeventh—Cmaj7:1,3,5,7DominantSeventh—C7:1,3,5,b7MinorSeventh—Cmin7:1,b3,5,b7Minor/MajorSeventh—Cmin(maj7):1,b3,5,7HalfDiminishedSeven—CØ:1,b3,b5,b7FullyDiminishedSeven—Cº7:1,b3,b5,bb7AugmentedMajorSeventh—C+(maj7):1,3,#5,7AugmentedSeventh—C+7:1,3,#5,b7Youhavealmostcompletedyourunderstandingofchords!Now,youwilllearnaboutchordinversions.

InvertedChords

Whenyouthinkofthewordinverted,whatcomestomind?Mostpeoplethink “upside down” or “backward.”When it comes to inverted chords,this isnot too far from the truth,actually.Start off by saying thateverytriadand seventh chord youhave seen in this bookhasbeen in “root”position. Root position means that the root of the chord (the tone itsnameisderivedfrom)isthelowestnoteinthechord.Now,therearealot

of timeswhenchordsappear in rootposition;however, it'snot theonlywaythatchordsfunction.Anyothernoteinthechordcantakethelowestvoice, and that is exactly what an inversion is: when the third, fifth, orseventhnote(ifpresent)isinthebassvoice.Inversionscanmakechordsabitharder tospotonpaperbecauseyoulose thatwonderful “thirdorder” that yougetused towhenyoustart tomemorize the triadnames.Regardless, invertedchordsare found inallstylesofmusic throughoutalmost theentirehistoryofwrittenmusic,soyoushouldknowalotaboutthem.Withinvertedchordscomesanewsetof symbols you also have to learnwhen you analyzemusic.Startwithtriadsandtheir inversionsandthenmoveontoseventhchordsastheyaretreatedabitdifferently.InvertedTriadsOkay, start off with your friend, your old pal, the root positionCMajortriad.

By now, you should be able to identify this chord quickly as a rootpositionC triad. If youwere to go a step further and analyze it with aRomannumeral,youwouldgiveittheRomannumeralI,becauseinthekeyofC,CisthetonicorIchord!Now,ifyouwanttostartinvertingthistriad,allyouhavetodoisraisethebassnote(whichisC)oneoctave.TheresultisFIGURE9.13.WiththeCraisedupanoctave,thethirdofthechord(E)takestheplaceasthelowest-soundingnoteinthechord.Wheneverthethirdofthechord

is inthebass(thelowest-soundingvoice),thattriadissaidtobeinfirstinversion.Now, in termsof naming this chord, there are twoways: theclassicalwayandthemodernway.Youwillbegivenboth.Theclassicalwayofnaming this triadwouldbe tocall ita I6.Why is itcalled a I6? If you look at the interval between the lowest note in thechord(E)totheC,theinterval isasixth,sothat'swherethesixcomesfrom. If you're wondering why the interval from the E to the G isdisregarded, it'sbecause it'sa thirdand it'saccepted thatyou'dhaveathird.It'sjustthewayit'sevolved.Whenanalyzing this chord in classical style, every first inversion chordwillhaveasmall6subscriptednexttoitsRomannumeral.Thisistruenomatterwhatkindoftriaditis;major,minor,diminished,andaugmentedinfirst inversion are all “6” chords. It also doesn't matter which Romannumeral they are functioning as. All seven chords in the harmonizedscalecanbeinfirstinversionwiththemarkingofasubscripted6.Now, as to the modern notation, this one is easy: The triad is simplycalledC/E,whichtranslatestoCchordwithanEinthebass.Theslash(/) is commonly referred to as “over,” as in “triad over bass note.”Regardlessofwhichiseasier,it'sreallygoodtoknowboth—ifyouwanttolearntraditionaltheoryatsomepoint,you'llneedtoknowthesefiguredbasssymbols.Ontothenextinversion!Rememberhowthefirstinversionwasmade?Yousimplytookthelowestnoteandpoppedituponeoctave.Well,togettoasecondinversion,youaregoing todoexactly thesame thing.This time, youstartwitha firstinversion triad and move the E up an octave. The result is shown inFIGURE9.14.

Thatwasn'tsohardtodowasit?So,tosummarizewhatyouhavenow:Youstill haveaC triadand thenotesC–E–G— thoseelementsneverchange;whathaschangedisthatthelowestnoteinthechordisnowthefifthofthechord(G).Wheneverthefifthofthechordisinthebassofany

triad,itbecomesasecondinversiontriad.TheclassicalwayofnamingthistriadwouldbetocallitaI64.It'saI64triadbecausetheintervalsfromthelowestnote(G)areasfollows:GtoEisasixthandGtoCisafourth,sothat'swhere64comesfrom.

INTIME

Inbaroquetimes,harpsichordistsreadinvertedchordswrittenas“figuredbass.”Figuredbasswasbasicallyabassnoteandabunchofnumbersunderthenotes.Theplayerwouldknowbasedonthenumberspresentwhat chord to play and inwhat inversion— this is verymuch like themodernjazzguitaristorpianistwhoreadsoffaleadsheet.AmodernmusicianwouldseethatchordasC/G,whichisdefinedasaCtriadwithGasitslowestnote.Sincetriadshaveonlythreenotes,youarealloutofinversions!Torecap:

Ifachordisinrootposition,nofurtheractionisnecessary.Ifachordisinfirstinversion(thethirdofthechordisinthebass),itwouldbecalledaI6orC/E(dependingonthetriad;Cisjustanexample).If a chord is in second inversion (the fifth of the chord is in thebass), itwouldbecalledaI64orC/G(ifCtriadsareusedasexamples).Anytriad,regardlessofitstype—major,minor,augmented,ordiminished—canbeinverted.Every chord in the harmonized scale can be inverted, so every Romannumeral fromI toVIIcanbe invertedusing the figuredbass symbols forfirstandsecondinversion.IfyouseeaRomannumeralwithnothingafterit,itisinrootposition.

Now,ontoseventhchords,whichinvertthesameway,excepttheyhaveonemorenoteinthemandthatchangeshowtheyarenamed.InvertedSeventhChords

Intheory,invertedseventhchordsarenodifferentfromtheinversionyoujust learnedaboutwith triadic inversions.Theonlydifference is that forstarters, a seventh chord has one extra note, so you get one morepossible inversion:the third inversion. The other difference is that theclassical music theory figurations that name the inversions arecompletelydifferent forseventhchords.Other thanthat, thesamerulesapply,andyoucanshootthroughtheseprettyquickly.You'regoingtousetheG7(G–B–D–F)chordinourexampleinthekeyofC,sothischordwouldfunctionasadominant,orV,chord.Inrootposition,nothingchanges,so there'snothingtoshow, it'ssimplyG7orV.ThefirstinversionofaG7chordmovestheGupanoctave,placingtheBinthelowestvoice.ThisinversionisspecifiedwiththesymbolV65.YoucouldalsocallthischordG7/B,orGseventhwithBinthebass.

The65mayseemconfusing,butit'snotreally;thereisasixthfromBtoGandafifthfromBtoF,sothat'swherethefigurationcamefrom.ThesecondinversionwouldputtheBupanoctave,leavingtheDasthenoteinthebass.TheinversionisspecifiedasaV43chord.ThefourthisfromDtoGandthethirdfromDtoF.ThischordcouldalsobecalledG7/D,orGseventhwithDinthebass.

ThethirdinversionofaG7chordplacestheDupanoctave,leavingtheseventhofthechord,F,inthebass.ThefigurationofthischordiscalledaV2chord.The2 issimplytherebecausethe interval fromFtoGisasecond(sinceeverythingelseinthechordisthirds,youdon'tneedtolistthem).ThischordcouldalsobecalledG7/F,orsimplyGseventhwithF in thebass.

PointtoConsider

Here'saneasyway to remember the inversion figurationsofaseventhchord.Startwith65forafirstinversion,43forasecondinversion,and2for the third inversion. The numbers simply descend from 6: 65-43-2.That'seasytoremember,right?TorecapSeventhChords:

Ifaseventhchordisinrootposition,nofurtheractionisnecessary.Ifaseventhchordisinfirstinversion(thethirdofthechordisinthebass),it would be called aV6 5 orG/B (depending on the chord;G is just anexample).If a seventh chord is in second inversion (the fifth of the chord is in thebass),itwouldbecalledaV43orG/D(ifGisusedasanexample).Anyseventhchord, regardlessof its type—major,minor, augmented,ordiminished—canbeinverted.Every seventh chord in the harmonized scale can be inverted, so everyRomannumeralfromItoviicanbeinvertedusingthefiguredbasssymbolsforfirst,second,andthirdinversion.IfyouseeaRomannumeralwithnothingafterit,itisinrootposition.

See, that wasn't so bad was it? You're essentially through the basicchords now. Now you'll learn a little bit about why composers useinversions,andthenyou'lltakealookatabriefexamplefromJ.S.Bachtoseehowamasterusesinversion.WhyInvert?Whyinvertchords?Invertedchordsmakemusicmoreinterestingtolisten

to! Using inversion can help chords move from one to another moresmoothly;thisiscalledvoiceleading.Inversioncanalsohelpkeepbasslinessmoothandmusical.Rootposition triads tend to “bounce”aroundthemusical staff in a very jagged fashion. Inversion enables chords tomove smoothly from one to another. Take a look at an example fromBachtoseeinversionsinaction.Justaquicknoteforthoseofyouwhoaren'tstudyingtraditionaltheory:inthemodernmusicworld,especiallytheguitar-drivenrockworld,inversioncan be a rarity, although youwill see inversions comeup from time totime.TheBeatles'“WhileMyGuitarGentlyWeeps”isagreatexampleofinversioninmodernmusic.Thefirstfourchordsaresimplyatonicminorchord with a descending bass note. Each chord is an inversion of thetonic chord in some way. Leave it to the Beatles to keep thingsinteresting.Ifyoulookhardenough,youcanfindmanyotherexamples,suchasthesecondchordofLynyrdSky-nyrd's“Freebird.”Keeplookingatmusicandseewheninversionshappenandwhattheendresult is inthemusic. Inmodernmusic, it's almost always to connect chords andtheirbassnotesinasmootherway.OntoBach!

QuickStudy:BachPreludeinC

Bachwastheman.Fewwilldisputehisgeniusandtheimpacthehadonmusic.Backintheday,morespecificallythebaroqueera,BachwroteasetofpiecesforsolopianocalledTheWell-TemperedClavier.Hewroteapreludeandafugueineverypossiblekeyonthepiano,justforfun.Hestartedoffwithabang!HisPreludeinCMajor isreallysomethingelse,andmostofyouwillrecognizeit.You'regoingtolookatonlythefirstfewchords of this piece (even though the rest of the prelude is full ofinversions).Eveninjustthefewfirstmeasures,you'llseewhatinversionsareallabout—especiallyseventhchord inversions.Takea lookat theexampleandseewhat'sup.

Boom!Justinthefirstfewmeasures,youseeabevyofchords,mostofthemininversion!Eachmeasureissimplyanarpeggiatedchordspreadacross the piano, so you'll have to take inventory of the notes thathappenineachmeasuretofollowalong.Lookatablow-by-blowrecapofwhatyousee.MeasureOne:Cmajorchord(I),rootposition.Nobigsurprisehere.MeasureTwo:Dminorchord(ii), third inversion!Notashockingchord,buttheinversionallowstheCtostayinthebassfromthefirstmeasure

—verysmooth.MeasureThree:G7chord(V)infirstinversion.Thefirstinversionallowsa B to take the lowest voice. That's only a half step down from thepreceding C in the measure before. Again, look how he's connectingthesechords.Measure Four: C major chord (I), root position. The B from the lastmeasure has come back toC. In fourmeasures,with four chords, thebassnotehaseitherstayedthesameormoveddownonlyonehalfstep.MeasureFive:Aminorchord(vi),firstinversion.TheCstaysinthebassbecauseoftheinversion!MeasureSix:D7chord(II—inallfairness,youhaven't learnedaboutmajor II chords,but thisone is toogood topassup,major IIchordshappenfromtimeto time), third inversion.The thirdinversionkeepstheCinthebassyetagain!MeasureSeven:G7chord(V),firstinversion.OurCfromtheprecedingthreemeasureshasfinallymoved,butonlydowntoB,onehalfstep!MeasureEight:Cmajor seventh chord (I), third inversion.TheB fromthelastmeasurewillstayinthebassbecauseofthethirdinversionoftheCmajorseventhchord. (GiveBachsomepropshere forusinga “jazz”chord200yearsbeforejazzcameintoexistence!)That's a good place to stop and take inventory. There are a bunch ofdifferentchords:C,CMajorseventh,Dminorseventh,D7th,G7th,andAminor.Ineightmeasures,youwentthroughsixdifferentchords,most, ifnotall, ofwhichwere in inversions.What's the result?The result isanabundanceofmusically interesting chords thatmove so smoothly fromonetoanotherthatitalmostsoundsasifthey'remoltenlavaflowingfromvoicetovoice. Inthoseeightmeasures,ourbassnotestartedatCandneverwentbelowB!That'sonlyahalfstepdown!Amazing!Youoweittoyourselftocheckouttherestofthepiece.Thebookstopshere because things start to get theoretically complex and Bachintroduceschordsandconceptsyouhaven't learnedyet.By theendofthisbook,though,youshouldbeabletoanalyzetherestofthepiecewithease.Andit'sworth lookingat—manytheoristsrelyonthispieceasaperfectexampleofcommonpracticeharmonyinaction.Nextup:Youget to learnhowchordsprogress fromone toanother—chordprogressions!

10

Movements:ChordProgressions

Understanding chords and how they are spelled is only one stage ofunderstanding.Once you can look at a chord and give it a name, youneed to look for context. What chord preceded this and what comesafter? Are there patterns to look at here? All these questions will beanswered in this chapter as you study how chords move from one toanother.

WhatIsaChordProgression?

Simplyput,achordprogressionisamovementofchordsfromonepointtoanother.Ifyou'veeverheardabluessong,you'veheardaprogressionofchords!Allthepopmusicfromthelast100yearsisloadedwithchordprogressions. If you play guitar or piano, you know all about chordprogressions.Thetricknowistofigureoutwhattheyare,whyyouneedtoknowthem,and,moreimportantly,howthisisgoingtohelpyou.ChordStacksWhenyoustudiedhowtomakechords,youlookedatthechordsafewways.First,youstackeddiatonicnotesfromthescalesandyousawanend result of seven different chords. You also dissected the intervallicpropertiesofeverytriadandseventhchordinexistence.Thisisonewayatlookingatchords.Butthereisanotherangletolookat.Whenyoutalkabout chords as being vertical stacks of notes, you essentially areadoptingaphilosophythatchordsare“objects,”morespecifically,verticalstacksofnotes.TheChickenortheEgg?When you study a single chord, the concept of vertical stacks worksprettywell.Asyoulookbackthroughthedevelopmentofmusic,youwill

seethatchords,althoughtheyareverticalstacksofnotes,areclosertobeingvertical collisionsof voices.Whatdoes thismean?Well, imaginethatyouarenotplayingguitarorpianoandthatyouareinachoir.Therearesopranos,altos,tenors,andbassvoices.Atthesimplestlevel,therewouldbeonesingerperpart.Now,ifyouareinthebasssection,singingonenoteatatime,areyousingingchords?No,you'resinginga line;amelody, to bemore specific. Since one voice can'tmake a chord, youlook at the net result of what all of you are singing. There are fourmelodiesgoingonatonce.Eachpartisdifferent.Now,ifyoufreezeanysingle“slice”ofverticaltime,youcouldlookatallthenotesthataresungon the first beat of the first bar and comeupwitha chord.Thatwouldmakesenseasmusicshouldsoundrichandconsonant,andchordsandharmonyallow this.Nowaskyourself if all the individual linesofmusiccame first, or if the chords were preplanned and the voices simplyfleshedoutthechordsastheywentalong.Theansweriscomplicated.It'shardtosayforsurebecausemostofthecomposers are dead, but throughout the development of music,especially classical music, lines ruled and chords were merelyafterthoughts.Putsimply:Composerswrotelinesofmelodiesthatsummedtogetheraschords when you looked up at them (vertical thinking). Since musictheoryhasthiswonderfulwayoflookingbackonmusicafterithasbeencomposed,it'seasytoforgetthatlinesruledsomuchofmusic.

PointtoConsider

Chords and melodies are tied together very tightly. When you play amelody, you can almost imagine what harmony is present with thatmelody. Because of this, it's possible to think melodically andharmonicallyat thesame time.Beyond the theoreticalunderpinningsofwhatmelody notes fit withwhich chords,when you listen to amelody,that melody has a way of telling you what chord it wants to haveaccompanyit—allyouhavetodoislisten.Now?Ismusicanydifferentnow?Dependswhoyouask.Dosinger/songwriterswriteinlines?Sure,theysingamelodyline,butdothechordstheyplayon their guitar or piano come from that same thinking (linear)?Nowadays,especially inpopmusic,chordsandchordprogressionsareunitsthathavelittletodowiththeoldmodel.That'snottosaythattheycan't,and thatpopularmusichasnovoice leading in it, but the largestamount of popularmusic is simply conceivedwith chords as blocks ofinformation,andmelodiesare layeredon topof thechords.Now,allofyou(theoldschoolandthenewschoolmusicians)canlearnfromeachother.Takealookbackathistoryandseewhathappened.

ProgressionsinTime

If youuse your theory tools, you can look back at any pieceofmusic,new or old, and figure out what chords are used and why. The betterquestiontoaskiswhy.Whydidanythinghappenthewayitdid?WhydidBachusecertainchordsandnotothers?WhydidBeethovenandMozartusesimilarchords?Weretheyworkingfromsomesortofrulebook,sotospeak?Theanswerisno.Harmonydeveloped.Simpleasthat.Diatonicharmonywasalongtimeinthemaking.Itstartedwithonevoice,thenasecondwasadded,andsoon,and theneventually triadsandharmony

fell into place. It wasn't until the baroque era that harmony started tosolidifyintosomethingrecognizable.Thiswasn'tbecauseBachandallofhisbaroquebuddieshadahandbookofsorts!Themusicsimplyevolvedbecause musicians listened and studied what had come before. Theytookwhattheylikedandmovedforwardfromthere.Theoristscanonlylookbackandtrytofitallthemusicintosomesetofrules.Butthisisnotalwaysinyourbestinterest.Itisworthnotingwhenacertainsequenceofchordshappensoverandoverandoveragain.Buttryingtofigureoutwhywilldriveyoucrazy.Tohelpyou tackle this issue, thisbook isgoing todoabout300years'worthofhomework for you, sorting throughall themassiveamountsofmusicandcomingtosomeconclusionsforyou.Intheend,you'llseethatthere are sounds that are associated with feelings, moods, and otherthingsthatcannotbequantifiedwiththeory.“Amen”canbesummarizedby playing a IV chord followed by a I chord. Much of music can besummarizedthisway,butthesparkofwhichchordtouseandwhenisupto you. After you've taken a look at a few examples of some commonprogressions,therestofmusicandcompositionisuptoyoutoexplore.Once you get beyond the basic tools, there areno rules. Some of thecoolestmodernmusicbreakseveryrulethereis,yetitsoundsbeautiful.Remember:musicfirst,theorysecond.Inthischapter,you'regoingtogetabunchof theory; it'sup toyou in thenextchapters to turn the theoryinto music. It's a good challenge worthy of anyone who loves musicenoughtostudyit.

DiatonicProgressionsandSolarHarmony

The logical place to begin iswith progressions that are purely diatonic(comingfromthemajororminorscales).Justusingthechordsfromthediatonicmajorscalecanmakealotofmusic.TakealookatthekeyofDmajoranditschords.

Ifyouare in thekeyofD,anyof thesechordswouldbeacceptable foruse,sincetheyaremadeupexclusivelyfromnotesintheDmajorscale(juststackedtogether).Now,you're lookingatsevendifferentchords,somemajor,someminor,andonediminished.Whichonesdoyouchooseandwhy?Well,firststartoutwitha concept,and thenyouwill explore thechordsyouseemostoften.Inanymusicalkey, thetonic,whether it'sanoteorachord,carries themostweightand importance.So, youcouldsay that the “one”chord isthe center of your universe and you'd be right. In harmony, especiallytraditionaltonalharmony,youprettymuchcan'tescapethefactthatthetonicisapointofresolution.Musictypically,ifnotalways,comesbacktothatonechord!Theanalogyaboutthetonicchordbeingatthecenterofyouruniverseisgoingtoserveyourmusical imaginationverywell. Imaginethat theonechordisatthecenterofthesolarsystem;it'sthesun,sotospeak.Alltheother chords rotate around that central chord with different degrees ofpull(moreonthatlater).Thisconceptiscalled“solar”harmonyandisn'tjust somethingmade up for this book; it's actually an acceptedway tolookatchords.Asyouwill learn,thetonicchordisreally important, justlikethesun.PrimaryChordsIn a major key, there are three “primary” chords, which are the basicchordsused tospelloutandharmonize thekey.Theprimarychords inanymajorkeyareI,IV,andV.Notcoincidentally,all threeof theprimarychordsaremajor.Now,whatcanyoudowith justprimarychords?Themajorityof folkmusic,sacredmusic, all of blues, and a good chunk of rock are based on primarychords. Ever heard the phrase “three-chord rock”?Well, those are thethreechords.Foran illustration, takea lookatasongmostpeoplearefamiliarwith:“AmazingGrace.”FIGURE10.2anexampleofaleadsheet.Foreaseofreading,thissongwaskept inDmajor.Themelody isontopandthechordsare listedbysymbolonly.Forthebenefitoftheguitarplayers,chordgridswereputin.Apianoplayerwouldhaveto“realize”thechordvoicingsonhisown,butthis does not change the fact that this simple folk melody is properlyharmonizedwiththethreeprimarychordsfromitshomekey.

Thisisthefirststeptoanalysis!ThekeysignaturetellsyouDmajororBminor,buttheexistenceofD,G,andAchordstellsyouforsurethatyouare in the key of D major as those chords— I, IV, and V— are theprimarychordsforDmajor.Theprimarychordscangoalotfurtherandtheyarenotrelegatedtopopandfolkmusic.Classicalmusicmakesheavyuseofprimarychords—alltonalmusicdoes.Threechordswillgetyouonlyso far,soyouneed to lookabitdeeperintothescaletoseewhatyoucanfindtouse.

SecondaryChords

The I, IV, and V chords will get you pretty far in music writing andanalysis,butyouhavemoreoptions:Youhavethesecondarychordsinthekey.Thesecondarychordsarethe ii, iii,andvichords inanymajorkey.AsyoucanseefromthelowercaseRomannumerals,all threeofthesechordsareminor.Onceyouknowwhatchordsarediatonictoakeyjustrememberthattheprimarychordsarethemajoronesandthesecondarychordsaretheminorones!

PointtoConsider

Butwhat about the diminished chord? The diminished chord is specialandneeds tobe treatedwithsomecare. Ingeneral,you find itmore injazzandclassicalthaninpop,althoughthat'snottosayitdoesn'texistinallstylesofmusic.Tolearnaboutthediminishedchord,youshouldlookat the solar harmony universe and the chord ladder to see whendiminishedchordsareactuallyused.Ismusicwrittenwithonlysecondarychords?Notoften,although if youlook for rules, you'll almost always find some rule breakers. What thesecondarychordsdoisembellishtheprimarychordsandgiveyourchordprogressions some more variety. Here is an example of a bare chordprogression (no melody) with voicings for piano and guitar using bothprimaryandsecondarychordsinthekeyofAmajor.

Asyoucanseeintheexampleandhearfromtherecording,thisexampleflowsalongwell.OnlychordsthatarediatonictothekeyofAmajorareused andwhile the resultmay not rock theworld ofmusic, it's a nice-soundingchordprogression.The key point here is that chords aren't chosen at random. There aresome very nicely established normswhen using chords. The first stepwouldbetogetahandleonusingdiatonicchordsandwritingwiththem.After you get a handle on diatonic writing, you can explore, throughanalysisofothermusic(musicyoulike),exactlyhowfaroutsidethelinesyoucancolor,sotospeak.

Now,you'regoingtolearnsometypicalwaysthatchordsprogressfromonetoanotherbystudyingsolarharmonyandthealmightychordladder!

ExtraCredit

Lookat the twoexamplesof chordprogressions in this chapter.Noticeanything?Well,tostartoffwith,eachstartsandendsonthetonicchord.Thepenultimate (second to last)chordwasaVchord ineachcase. Isthismerelyanaccident,ordoVchordsprecedeIchordsattheendofaprogression (alsocalledacadence)?You'll justhave to readon to findoutforsure.

SolarHarmonyandtheChordLadder

Whiletherearesevendiatonicchordstouse,whichonetouseandwhyhas no steadfast rule to it — no one can tell you how to compose!However,it ispossibletolookbackovertheevolutionofmusicandseesometrendsthatareworthstudyingevenifyouchoosetogooffinyourowndirectionandlookatchordsdifferently.Earlierthisbooktouchedbrieflyonsolarharmonybystatingthatthetonicchord is themost importantchord inanykeyand that theotherchordscirclearoundit.Nowyou'lldiscoverwhatthisactuallymeans.Intonalmusic,thetonicchordservestworoles:thestartandtheend.Itbeginsyourphrasesandendsthem.Thetermgravity ishardtoexplainonpaper,butyouknowitwhenyoudropsomethingonthefloor.Musicalgravity is such that when you write tonal music, progressions tend togravitate back to the tonic chord each time. Because phrases tend towant to come to rest and end there, much of music history sawcomposersworktheirhardesttoprolongtheinevitablemomentofcomingbacktothestrongtonic.Eventually,tonalityinclassicalmusicfelloutoffavor because for too many composers, the strong tonic chord grewincreasinglydifficult to findnewways touse.Amazinglyenough, to thisday, tonal music thrives, and harmonic gravity is what gives music itspowerandbeauty.

Hereisareallygoodexampleoftonalgravity.Makesuretolistenorplaythisexampleonsomeinstrumentrightnow.

Isn'tthatbrutal?Doesn'tthatF#wanttopulluptotheGmorethanyoucanexpress?Whydoesitdothat?Nooneknowsforsure,butwhatyouhave hit on is exactly what makes melodies and chord progressionsmove:theinevitablepullbacktothetonicnote.Yousawitwithasimplemelody;itappearsinFIGURE10.5withasinglechordvoicing:

WhyisitthatthischordrefusestositWhyisitthatthischordrefusestositstill?Thischord,aG7chord,isdiatonictothekeyofCmajor.ItistheVchord,ordominantchord. In thisexample, it isaseventhchord.So,whydoes this chordwant togo someplaceelse?Harmonicgravity. It'snotthetonicchord,it'sactuallyonestepremovedfromit;it'stheclosestchordtotonic(moreonthatinonesecond),anditwantstogototonic.

So,here'showitresolves:You cameback to the tonic, back to the center of themusical system,andfinallyyouhaveresolution.Tensionandreleasearewhatmakethiswholegamework.You've heard about two chords: I and V. Now, look at the rest of thechordsandhow theyalignwith the tonicchordby lookingat thechordladder.TheChordLadderThechordladderisaneatlittlethingthatexiststoshowtherelationshipsamongallthediatonicchordsinakey.Takealookattheladder,andthenyou'lllearnmoreaboutexactlywhatit'sshowingyou.

It'saladderwithchordsonit!Basically,thisladderisareferencetothe“harmonic”gravitymentionedearlier.All thechords in someway fall totheIchordattheend.Thereareafewthingstolookathere.First,noticethattherearedifferentstepson the ladder,andoccasionally, there ismore thanonechordonthosesteps.Whatdoesthatmean?Whentwochordsoccupythesamesteponachordladder,itmeansthatthechordscansubstituteforeachother.Beforeyougoanyfurther,youneedtoknowwhatmakesachordsubstituteforanotherchord.ChordSubstitutionsIfyoulookatthefirststepofthechordladder,youseetheI(tonic)chordandaverysmallvichordonthefinalstep.Theyoccupythesamestepbecause both chords can substitute for each other. They can do thisbecause they share common tones; more specifically, they share two-

thirdsof their tones. In thekeyofCmajor, Iandvi share the followingtones:

Oneverystepof the ladder,whenyou find twochords thatoccupy thesame place, it's because they can substitute for each other due tosharingoftones.LadderofFifthsYou've seena circle of fifths, but a ladder of fifths?Many,many chordprogressions are based onmovements of fifths.So, take a look at thechord ladderwithout the extra chords and view it as strictly fifth-basedmovementsfromthetonicchordup.Youendupwithaprogressionofiii,vi,ii,V,I.LookatthatforpianoandguitarinFIGURE10.10:

Thisexamplesoundsfinedoesn'tit?Suredoes!Thenextthingtodowouldbetostarttothrowinsomeofthesubstitutechords.SeewhatreplacingtheiiwithaIVandtheVwithaviiºchordlookandsoundlike.Yougetanice-soundingprogression!Unfortunately,nomatterhowyousliceanyoftheseprogressionsandnomatterhowcraftyyouare,whenyougettotheV(oritssubstitute,theviiºchord),youpullbacktoI.Ordoyou?RememberthesmallvichordnexttoIonthechordladder!

DeceptiveResolutionsThesmallvichordisthereasadeceptiveresolutiontotheIchord.Youessentiallybreak thepattern thatVhas to resolve to IbyallowingV toresolvetovi.It'scalledadeceptivecadence.Here'swhat soneatabout theprogression: Justwhenyou thinkyou'regoingtocadencebacktoIandessentiallyendtheprogression,themusicpullsafakeoutandgivesyouavichord.Whatthisdoesisitprolongstheprogressionasitsetsyoubackabunchofstepsontheladder,givingyoumoretimetokeepthemusicalphrasealiveandcontinuetheprogression.Ifyouwonderedwhythevichordwasinverysmallprint,that'sbecausewhileitsubstitutesforthetonicchord,it'smoreofatransport,magicallylinking you back to the real vi chord on the chord ladder. Maybe theladdershouldhavelookedlikethis:

The chord ladder does not dictate what you should or should not usewhenwritingmusic. It issimplyanumberofchoices thatwillworkwelltogether.Youdon'thavetoadheretoitatall.Whattheladdershowsisasummationofhowchords“typically”progressindiatonicsituations.Feelfreetouseitasastartingpointandgoyourownwayfromthere.

11

MoreChordProgressions

The next thing to do is actually spell out some very commonprogressions, lookat how theminor scalediffers from themajor scale,andonceandforallexplainexactlywhyVpullstotheIchordsoheavilyeachtimeitcomesaround.Nowyouwilllookatthenormsandfigureoutcreative ways to go beyond them. Chord progressions and harmonycompriseavastsubjectandyouhaveonlystartedtoscratchthesurface.Other chords and scales exist and yield great possibilities for analysisandcomposition.

TonicandDominantRelationships

Beforeyouget intootherchordsoranyother information, thefirst thingyouwanttodotostrengthenyourunderstandingofchordprogressionsistoreallyunderstandtherelationshipbetweentonicanddominantchords;especially the dominant seventh and the diminished chord that oftensubstitutesforit.Inthelastchapteryousawjusthowstrongapulltheleadingtonereallycouldhavebyplayingascaleandstoppingontheleadingtone—leavingthescaleyearningtoresolve.Youalsoplayedasingledominantseventhchordandletithangouttodry,sotospeak.Boththedominantseventhchord and the leading tone simply felt unresolved. In the case of theleading tone, you achieved resolution by completing the scale, playingthe full scale and concluding on the tonic note. When it came to thechord,youhadtoplayanotherchordafterittoresolveit.Thefactthatthedominant seventhchordwasactingasaV7chordwassolidifiedby itsresolutiontoaI,ortonic,chord.So,hereitgoes:Harmonicallyspeaking,theexistenceofaV7andaI(or

i)chordindicatesthatyouareinthekeyofthetonicchord.That'sallyouneedwhenitcomestoharmonytodefinewhatakeyis.Ithasalwaysbeenachallengetodefineclearlywhatakeyis,butintonalmusic,andespecially thecommonpracticeperiod thatmusic theorysooften studies, the tonic dominant relationship iswhat you search for toidentifyexactlywhatkeyyouarein.Now, lookatwhatmakesadominantchordpullsostrongly to the tonicchord.VoicesinMotionIfyouwant toget to theheartof thematter, therelationshipbetweenVandIisallabouttensionandrelease.Youknow,yinandyangandallthatgoodbalance stuff.V chords, especiallywhen theyhave seventhsandeven more when they are substituted by vii (diminished) chords, areextremelytense.Thetensionliesinthechorditself.LookattheV7chordandseewhatyouhave.

Stay in the key of Cmajor to keep it simple. TheG7 chord shown inFIGURE11.1containsthefollowingtones:G,B,D,andF.Now,gobackand remember what you learned about leading tones. Remember howstrong those littlebuggersare? In thekeyofC, the leading tone is theseventhdegreeofthescale,whichhappenstobeaB.Guesswhat?TheG7chordhasthatnoteinit.AndwithintheCscale,thereexistsanotherleadingtoneofsorts.Betweenthefourthandthirddegreeisanotherhalfstep.Whenyoustoponthefourthdegreeofthescale(F),itpullsdowntoEfairlyheavily.It'snowherenearasdramaticasthepullfromBtoC,butitisthere.Checkitout:

Inthatexample,youheardafullscale,whichwentuptothefourthabovethe octave (which still counts as the fourth). Again, the note does notwant tostay there; ithasgravityof itsownandpullsbackdown to the

thirdofthescale.InaV7chord,youhavetheotherleadingtone(F).So,in one chord, you have the two unstable tones played together at thesametime—nowonderitsoundstense!Butwait,there'smore,Youcangoonestepfurtherintothischord.SinceBandFhavebeenidentifiedasyour tension notes within the dominant chord, look at the interval thattheyproduce.

Bytakingthesenotesoutofthechordandplayingthemtogether,yougetanevenbetter senseofwhat's goingon.The interval fromB toF is atritone,whichisthemostunstableanddissonantintervalyouwoulddealwithonmostnormaldays.So,notonlydoestheV7chordcontainbothleading tones (the fourth and seventh of the scale), but the intervalcreatedbetweenthosetones isatritone(anotherunstablesound).Thissomething.chordisclearlywaitingtodosomething.TheBandtheFneedtoresolve.TheBwantstogouptoC.TheFwantstomovedowntoE.YoualreadyhaveaG,intheG7chord,soitdoesn'tneedtomove.Rightthere,youspelledtheresolutionofV7toI.TheDintheG7chordcanresolvetoeitherCorEintheCchord.Eitherwayyousliceit, thethirdoftheG7chordmustgoupandtheseventhoftheG7chordmustgodown.

That's it folks,nothingmoretoseehere.Ifyoucangrabontothis,youwill understand tonality. The relationship between V and I is thecornerstone of tonal harmony. Sure, there is music that doesn't make

heavyuseofit,butyou'llseemoredominanttotonicchordsthanyouwillknowwhattodowithonceyoulearntoseethem.Thediminishedchord in themajor scale (viiº) oftensubstitutes forV. Ithasºa“dominantfunction”becauseitalsopullsverystronglytoI.Theviiºchordcontainsboththe leadingtonesdiscussedearlier,and ifspelledas a fully diminished seventh, it adds an additional leading tone (theloweredsixthofthescale),whichpullsdowntoanoteinthetonicchord.ThisiswhyVandviiºcansubstituteforeachother.Nowthatyouhavethatfiguredout,it'stimetotalkaboutminorkeysandtheirchordprogressions.

PointtoConsider

One of the reasons that the relationship between dominant and tonicchordsissoimportantisthatifyouinventorythetonesbetweenbothofthe chords, you essentially spell the entire scale out (well, almostentirely).TheCandG7chordscombinetogiveusC–D–E–F–G–B–C(aCmajorscale,excludingA).That'sexactlywhytwochordstellyouwhatkeyyou'rein;theyspellitoutforyouwiththeirtones.MinorChordProgressionsMinorscalescomedirectly frommajorscales.With that fact restated, itmakessensethatwhenyoucreatediatonictriads,you'llhavethesametriads you had with the major scale—the only difference is that theRomannumeralswillchangeposition.LookatadiatonicBminorscale,harmonizedintotriads.

Now,ifyoucomparethiswiththerelatedmajorkeyofDmajor,youseethesametriads,justinadifferentorder.

Now,when it comes to thechord ladder, theminorkeydoesn't lookallthatdifferentfromthemajorversionofthechordladder.

Youwillnoticeafewthings:

The ladder progresses in movements of fifths, just like the major chordladder.Thesubstitutechordsalwayssharetwonotesincommonwiththeirpossiblesubstitutions.TheVandviiºchordslookfunny.“TheVandviiºchordslookfunny”?Well,ifyoucomparethemtothediatonictriadsinFIGURE11.5,youseetwomaindifferences:TheVchordhasbeenchangedfromaminortriadtoamajortriad.The viiº chord has not only changed from amajor triad to a diminishedtriad,butitsroothasalsomoveduponehalfstep.

Whatwouldcausesuchdramaticchanges in theminorscale?Toput itsimply, it's not the same scale (the “natural” minor scale). When youharmonizeinminorkeys,99.9percentofthetime,youusetheharmonicminorscaleas itgivesyouamajor(anddominantseventh)chordonVandafullydiminishedchordonviiº(whichcreatesadiminishedchordontheleadingtoneandsubstitutesforV7).WediscussedhowimportanttherelationshipbetweenVandIwasatthebeginning of this chapter. The relationship is just as important in the

minorscale.Thenaturalminorscaledoesnothave theproperVchord(diatonically,it'sminor),andthebVIIchorddoesnotsubstituteorpulluptothetoniceither.Soyousimplyaddaraisedleadingtonetothescale(raisedseventh tone),whichaffects theVandviiºchords,makingthemboth true “dominant”chords.Lookat theeffectof thesenewchordsonsomesamplechordprogressionsinminorkeys.

UsingDominantChordsinMinorKeys

Minorkeyprogressionsaren'tthatdifferentfrommajorprogressions.Youstill see lotsofmovements in fifthsand thechord ladder isdefinitely ineffect, but the one thing that you need to really watch out for is thedominant chord functions. As explained above, V and viiº chords arealmost always changed in minor keys. Take a look at a simpleprogression:thei–iv–vprogression.

What's wrong here? Well, listen to it. What's missing? You have acommonprogression, the i–iv–v,and itworksonyourchord ladder,butsomethingsoundsoff.Thequalityofthevchorddidn'tchange.Becauseit's aminor chord, it simply doesn't have that “gravity” that is expectedfrom the V chord (which should be about as strong a chord as theycome).IfyousimplychangetheVtoamajorchord,thingsgetawholelotbetter;justlisten.

OK, now it sounds better. You always have the option of adding aseventhtotheVchordforevenmorepull,whichyoucandoeasily.

Functionally, both progressions “work,” but the added seventh makesthingsresolveatouchstronger.Anyofthechordprogressionsfromthemajorkeywillworkwell,andaslongasyoumindyourdominantchords,allwillbecool!So,whatchanges?Well,whilethechordladdermaylooksimilar,minorkeys sound completely different because the function of each chord isdifferentthaninamajorkey.Allofasudden,ivchordsareminorandVIchordsaremajorintheminorkey.Also,thedistanceyoutravelfromnotetonoteisdifferentintheminorkeybecausetheminorkeyhasadifferentintervalpatternfromtherootand,thus,soundsdifferent.Takeaparallelprogressioninmajorandminortocomparejusthowdifferenttheysound.LookataI,vi,IV,VprogressioninCmajor.

Now,whenyoutransferthisdirectlytoCminor,lookatandlistentohowmuchthingschange!

What's the lessonhere?Tostartwith, youhave to listen toeverything.TheRomannumeralsbegin toall look thesameafterawhile,andyoucan'tallowtheorytoexistsolelyonpaper;ithastocomealive.Now,whenitcomestotherestoftheprogressions,startbymixingandmatchingchordsasyou feelappropriate in thekeys.Use theacceptedladderofchordsasastartingpoint,butrememberthatitisbynomeansa set of rules—far from it! The ladder of chords is a common startingground.Asyoustarttoanalyzemusiconyourown,whichyouwillhavetoasyouarenotgoingtogetanymoreexamplesofchordprogressionsright now (the music you already have and know holds plenty ofinformation), you will see a great deal of music that uses the chordladder.Great,youfilethatmusicawaybyhowitsounds.Doyoulikethewayitsoundswhenthescalesareuseddiatonically?It's a very agreeable sound. As you analyze, youwill find somemusicthatdoesnotgothroughtheexpectedsetofchords.Youmayseesomehuge“rules”broken.Youmayseechordsthatsimply“don'tbelong.”Youcanfilethatawaytoo,becauseintheend,nooneapproachwillwin.Themost important thing toaskyourself is,Do I like thesoundofwhat I'm

hearing?Nomatterwhatyouransweris,yesorno,analyzeitandfigureoutwhatmakesitwork.Ifyouloveit,seeifyoucanadoptsomeofthosemovementsintoyourchordprogressions.Ifyouhatesomething,it'salsogoodtoseewhattoavoidinyourownwriting.Eitherwayyoulookatit,it'sallgood,andyouwilllearnthemostbylookingatasmuchmusicasyoupossibly can.Youhavea very good set of tools now, and youwillcontinue to strengthen them as you go along, especially in the etudesectioncomingup,whereyougetnotonlytoanalyzebutalsotocreatesomemusicofyourownbasedonwhatyouhavelearned.

HarmonicRhythm

Another concept that is worth talking about separately is harmonicrhythm.Whenyoustudychordsandchordprogressionsasyouhavetothis point, it becomes clear that youare lookingat “slicesof time” in averyabstract fashion. In certain stylesofmusic, you simplymove fromchordtochordveryquickly,backandforth,repeatingasyougo.Inotherstyles of music, chords progress very slowly. The pace at which thishappensiscalledharmonicrhythm.

INTIME

The harmonic rhythm of jazz is typically very fast. Usually, there is atleastonechordpermeasureinmostjazzstandards.Becausechordsareimprovisational“milestones”forimprovisers,theytendtochangerapidly.A good counterexample of this is the “modal” jazz of Miles Davis'sfamousKindofBluealbum,whichfeaturesexactlytheopposite:chordsthatrarelychange.The chord progressions you have studied here thus far have hadabsolutely no rhythm attached to them because they are examplesdevoidofmusic:Theyarejusttherawdata.Realmusicmovesinrhythmand so do the chords. So, before you take a simple progression anddismissit,startplayingaroundwiththedurationofeachchord.Alsopaygreatattentiontothemusicyoulikeandseehowoftenthechordsmovefromonetoanother.Ingeneral,classicalmusiccangoeitherway,eitherlongordrawnout,orveryfast.Popmusictendstomoveatafairlygoodclip.It'sveryhardtogeneralize;again,youneedtolookatwhatyoulike.

VoiceLeading

The term voice leading comes up often in discussion of music theory,especially when you talk about chords and chord progressions. Voiceleadinghastwodefinitions:

1. Theartofconnectingchordtochordinthesmoothestmannerpossible.

2. Aparticularpracticeinmusictheorythatteachesasetofrulesforexactlyhowvoicesshouldmovefromchordtochord;thisisalmostalwaystaughtinfour-partwriting.

Now,foryourpurposes,youcanconcernyourselfwiththefirstdefinition

only.Voiceleadinginthetraditionalsenseisanacademicpracticethatistaughtwhenyoustudymusictheorydeeplyinhighschoolorincollege.It's valuable for some things, especiallywhen you consider that all the“rules” are almost exclusively taken fromBach'swriting style. BecauseBach was such a genius, it's not a bad thing to study. But too manystudentsgetveryboggeddownwithalltherulesandbelievethatmusichastoadheretothem.

ExtraCredit

GobacktothelastexampleinChapter9(Bach'sPreludeinC)andlookatthevoiceleadingfromchordtochord,especiallytheinversions.Betteryet, go through the Roman numeral analysis and play them as blockchordsandlistentohowdifferentlytheysound.Goodvoiceleadingcantakeasimplechordsequenceandtransformitintoamasterpiece.The challenge is teaching voice leading in away thatmakes sense toeveryone.Youcanallowtheacademicstoteachvoiceleadingtheirownway;here,youwillexperienceadifferentapproach.PracticalVoiceLeadingHow can you get practical about this?Well, for starters, chords rarelyappearintightlyvoicedtriadslikethis:

Takethisstandardguitarchordforexample:

Allthevoicesarefairlyspreadout.Theobjectofvoiceleadingistotrytosmooththetransitionsfromchordtochordasmuchaspossible.Here isasimplewayof lookingatvoice leading. In thisexample,voiceleadingisintentionallyomittedthroughaii–V–Iprogression.

See how all the block chords in the treble staff bounce from one toanother?Itlooksbadandsoundsevenworse.Ifyoutakethefollowingasamantra,you'llbeamazedatthedifferenceinthesound:Whereveryouare, get to the closest note in the next chord. Here is the sameprogressionwithbettervoiceleading:

Notonlydoesitlookbetter,itsoundsbetter,too!Thechordshavemoreof a flow to them than in the previous example. Always try to connectyour chords when you write them. If you remember the premise thatchordsarenotblocksofinformationbutvoicesthatcometogether,you'llbeontherighttrack.Keepyourindividualvoicesmovingassmoothlyasyoucan.Asyoukeeplearningabouthowtousechordprogressionswithinvertedchords,yourvoiceleadingwillonlyimprove.

12

MelodicHarmonization

You have read about chords for several chapters, and now it's time tolearnaboutmelody.Understandinghowchordsandmelodyare relatedwillcompleteyourknowledgeofharmony.Chordsneverexistaloneandmelodiescan'tsurvivewithoutchordstosupportthem.Youhavelearnedabout scales and how they make melodies. You have learned aboutchordsandtheirorigins.Youhavestudiedhowchordsprogressfromonetoanother,but it's timeto learnhowmelodyandharmonyrelate tooneanother.

WhatIsMelody?

Youhavestudiedsomanythingsinthisbooksofar,yetyouhaveneveraskedthissimplequestion:Whatisamelody?Certainly,melodyisaveryimportant aspect of music! You have learned about scales, which canleadustomelodies,butneverwhatamelodyis.Well, there is a good reason for not broaching this question—it's reallyhardtoanswer.Atitssimplest,amelodyisthe“tune”ofasong.Justsing“HappyBirthday” to yourself:You just sang themelody.Thatwaseasybecause thatparticularsong ispracticallyallmelody.What ismeantby“allmelody”?Well, inthecaseof“HappyBirthday,”whileyoumayhavesomechordsbehindit,it'snotnecessary;thetunestandsonitsownwithorwithout chords.Besides thesingle lineofmelody thatmakesup thetuneof“HappyBirthday,”there'sreallynothingelsethere.Now,forsomecontrast, listentoaBeethovensymphonyandtrytosingbackwhatyoufeelisthemelody.You'regoingtohaveahardertimedoingsobecauseasymphony is not as clear-cut! There aremultiplemelodies going on atonce.Youstarttoseewhatthissectionisgettingat.So,whygotoallthis

trouble?Well,therelationshipbetweenmelodyandharmonyissocrucialtoyourknowledge thatyouneed to learn todefine thisasbestasyoucan.Nomatterhowwellyouunderstandscalesandchords,ifyoudon'tunderstand how they relate to one another, your knowledge will beincomplete.SupportiveChordsTostarttounderstandthecorrelationbetweenmelodyandharmony,useananalogy toview the relationship.Chordsare like ladders,supportingmelodies.Atitssimplest,asinglemelodictonecanbeharmonizedwithachordaslongasthechordhasthemelodictoneinit.So,ifyouareinthekeyofCmajorandyouhaveamelodynoteCandyouwanttofigureoutwhatchordwouldworkwiththatnote,you'dlooktothekeyofCmajorand itsharmonizedchordsandyou'dselectachordthat had the noteC in it as one of your choices. If you did that, you'dcometothesethreechoices:

Now, as to which chord you'd choose, that's dependent upon a fewthings. You could listen to each one and select the one you want.However, you're dealing with one moment frozen in time, and you'dprobablywanttoseethecontext thatthisnoteoccurs inthroughoutthepiece,takingintoaccountchordsthatprecedeandfollowit.What's important is that youunderstand that at themost basic level, asinglenoteissupportedbyachordthatsharesthesamenote.Thenextchapterwillexpandonthisgreatly,butifyoueverwonderedwhy“insertanychordhere”isbeingusedatanymomentintime,looktothemelody;italwayswillberelatedinsomewayoranother.

PointtoConsider

Whenharmonizingsinglenotes,rememberthatthechordyouchoosewillcontainthemelodynoteaseither itsroot, third,or fifth. Ifyoustickwithsimple triads only, you will always have three choices. Add a seventhchordintothemixandnowyouhavefourchoicesforchords.It'snicetohavechoices!PointforPointAs you start this process, you should learn how to harmonize a scalepoint for point,meaning that each note of the scalewould get its ownchord.Ifyourealizethateachmelodynotehasatleastthreechoicesforchords, you come to a staggering number of choices. Rather than listthemall,hereisanexamplethatworkswellforyourpurposes.Insteadofchoosingrandomchords,thechordladderwasusedasaplacetostart,andtherestwereselectedbyear.Hereistheresult:

Now, that gives you an idea of how to proceed in choosing chords formelodictones—anddigthatgroovyfluteplayingthemelodyontheCD!Now,doeseverymelodynotegetitsownchord?Notalways.Gobackto

theexampleof“AmazingGrace”foundearlierinthisbookandseewhat'sgoingon.

You can see clearly that the harmonic rhythm (the pace at which thechords appear and change) has been slowed down considerably. Thetruth is thatnoteverynote inamelodyneeds tobeharmonizedwithachordofitsveryown.Thathonestlywouldbemorethanoverkill!

ExtraCredit

Runouttoanymusicstoreandlookatthesheetmusictoanypopsongyou like. You will see that 99.9 percent of the time, chords supportseveral melody notes. You'll almost never see a new chord for eachmelody note unless the melody is very, very slow—at which point theharmonyiskeepingthesongfromsoundinglikeadirge!

ChordTonesandPassingTones

When you talk about the interaction of chords and melodies, you aretalking about one basic point: chord tones or passing (nonharmonic)tones. In FIGURE 12.2, you saw each note of the major scaleharmonized with its own chord. Since eachmelody note was found ineach chord that supported it, only chord tones were used. In the“AmazingGrace”example,morethanjustchordtoneswereusedintheharmonization; passing tones were used as well. Now revisit thatexampleandseewhat'sreallygoingon.

The highlights indicate the chord tones; all other notes are passing ornon-chordtones.If youcompare theharmony to themelody, youwill seemanydifferentpointsofsimilarity.Firstoff, ingeneral, foraharmony to “work” foranygivenmelody, themajorityof themelodic tonesshouldbecontained inthechordthatsupportsit.Thereisnosteadfastruleofhowmanyperbarandsoon,butformusictosoundconsonant,themelodyneedstolineupwiththeharmonyenoughtimestomakeyoufeellikethey'reinthesamekey.IntheexampleinFIGURE12.4,youcanseechordtoneshighlightedand the passing/nonchord tones printed normally. A passing tone doesnotnecessarilyhavetobeatonethatmovesbysteptoandfromachordtone,butifyouthinkoftheodds,atriadhasthreenotesandascalehasseven,you'remost likelyusingapassing toneas the triad takes three-seventhsofthescalewithitandleavesthreeoftheotherfourtonesaspassingtones.Onlyonetonewillexistasatrue“nonhar-monic”tone,butthenagain,itmaysoundjustfine.

PointtoConsider

You're back to thinking vertically again,which is good. It's important tosee theeffectofharmonyagainstmelodiesandviceversa.Abitof thechicken-or-the-egg question, which one actually came first. In all yourvertical thinking and analysis, don't forget to listen and play eachexamplesothatyoucanhearandnotjustthinkaboutthemusic.Certainthingswon'tmakemuchsenseonpaperbutwillworkwonderfullyasyoulisten.KeyControlOneofthenicethingsaboutmelodicharmonizationisyourabilitytosetupthekeysyou'dliketouse.Whenlookingatasingle-notemelody,it'salmostimpossibletotellwhetheryou'reinamajororaminorkeyunlessyouhavesomeharmonytosupportit.Whenyoustartwithjustamelody,youcancontrolthemoodofthepiecebychoosingeitherthemajorortherelatedminorkey.Sinceanymelodictonecanbetakenbyatleastthreedifferentchords,youcancontrolyourkeysveryclosely.Hereisaverysimpleexample,usingakeysignatureofnosharpsandnoflats, which could be either C major or A minor. The example uses awhole-notemelodyoverafewbars.Lookatthemelodybyitself:

Now,whileamelodycouldgoeitherwaykeywise,thereisonethingthatcouldswayittotheminorkey.Remembertheleadingtone?InthekeyofAminor,theG#isatelltalesignthatyouareinthekeyofAminor.Themelodycarefullystayedawayfromthat—completelyonpurpose—asthatwouldhavelockedyouintothatkey.Gettingbacktotheexample,sincetheGwasavoided, lookathowthiscouldbemadeaCmajormelody:

SimplybychoosingchordsfromthekeyofC,makingsuretothrowtheall-important dominant V chord in, the key of C major is established.Theremighthavebeenachordladderused,butitwasmoreofaprocessof elimination at a piano or guitar to see what chords fit best with thenoteswritten.Now,ifyouwanttopushthisinthedirectionofAminor,that'seasytodo—justusechordsfromthekeyofAminorandmakesurethat ithas itsowndominantVchord,inthiscaseE7.Hereistheresultofthat:

By sticking toAminor chordsand typical progressions in that key, it isprettyeasytomakethis intoanAminormelody.Amazingthatasimplemelodyreallyhastobedefinedbyitschords.Thisisthegeneralbalancethat you have to follow: Melodies and harmonies rely on each other.Neitheronecanexistsolelyonitsown.

ExtraCredit

Oneof thecoolest thingsyoucandowithharmony is takeaphraseofmusic(liketheexampleabove)andharmonizeitinonekeyandthenatsomeotherpoint inthepiece,harmonizeit inanotherkey.Youwill takethesamemelodicmaterialandgiveitsomecontrastandanotherflavor.Itwill allow you to reuse good material without allowing it to soundstagnant.

TrueMelodicHarmonization

Move on to another aspect of melodic harmonization, something thatdoesn'thavetodowithharmony!Thinkofafewrecentmusicalactsthatuseharmony:SimonandGarfunkel,theIndigoGirls,andtheBeatles(andothers). The harmony referred to here is true melodic harmony: whatnotessoundconsonantwitheachother.You'venodoubtheardsomebadattemptsatharmony,usuallyatChristmaspartiesafterafewglassesofeggnog. Someone gets up and tries to sing a second part to “SilentNight”orsomeothertune.Theresultisusuallylessthandesirable.Whatyou'dliketodoishaveanideaingeneralofwhatnotesworkwhenharmonizing single linemelodies. Historically, this was the evolution ofhowchordsemerged.Gregorianchantstartedwithasinglelineofmusic,called monophony. As time went on, a second voice was added. Theintervalsthatwereallowedwerelimited,usuallyfourthsandfifths(hencethey are called perfect). Over many hundreds of years, a system ofharmony built on thirds, tertian harmony, evolved. Tertian harmony hasbeenthefocusofthisbookasitisthebasicformulaforharmony.Sincetertianhasasitsroot“tertiary”or“three,”thirdsareagreatplacetostart.OneThirdFitsAllThefirstplacetolookisthirds.Simplyput,youcanspotharmonizeanymelodybyharmonizingadiatonicthirdabovetheoriginalmelody.

The“diatonic”partissokeyhere.Youcan'tjustplayanythird(majororminor)thatyoufeellike,youhavetoknowwhatkeythemelodyisinandplay the right notes that fitwith it. Lookat a very simpleexample inDmajor,consistingofashortmelody.

Toharmonizethismelody,you'dsimplystartasecondpart, threenotesup in theDmajor scale, and follow the contour of the originalmelody.TheresultisshowninFIGURE12.9.

Thesecondlineisharmonizeda3rdabove.InverseTheinverseofathird isasixth,andasixth isanotherverynicewaytoharmonize a melody. Typically, you'd harmonize a sixth down,diatonically.Whatthisbringsyoutoistheexactsamenotesthatyouhadwhen you went a third up. The difference is that the harmony is nowbelow the originalmelody note.Both approachesworkwell.Check outourfirstexample,thistimewithparalleldiatonicsixthharmony.

Thesecondlineisharmonizeda6thbelow.Bothsoundquitenice.

INTIME

Historically,whenitcomestoharmonizingnotesandespeciallythetopicof voice leading, moving notes in parallel with each other (where onevoicefollowstheexactshapeoftheoriginalmelody)wassomethingyoualways had to be careful with. Thankfully, thirds are always nicewhenusedinparallelmotion.IntervalsYouCanUseWhen it comes to harmonizing, there are certain intervals that workalmostall the time,andsome thatareveryhard todealwith.Hereareintervalsby typeasa reference for you.Remember thatwhenyouareharmonizingmelodiesinkeys,thinkdiatonicallyforyourmelodynotes!

Unison/Octave.Notreallya“harmony”perse,buttheeffectof“doubling”amelodycanbeaverynicewaytoaddsometextures.Seconds.Secondsvergeontheedgeoftensionanddissonanceandshouldbe handled with care. They can work at certain points in a harmony forsomecolor,butyou'll rarely findmore thanone ina row;youcan forgetparallelism.Thirds.Youcan'tgowrongwiththirds.Theyjustalwayssoundnice.Theyworkgreatinparallel,too.Fourths.Fourthscanbenice,butnotinparallel.Parallelfourthsareoneofthemajor no-no rules of voice leading. However, since there is a fourthinterval from the fifthofa triad to the root, a fourthcanbe just the rightinterval.Fifths.Fifthsarealsoconsonant intervals thatworkwell.Youdon'twanttheminparallelseitherastheybreaktheothermajorruleofvoiceleading.Plus, if you harmonize with straight parallel fifths, it will sound likeGregorianchant.

Sixths.Sixths,theinverseofthirds.Thesealsoalwayssoundverygoodallthe time.Thesework in almost all situations andwork especiallywell inparallelmotion.Sevenths. Another dissonant/tense interval. They may work at certainpoints, but in general, they won't sound consonant. You're also rarely, ifever,goingtoseetheminsuccessiononeafteranother.

In general, the “tense” intervals, the seconds and sevenths, are notsomethingyoushouldavoid.Abitoftensionandreleaseiswhatmusicisbuilton,sousingthoseintervalssparinglymayaddjusttheperfectcolortoyourmusic.

ExtraCredit

Ifyouwanttostudyharmonyinevenmoredepth,youshouldcheckoutcounterpoint. Counterpoint is best exemplified in the fugues by Bach,Mozart, Beethoven, and Shostakovich. Theorist J. J. Fux's treatise oncounterpointstill remains thequintessentialwork for learningabout thissubject. A highly recommended read for those of you interested inlearningmoreabouthownotesinteractwithoneanother.

SingleLineHarmony

Harmony has been the domain of chordal instruments throughout thisbook.Sure,aclarinetinanorchestracontributestoasenseofharmonywhen you look at the whole score, but how can all of the single lineinstruments (ones that canplayonly onenoteat a time) get in on thisparty?(Therearemoresinglelineinstrumentsthanchordalinstruments.)Remember that thingcalledanarpeggio?Sureyoudo—anarpeggio isjustachordplayedonenoteatatime.Playenougharpeggiosandyouendupwith chords.Theyaren't chords in the vertical sense, as singleline instruments can't play that way, but they are harmony, morespecifically“implied”harmony.The good news is that if you play a single line instrument, you'veprobably already played harmony this way—many of you didn't evenknowyoudid!Hereisanexample:

Since thearpeggiosare labeledandnamedwithRomannumerals,you

can clearly see that harmony is definitely going on here. It's simplymovingacrossthepageinsteadofupanddownit.

ExtraCredit

Ifyouwanttoseesinglelineharmony,hereareafewplacestolook:thesolo cello suitesbyBach (andhis fluteand violin soloworks, too) andconcertosbyVivaldi,Mozart,andBeethoven.Thosearethewell-knownones. Every instrument has some principal composers; for example,Kreutzer is known exclusively as a “violin” composer. Regarding yourown instrument, you'll easily find etudes and pieces you've played tostudy.Singlelineharmonyisanunavoidablepartofplayingtonalmusic.Thinkofitthisway:Everythingstartsasscales.Scalescombinetoformchords,which,inturn,formharmony.It'salmostimpossibletowritemusicwithoutbeingawareofharmonyandits implications.Musicforthosesingle lineinstruments would be really boring without some sense of harmonicimplications.Themusicwouldsortofwanderwithoutpurpose.Takeagoodhard lookat thecontentofanypieceofmusic forasingleline instrumentandyou'regoing to finda lotmore than justnotes.Thenext etudewill showyou someexamples to look at further, but searchyourownmusicalarchives;you'resuretofindmorethanenoughtoworkwith.

DealingwithAccidentals

Hereisashortbutimportantquestion:Howdoyouharmonizeanotethatisnotdiatonictoascale?Sayyou'reinthekeyofCmajorandyouhaveamelodynoteofF#.Thatnoteisn'tinanyofthediatonicchords,sowhatdoyoudo?Well,youshouldgotothenextchapter(aftertheetude)andlearnabout advanced chordprogressions, specifically how todealwithchromaticharmony(harmonizingnotesoutsidethescale).

13

EtudeTwo:ChordsandHarmony

SpelltheFollowingMajorTriads

SpelltheFollowingMinorTriads

SpelltheFollowingDiminishedTriads

Spell Major Scales, Add Key Signatures, Add Diatonic Triads andNametheTriads

Spell Minor Scales, Add Key Signatures, Add Diatonic Triads andNametheTriads

WriteTheFollowingInvertedTriads

WriteTheFollowingInvertedSeventhChords

NameTheFollowingTriads,7thChords,andInversions

AnalyzetheFollowingMajorChordProgressionsUsingRomanNumeralsandTraditionalChordNames

AnalyzetheFollowingMinorChordProgressionsUsingRomanNumeralsandTraditionalChordNames

14

AdvancedHarmony

Diatonicharmonywillgetyouonlysofarinyourunderstandingofmusic.As music progressed, the variety and complexity of harmony alsoevolved. Diatonic chords were augmented with other harmonies toexpand the timbre and color of music. In this chapter, you will beintroducedtoothercolorsyoucanexploreasacomposerandlearnmoreofwhatyouwillencounterasyouanalyzemusic.Youwillalsocovertheimportanttopicofchangingkeysandmodulation.

BeyondDiatonic

As a student of music theory, it's only logical to start learning aboutdiatonicharmony,bothmajorandminorharmonies.Diatonicharmonyisagreat start, but aswithany set of guidelines, composers foundwaysaround these “rules” and started to addother chords into the canonofharmonytogivegreatervariety.Diatonic harmony supports diatonic melodic writing. How do you dealwith melodies that contain notes outside the scales? Also, the chordladderseems tobesomethingyoucan'teasilygetaway from.Howdoyou create interesting progressions that don't simply follow the ladderfromend toend?Youhavealready learned that thedominant chord isthe basic “end” of the progression because when you get there, youroptionsaretoeithercadenceandbeginanewphraseorresolveinsomesort of deceptive way. Composers over the course of music historysoughtwaystoprolongtheamountoftimeittakestogettothedominantchord.Withdiatonicharmony,thereisonlysomuchthatyoucando.Byprovidingsomeadditionalchords,composerscould“keeptheballintheair” a bit longer, so to speak. This refers to extended harmony, more

specifically,secondarychords.SecondaryChordsAsecondary chord is a simple concept:Takeany chord in thediatonicscaleandprecede itwithachord that is related,yetoutof thediatonicscale,addingabitofcolorandanextrasidestepintheharmonicpicture.Secondarychordscomeintwoflavors:dominantanddiminishedchords.Secondarychordscanbeusedwithfullydiatonicmelodies,addingmorerichnesstoalreadyfunctional,melodicwriting.Since dominant and diminished chords are essentially substitutes foreach other, you should know why a secondary chord works in anysetting.SecondaryDominantChordsHere'swhatyouknowaboutdominantchords:Theyare typically theVchord of a key and they have a very strong tendency to resolve up aperfectfourthordownaperfectfifth(you'llarriveatthesamenote)toatonic I chord. You know that they are so strong as to define keys bythemselves,soifyoumovedtheVchordtemporarily,toprecedeanotherchordinthekey,woulditwork?Theanswerisyes.Asecondarydominantisasimpleactionthatplacesatemporarydominantchordafifthawayfromanychordinthekey.Thinkofthisasaharmonicdetour.Nowsetupanexample.UsetheIVchordasyourtargetchord.YouwanttoprecedetheIVchordwithadominantchord.InthekeyofCmajor,IVis F major, and F's dominant chord (a perfect fifth away) is C7. Theprogressionwouldhavegonelikethis:

Now,ifyouaddthesecondarydominanttoIVintheprogression,yougetthisprogression:

Twothingstotalkabout.First,theadditionaldominantchordreallyaddsagreatflavortoanotherwise“stock”progression.IfyouthinkoftheotherchordsthatcouldhaveprecededIV,fewhavetheflavorofthesecondarydominant.Second,whatdoyoucallthischord?Intheprogression,thereis a temporary “?” in place. The chord is C7, so you could call it a I7chord,butthatwouldmisstherelationshipbetweenthesecondarychordand itsdestination. Instead,youwouldcall thatchordV7 /IV,or “fiveoffour.”Thewordof isdepictedasaslashandshowsclearlythatyouareaddingachord that is related to the IVchord, instantly resolving to theproperdestination:IV.So, here is the proper naming for the progression using Romannumerals:

ItisperfectlyclearwhatthefunctionofthenondiatonicC7chordisintheprogression, and you could easily realize this progression (write oneyourself)inanotherkeysimplyusingtheRomannumerals.

PointtoConsider

In functionalharmony,whenyouhaveasecondarydominantchord likeV7/IV, the IVchordshould follow it.Otherwise, therelationship thatyouarecreating—adominantseventhchordthatresolves—fallsshortsimplybecausethedominantchordneverresolves!SecondaryChromaticWhen you add a secondary dominant chord to a progression, you arealwaysaddingatleastone“chromatic”notetotheprogression(V/iiiaddstwo). Since these chords have notes in them that fall outside of thediatonic key, you simply get a greater variety of tones. In the exampleabove,theBbwouldseemtosmashoursacredleadingtoneinthekeyofC (B),butsince it'spartofadominantchord, itsidesteps thekey forasecond and sets up an expected point of conclusion: IV. Once youresolve,it'sbusinessasusualandtheactualVchordinthekeyrestorestheBbtoaBnaturalandthekeyhasfunctionagain.WhichChords?Which chords can have secondary dominant chords? In a diatonicprogression, all chords except the viio chord can have secondarydominants. Inall fairness,youcan'tcount Ieither,since itsdominant isnotsecondarybutdiatonic.So,here isa listofchords thatcansupportsecondarydominants:

iiiiiIVVvi

JustexcludeIandtheviio(diminished)chordandyouareallset.Now,youcan't just throwthesechords inwheneveryoufeel like it.Well,youcan,ifyouarewritingchordprogressionswithoutmelodies.Butifyouareharmonizing melodies, you need to be a bit more careful; certainconditionsneedtobemet!Whatconditions?You'reabouttofindout.WhatConditions?Where exactly can you use these chordswith amelody that you havealreadywritten?Well, a few thingshave to align for this towork. First,whenyouaretalkingaboutsecondarydominantchords,youareactuallytalking about two chords: the secondary dominant and the chord itresolvesto.Sincebothofthesechordshavetohaveconnectionstoyourmelody,youneed to have a situation where your melody supports both chords insuccession.Hereisanexamplewhereitworksreallywell:

Usingasimplewholenotemelody,youcanseethatthesecondandthirdchordsareyourpointswherethesecondarychordscomeintouse.Themelody in bars two and three use the notes E and F. Now, you couldharmonize E and F lots of different ways.When this progression wasbeingconstructed, itwasobvious that itwouldcadencewitha ii–V–I; itjustsoundedrightafterafewtriesatthepiano.ButwhattodowiththeharmonyundertheE?Therewereseveralchoices:AI6chord(C/E)couldhavebeenusedtoharmonizetheE.AvichordcouldhavebeenusedtoharmonizetheE.AiiichordcouldhavebeenusedtoharmonizetheE.Theoretically, they all worked on paper. As sounds, there were some

issues.TheI6chordsimplysoundedfunnygoingtoii;thevoiceleadingofthebasslinegoingfromEtoDjustdidn'tsitright.Theiiichordsimplyhasnever sounded that compelling inanydiatonicprogression (it's toofarfromI),sothatwasout.Thevisoundedgoodandwouldhavebeenasolid choice; however, the V7/ii, which is an A7 chord, was ultimatelychosen. The vi chord is an Aminor chord; the A7, which was choseninstead,has thesamebassnoteand two-thirdsof thechord tonesarethesame.Nowonderitworkedsowell!

ExtraCredit

How do secondary dominant chords apply to minor keys? The exactsameway theydo inmajor keys.The key is not the crucial stephere,onlythechordsthemselves.Asecondarydominant isadominantchordthat resolves to a chord in the key. It is not a key change, rather atemporarysidestep,whichcanhappeninbothmajorandminorkeys.Thetrickypartisfindingspotstousetheminyourmusic.Sometimesyouuse them and don't even know about it! Secondary dominant chords,especiallyV/V, are quite common in folk, country, and rockmusic.Youmayjuststumbleupontheminagrand,happyaccident!SecondaryDiminishedChordsWhenthefunctionofchordswasdiscussed,especiallywhenitcametothe chord ladder, you learned about what chords could commonlysubstituteforeachother.TheV(dominant)chordcanbesubstitutedbythe viiO chord. Both chords function as “dominant” chords in that theyresolve back to tonic with strength and great pull. So, in the spirit ofsecondary dominant chords,what about secondary diminished chords?Yes, thoseexist too. If thechordsbasically function thesameway,youcanusethemthesameway.Secondary diminished chords have their own set of rules. Think aboutregulardiminishedchords.Typically,youseethesechordsasviiºchords,soyoucaninfersomerulesabouttheiractions.Asecondarydiminishedchordwill:

Beeitheradiminishedtriadorafullydiminishedseventhchord.Bebuiltahalfsteplowerthanthechorditisresolvingto.Alwaysresolveupbyahalfstep.

As for their written symbols, instead of calling them V/something, call

themviiº/something.Youseesecondarydiminishedchords in classicaland jazzmuchmorethan you do in pop music because the diminished sound is not asacceptedandcommonasotherchords.Regardless,theyareverynicechordsbecausetheyhaveaveryslipperysoundtothem.Whatdoes“slippery”havetodowithmusic?It'sallaboutthevoiceleading!Here'sademonstrationinthesameexampleyouhadbefore:

Here is the samemelodyas inFIGURE14.4. Thenote that had to beharmonizedwasanE.Everythingelsewasmoreorlessset.InFIGURE14.4, V/ii, an A7 chord, was chosen. In this example, viiO/ii, a C#diminished chord, was selected. Since the chord was only a half stepbelowtheiichord,thesecondarydiminishedchordslidintotheiichord.Even the bass line from the beginning of the progression—C–C#–D—wasaverysmoothandslipperymovementofbassnotesandharmonies.BothA7andC#diminishedsupporttheEasamelodynoteastheybothhaveEintheirchords,butmorethanthat,ifyouweretostepoutsidethekeyofCforasecondandthinkaboutA7asadominantchord,youwouldhavetoimaginethekeyofDforasecond(thekeywhereA7isV).Thesubstitute dominant chord in the key of D is C# diminished! If youcompare FIGURE 14.4 and FIGURE 14.5, you'll see that all thathappenedwas thatasecondarychordwaschosen for the ii chord,buteachexamplesimplysubstituteda“dominant”chordofsomesort(eitherdominantordiminished)thatresolvednormallytotheiichord.A“temporary”VI(dominanttonic)relationship,onanotherchordbesides

the“real”tonicchord,hasbeenprovided.That'swhythesechordswork—theyprovidethepull, thetensionandreleasethatyouneed,but theydo so at other points in the harmony. I know this may seem a bithypothetical,butjustputittouseandyouwillhearitforyourself.ChromaticHarmonyThesecondary chordscomeunder theumbrellaof chromaticharmony,meaning that they provide notes outside the key or they help toharmonize melodies that use notes outside the key. Here is a simpleexample of a chromaticmelody that is basically inCmajor but addsachromaticnotethatisneededtoharmonize:

ThemelodyislargelyinC,buttheF#sthatareaddedneedtobedealtwith.Youhavenochords thatdealwithF# thatarediatonic toCmajor.Butyoumayhavesomesecondarydominantsordiminishedchordsthatdoso.TryyourbesttoharmonizetherestofthechordsandexcludetheF#(oratleastthemeasurethatit'sin).

YouareleftwithafairlybenignI–vi–?–V7–Iprogression.Todealwith thechord in “?”youneed to look to thechordafter it,aVchord,G7inthiskey.What'sthesecondarydominantofthatchord?V/VisD7,spelledD–F#–

A–C,soitworks!Plugitinandseehowitsounds:

Look, itworks!Not only did you take careof the chromatic note in themelody, but you also generated a pretty interesting chord progression,onethatanytheoryteacherwouldbeproudtosee!Note: You could have also used viio/V (F# diminished) as a goodsubstitutechord for theD7asbothD7andF#diminished; in thiscase,sincetherewasaDinthemelodyandthediminishedchordhasanEbit'sbesttostickwithD7.Functionally,itwouldhavebeenokay,buttotheearit'snotpretty.Chromatic harmony is a very interesting topic. Take note of howcomposers deal with chromatic notes in their melodies and whichchromaticchordstheyuse.

INTIME

Therearetwootherchromaticchordsthatareoftenstudiedinhigh-leveltheory.OneiscalledtheNeapolitansixthchord,andthentherearewhatare called augmented sixth chords. Both are important chords in thedevelopment of harmonybut are a bit beyond the scopeof this text. Ifyou further your study, you will no doubt encounter these chords fromtimetotime.

ModalMixture

Whatisamodalmixture?It'sverycommonwhenyouareinamajorkeytobasicallyborrowaspects fromotherkeysasyougoalong.Themostcommonwaytodothis istoborrowchordsfromtheminorkeywiththesamename(Cmajor/Cminor).Thesearecalledborrowchords,andtheyareaprettyneatwaytospiceupyourharmony.Becausethemajorandminor key are so close in some respects, you can interchange thesechords for some really cool sounds. Look at some examples and seewhatchordsyoucanborrow!BorrowedChordsfromMajorHere,youareinaminorkey(anyoneyouchoose)andyouaregoingtoborrowsomechordsfromthemajorkey.Lookatthediatonicmajorandminorkeystogethertoseewhattheirharmonicdifferencesare.If you look at the chords, number by number, you, of course, seedifferences; they are, in fact, different keys! Now, think about this: Youtypically talk aboutminor keys, and you also talk about the addition ofdominant chords on V and diminished chords on vii tomake the keysfunctionbetter.Thisisalsoanalogoustothediscussionoftheharmonicminorscaleanditschords.Inasense,youhavealready“borrowed”theVandvii chords from themajorkey.Theothermostcommonchord toborrowistheIVchordfromthemajorkey.

Hereisanexample,usingamajorIVchordinaminorkey.

Youcouldcertainlytakeanychordfromthemajorkey,butifyoucountIV,V,andviiº, that's three typical chords thatyouseeoften inminorkeys.Addtothatsecondarydominantanddiminishedchords,andyouhaveaprettynicelineupofharmonicchoices.YoucouldeventhinkofaPicardythird(araisedthirdthatformsamajortriad inthefinalchordofacomposition inaminorkey)asaborrowedIchord, but since it happens only at the end of pieces, it's not a trueborrowedchord.Whenyoustart lookingatborrowingfromtheminorkey,intomajor,youseealotmorechoices!BorrowedChordsfromMinorIn anymajor key, you can borrow a bunch of chords from the parallelminorkey.LookingbackatFIGURE14.9, youcansee thedifferences.The typical chords that are borrowedare: iv, bVI, and bVII. In the jazz

chapter (coming up next), you will hear about one other chord that isused inmodernmusic, the iio.Fornow, youshould knowabout the iv,bVI,andbVII.Startwithiv.Theivchordisverycommonlyusedinmajorkeysand it'sallovermusicofallgenresandage!You find it inMozartandtheBeatles.Hereisaniceexampleusingaivchordinamajorkeycontext.

You don't even have to look that hard to find this borrow chord. It'sactuallymore common in folk and popmusic than in commonpracticestyles.It'sallovertheBeatles'music!ThenexttwochordsarethebVIandbVII.In FIGURE 14.12, you see these particular chords, bVI and bVII,commonlyascendingtowardtheIchord,typicallycomingbetweenVandIastheexampleillustrates.Thereareotherwaystousethem,butthisisbyfarthemostcommon.Thereasontotalkaboutborrowchordsatall(it'sconsideredafairlyhigh-levelsubject) isbecauseyouseethemsomuchinalldifferentstylesofmusic,acrossgenresandtimeperiods.Most importantly,youseetheminpopmusicaswell, so thismayeliminate someof the chords you'vebeentryingtoanalyzethatsimplydidn'tseemtofitintothekey.

Modulation

Here's a huge topic: How do you change keys? This topic is largeenough for its own book, but the title The Everything®HarmonicModulationBook just didn't seem to flow, so it will get a section here.Modulationissimplytheartofshiftingthetonalcentertoanotherkeyandstaying there.What do you know about tonal centers?Well, you knowthatbasically,theyinvolvechordsandmelodiesthatdefinecertainkeys.Most importantly, dominant V chords and tonic I chords are the basicingredients.You have learned about secondary chords; they provide a temporarytonal shift. This shift is only for amoment. But if you took the idea ofsecondary chords and simply held on to them for a long enough time,then you could shift the tonal center to another key. You could finallymodulate!Whatkeyscanyoumodulateto?Thesimplestwaytochangekeysistogotoakeythatisspelledverycloselytothekeyyouarein.Theruleofthumbissimple:Thefewernotesyouhavetoshift,theeasieryourjobis.Starttolookatthe“related”keys.RelatedKeysRelatedkeysarekeysthatsharenotesincommonwithoneanother.Themorenotestheyshare,themorecloselyrelatedtheyare.Gobacktothekeycircleforasecond.

SayyouareinC(anoldfavorite).Theclosestrelatedkeywouldbeonekeytotherightoronekeytotheleft,soGandFarekeysthatyoucanmoveintoeasily.Asyoustarttolosenotesincommon,itbecomesmoredifficulttoslipintoanewkey.Nothing'simpossible,buttypically,youseemovementsbyfifth,eitheruptoGordowntoF,ifyoustartinC.NewDominantsWhenyouthrowasecondarydominantin,youalterakey'slandscapebyaddingachromatictone.Inthesesituations,thatchromatictonealways

goesaway.Well,what ifyoustuckwith it?What ifyouhadasectionofmusicthatyoukeptanalyzingV/V,VanditneverreallycamebacktoI?Well,youmayhavejuststumbledontoamodulation.Here'sanexample.Startout inCandendup inG.Thiswillbea fairlylongprogressionbecauseyouwanttosetuptheideaofthekeychangeandestablishthenewtonic/dominantrelationshipsothatitsticks.

As you can see and hear, you started in one key and ended up inanother. You achieved this with two devices. The first is a secondarydominant to the new key. Your goal was to move to the key of V (Gmajor),sotodoso,you'dneedVinthenewkey(VofGisD7),soyoumadesuretodothat.TheminutetheV/Vshowedup,youhadanF#inthe key. The trick is not letting it go back to F§, so you did theprogressionagain to reallysolidify thesoundof thenewkey.Theotherway that this is accomplished iswith common chords. For example, tochangekeys,youneedto think in thenewkey forasecond.A I– IV–Vprogressioninanykeyisprettystrong.Youcanpulloffthatprogressionbyusingcommonchords.I–IV–VinthekeyofGisG–C–D.InthekeyofC,youhaveCandGchordsalready!Theonlyaddition is theD,which

you get via the secondary dominant chord (V/V). The real trick is notmakingtheGchordaG7.G7wouldpullbacktoC; intheexample, it'skept simply a triad. Common chords can go further in helping youestablishanewkey. I–IV–V isnot theonlyprogression,asyoualreadyknow. Look at other common chords. (Notice how you can analyzeFIGURE14.14inbothkeys?TheanalysisisprovidedforyouinCandG.ItmakesmuchmoresensetolookatthesecondlineinG.)CommonChordsWhenever you are thinking aboutmodulating to a new key, it's nice toknow what chords the two keys share; these chords are easy to useeffectively.UsethekeyofCandFthis timeand lookathowyoumightmodulate.TheV/Visneveracommonchord;youalwayshavetochangethekeyforthatone,butyouhaveabunchofotherchordsthatdowork.HerearethediatonictriadsofCandFmajor.

Youseeabunchofchordsinbothkeys—C,Dm,F,andAm.InthekeyofF,thosechordsareV,vi,I,andiiirespectively.So,youactuallydohaveaV/Vchord in thiscase—it's justnotaC7chord—whichyouneed to fixwithachromaticnote.InthekeyofF,thevichordisimportant.Whatyouaremissingisapre-dominantchord,eitheriiorIV.Bothofthosechordsarenotcommon,butnoworries,onceyou'vedonethewholesecondarydominant (or diminished) thing, the next progression after the cadencecancontinueonasifit'sinthenewkey.TheGminorchordyou'regoingto add won't sound odd, because you've already introduced thechromatictone(Bb)tothekey;itwillactuallysoundlikeitbelongstothekeyofF!

Thewaytomakeasecondarydominantnotfeel“secondary”istosimplynotturnbacktotheoldkeyatall—yousimplykeepgoinginthekeyofFandusetypical,diatonicprogressionsforthatkey.Asyoukeepwritinginthenewkey, the listenerwill forget about the keyofC since youhave“tonic-sized” the F chord so many times it sounds like you havemodulated,andyouhave.Modulation is a big topic with some very simple rules. You know howharmonyworksandyouknowthattomoveyouhavetoshifttheharmonyto the new key. The trick is to do some analysis of music, especiallyclassical music (because of the common modulations), to get used toseeingexactlyhowit'sdone.Justawordofwarning:Sometimesthehardestpartaboutmodulationissimply knowing a modulation when you see it. As soon as you seechords that don'tmake sense in your original key, take that as a clearsignthatyoumaynotbeinthatkeyanymore!Lookforpatternsinotherkeys. If you can fit the mystery progression into another key, thenchances are that's exactly where you are. One last thing: You can'tmodulatewithoutachromaticnote.Ontheotherhand,chromaticnotes

do not always signal movement into other keys. They could be slightdiversionsandresolve.Eitherway,lookforthesignpostsand,mostofall,listen.IfachordsoundslikeaI,itprobablyis!

15

JazzHarmony

You have already dealt with harmony on many different levels in thisbook.Yet,inmoderntimes,harmonyhasdivergedintoaveryuniqueartform that is trulyAmerican: jazz.Although jazzharmony remindsusoftraditional tonalharmony, it looksandfeelsquiteabitdifferent.Nowit'stimetolookatwhatmakesjazzharmonyunique,asit'sacrucialpartofthehistoryofmusic.

WhatIsJazz?

Jazzisaveryyounggenreofmusicthatcontinuestoevolveandreshapeitself at a breathtaking pace. Every ten years or so, jazz seems toreinvent itself; the rate of change in jazz is quite astounding. Jazz iscategorizedbyseveralimportantcharacteristics.Oneisinstrumentation:bass, piano, drums, saxophone, and trumpet come tomind when onethinksof jazz.Theothermainpart of jazz is improvisation. It's actuallythestrongestcomponentofplayingjazz:improvisingmelodicsolosoverchordchanges.It'soneofthethingsthattrulysetsjazzonitsown!Now,lookattheelementsofjazzastheyrelatetomusictheory.

INTIME

JazzisoneofthefewpurelyAmericanartformsthatdonotdirectlycomefromtheEuropeantradition.Instead,itwasslowlyformedfromitsoriginsingospelmusicandthebluesmusicof theDeepSouth. ItquicklygrewintoartmusicthroughthegreatjazzinnovatorssuchasLouisArmstrong,MilesDavis,CharlieParker,andJohnColtrane,justtonameafew.Howis jazzdifferent fromotherstylesofmusic?Primarily improvisationandinstrumentation;thoseareaspectsthatareuniquetojazz.Considerjazz in relation toother stylesofmusic.Does jazzuse scales, diatonicchords, triads? How does its harmony work? What are the essentialingredientsof jazz?Therestof thischapter isdevoted tobreaking jazzintoitssmallparts.

JazzHarmony

Jazzharmonyisunmistakablyrootedinthetraditionofmusictheorythatyouhavestudiedthusfar.Itreliesonmelodiesthatareharmonizedwithchords. The principal difference between jazz harmony and otherharmony is its use of chords that are taller than triads. “Taller” as invertically,onthepage,likethisG13chord.

TheG13chordisconsidereda“tallchord,”asit'stallonthepage.Itfitsintoaclassof chordscalledextendedchords.Tounderstandextendedchords, you need to understand extended intervals. This book's earlierdiscussionofintervalsdidn'tsaymuchaboutextendedintervals,butjazz

harmony requires it. You need to knowwhat a 13th really is andwhatextendedintervalsare.ExtendedIntervalsBy now, intervals should be a common part of your music theoryexperience.Funnyhowthere'smoreto learnabout themnow! Intervalshaveshownyoutheexactdistancebetweenanytwonotes.Upuntilnow,you have not distinguished intervals larger than an octave. You heardaboutthem,butyouneversawthemputintopractice.Do a quick review: After you pass the octave (which is also called an8th), you distinguish these larger intervals with, you guessed it, largernumbers.Any interval larger thananoctave isconsideredanextendedinterval.However,therearesomeintervalsthatareneverextended.Music theory does not distinguish the distance of a third or a fifthdifferently, no matter what octave it is in. Much of this has to do withhistoricalpractice,buttherealreasonliesintriadicharmony.

PointtoConsider

Since the majority of jazz chords include extended intervals, you justneedtorememberyourruleofnineinordertodecipherwhataninthfromCis,forexample.Injazz,theseventhchordisthesmallestunityouwillsee,andtypically, tallerchordsaremorecommonthanseventhchords,soyou'llneedtoknowyourextensionsinordertosucceed.Ifyoustartstackingthirdsontopofoneanother,yougetthisorder:C–E–G–B–D–F–A–C.Oras intervals: root, third, fifth,seventh,ninth,eleventh, thirteenth,androot.Usingtheruleofnineyoulearnedintheintervalchapter,youknowthattheextendedintervals(ninth,eleventh,andthirteenth)spellthesameasasecond,fourth,andasixth; theyare justanoctaveaway.Thereasonyou don't see tenths and seconds (thirds and fifths) is that when youstack thirds, those intervals simply don't come up. Once you get tothirteen,thenextthirdbringsyoubacktotheoctave.The other reason that thirds and fifths are not counted as extendedintervalsbecomesclearwhenyouhearthemcomparedtootherintervals(such as seconds versus ninths). Tomost ears, thirds and fifths soundthesamenomatterwhatoctavetheyoccurin.Thisisnottosaythattheysound identical, but the difference is so minute that you don't needanothernameforthembasedonwhethertheyaremorethananoctaveapart.Asecondsoundsverydifferent thananinth.Try thisoutonyourinstrumentandhearforyourself!ExtendedChordsNow that you know about extended intervals, you need to look atextendedchords.Youlearnedaboutfourfamiliesofchords:major,minor,diminished,andaugmented.Whenseventhsareaddedintotheequation,you get a fifth chord family: dominant chords (major triads with minorsevenths). These basic five chords and their extensions make up themajority of jazz harmony. To get by in jazz, you need to understand

major,minor,anddominantextensionsfirst.Youwilldealwithdiminished(whichistypicallynoteextended)andaugmentedchordslater.ExtendedMajorThebasic jazzmajorchordisthemajorseventhchord.Asyourecall,amajorseventhchordisamajortriadwithamajorseventhintervaladdedto it. Inaddition to theseventh,youseemajorchordextensions.Majorchords can be written the following ways and all still fall under theumbrellaof“major”and,thus,substituteforeachother:

CMajor7thCMajor9thCMajor11thCMajor13th

The formula for these chords is pretty simple to spot: root (major)“extension.”Anychord that follows that formula is in themajor seventhfamily. For example: FMajor 9th is amajor seventh chord, butF9th issomethingelsebecauseit lacksthenecessary“major”component in itsname.Knowing thesebasic ruleswillmake lifemuch lessconfusingasjazz deals with chord symbolsmore often than actual written voicings.That'sright,injazz,youturnsymbolsintosounds.Injazz,allmajorchordextensionstaketheirnotesfromthemajorscalebuiltofftheroot.ADMajor13thchordwilltakeallofitsnotesfromtheDmajorscale.Thisisimportantbecausethespellingoftheindividualnoteshastofollowthehomescaleorthechordwon'tsoundright.ExtendedMinorThebasic jazzminorchordistheminorseventhchord.Asyourecall,aminorseventhchordisaminortriadwithaminorseventhintervaladdedto it. Inaddition to theseventh,youseeminorchordextensions.Minorchords can be written the following ways and all still fall under theumbrellaof“minor”and,thus,substituteforeachother:

Cminor7th

Cminor9thCminor11thCminor13th

The formula for these chords is pretty simple to spot: root (minor)“extension.”Anychord that follows that formula is in theminorseventhfamily.Forexample:Fminor11thisaminorseventh–typechord,simplyextended.Injazz,allminorchordextensionstaketheirnotesfromtheDorianscalebuiltoff theroot.ADminor13thchordwill takeall itsnotes fromtheDDorian scale. This is important because the spelling of the individualnoteshastofollowthehomescaleorthechordwon'tsoundright.Injazz,thehomescaleforminorchordsistheDorianmode,notthe“expected”naturalminor scale. This is one of the placeswhere jazz starts to pullaway from traditional harmony— its use of modes for harmonic andmelodicpurposes.ExtendedDominantThe basic jazz dominant chord is the dominant seventh chord. As yourecall, a dominant seventh chord is amajor triadwith aminor seventhintervaladded to it. Inaddition to theseventh,youseedominantchordextensions. When used in practice, many jazz players will simply callthesechords “seventh”chordsand leaveoff themoniker “dominant”asit's implied.Dominant chords can bewritten the followingways and allstill fall under the umbrella of “dominant” and, thus, substitute for eachother:

C7thC9thC11thC13th

The formula for these chords is pretty simple to spot: root “extension.”

Anychordthatfollowsthatformulaisinthedominantseventhfamily.Forexample:F11thisadominantseventh–typechord,simplyextendedtotheeleventh.Typically,withdominantchordscomeschordalalterations.Analterationis some sort of change to the fifth or ninth of the chord. An altereddominantchordmayreadlikethis:•C7b9#5Eventhoughthatchordlookskindofscary,it'sstillveryplainlydominantbecauseatitscore,it'saC7withotherstuffaddedtotheendofit.Youwill look at this inmore depth in the section entitled Substitutions andEnhancements.Injazz,alldominantchordextensionstaketheirnotesfromtheMixolyd-ianscalebuiltofftheroot.AnE13thchordwilltakeallitsnotesfromtheE Mixolydian scale. This is important because the spelling of theindividualnoteshas to follow thehomescaleor thechordwon't soundright. In jazz, the home scale for dominant chords is the Mixolydianmode, not the major scale (that's reserved for major seventh chords).Thisisanotherexampleofmodaluseinjazz.OtherChords?What about diminished and augmented? Well, in jazz, the diminishedseventhchordisverycommon,anditiswrittenexactlyhowyou'dexpectto see it:Co7. The other type of diminished chord, the half diminishedchord,isfoundinjazzveryoften,butitrarelygoesbyitsclassicalsymbolofCØ7.Thesymbolsforfullandhalfdiminishedsimplylooktooclosetoeachother. To rectify this, half diminished chordsarewrittenas “Minor7b5” chords,which gets you to the same chord and completely avoidsconfusion with the other diminished chord. Almost 99.9 percent of thetime, if you seea diminished chord, assume that it's a fully diminishedseventhchord.As for augmented chords, theyappear as you'd expect them to, in thetwo varieties you studied in the seventh chord chapter:Cmaj7+ (C–E–G#–B)andC7+(C–E–G#–Bb).Youcanextendanaugmentedchord,butit's pretty rare. For most things, if you can decipher the major, minor,dominant, diminished, and augmented chord symbols, you're mostlythere.

JazzProgressions

Ifyouwanttostudytheharmonyofjazz,you'regoingtohavetoheadtoTin Pan Alley. Jazz players took songs from the Great AmericanSongbookandusedthemasvehiclesforjazzimprovisation.Theywouldplaythemelodiesinstrumentally(orsingthemifavocalistwasinvolved)atthestartofthetune;thisiscalledplayingtheheadofthetune.Oncethatwasdone,thechordsthatformedtheharmonyofthesongremainedwhilethesoloist improvisedanewmelody; this iscalledblowingonthechanges.Attheend,they'dplaythemelodyonelasttimeandthatwasit.

INTIME

Tin Pan Alley was the gathering place of a group of composers whowroteinthelatenineteenthandearlytwentiethcenturiesandcreatedtheGreat American Songbook, which is simply a collection of Broadwaysongs and other tunes that definedAmericanmusic during this period.StephenFoster,ColePorter,andJimmyVanHeusenareallcontributorstothisgenre.Because jazzplayers favoredthesesongssomuch, theirmelodiesandharmonies became the foundation for what is known as jazz harmony.These songs became the songs that all jazz players know and playtoday;theyareaptlyreferredtoas“standards.”Theharmoniesofthesesongshavesomeregularpatternsthatappearoverandoveragain,andthankfullythesecanbestudied!Startwiththediatonicprogressions.TheDiatonicProgressionsIn jazz, ifyousimply take thediatonicmajorscaleandharmonizeeachchord up to the seventh, you can learn a lot about how jazz harmonyfunctions.HereistheAbmajorscaleharmonizedinseventhchords.

You'llbehappytolearnthatthebasicjazzprogressionsarediatonicandstillfollowthechordladder.Startwiththemightyjazzprogressionoftheii–V–I.ii–V–IInjazz,nothingismorecommonthantheii–V–Iprogression.Takealook:

If jazzharmonyweredistilleddowntoonecentralpoint, itwouldbetheii–V–Iprogression. It's simplyall over jazzmusic.Sure, jazzgetsmorecomplicated,buttheii–V–Iisthebasicharmonicunitthatalljazzplayersuse.What'sinterestingisthatessentially,aii–V–IisasubstitutedIV–V–I(asiiandIVsubstituteforeachother),whichisjustaI–IV–V(rememberthosesimpleprimarychords?)reordered.WhychangetheIVtoii?Bydoingso,you create three different chords: a minor seventh chord, a dominantseventh chord, and a major seventh chord. That sound became thesoundthatmadejazzsounddifferentthanotherstylesofmusic.Addsomeextendedchordsandyougetaverydistinctivejazzyvibeoutofthisprogression.

Adda fewmore chordsbefore the ii andyou reach theother commonjazzprogression,theiii–vi–ii–V–I:

MinorProgressionsThereisaminorkeyequivalenttotheii–V–Iprogressioninmajor.It'sstilla“twofiveone,”butthequalitiesofthechordschange.InsteadofitbeingDm7– G7–Cmaj7 (in the key of C major), the progression becomesDm7b5–G7–Cm7.

This progression is easy to spot because you also have three distinctchords,withadominantchordinthemiddle.Lookforthemin7b5,that'susuallythesignpostthatscreams“Hey,minortwofivecoming”andlooktoseeifthechordsthatfollowitlineup.Now,lookathowarealjazztuneisputtogether.Hereisaverycommonstandard, without the melody, just the changes (jazzspeak for thechords).

Notice the analysis under the chords. You see loads of ii–V–Iprogressions,inmanykeys,bothmajorandminor.Thisisverystandardpracticeforjazz(changingkeysoften),butbeyondthat,theprogressionsarefairlysimple;it'sjustmodulatingoften.

INTIME

FIGURE15.7isessentiallyaleadsheet.Thisskeletalformofmusictellsyouwhatchords toplayonwhatbeats,and ifamelody ispresent, themelodic line. IfFIGURE15.7 had amelody, itwould be enough for anentire band to play with. The chords would be “created” from thesymbols,thebassplayerwould“walk”abasslinethatmadesensewiththe chords, and the melodic players would improvise on the chordchanges.SubstitutionsandEnhancementsOneof the cornerstones of jazz is the ability to change aspects of theharmony as you see fit. Listen to ten different versions of the stalwartstandard “Autumn Leaves,” and you will hear strikingly differentapproaches to a tune that is known by practically every jazzer in theknownworld.Thereasonthatyoucanchangethingsupsomuchliesintheessenceofjazzsubstitution.AsyousawinFIGURE15.7,jazzharmonyisexpressedaswrittenchordsymbols.Theplayerhasto“realize”thesechordvoicingsandplaythemin his or her ownway. There is no setway to voiceCMajor 7 on thepianoorguitar; thereare literallyhundredsofdifferentways toplay thesame chord (see theEverything®Guitar Chords book as an example).You rarely get the written voic-ings; it's always up to you to voice thechordsasyouseefit.Whenyouvoicethechords,youcanenhancethechords;actually,you'reexpected to.Thinkof it as “supersizing.”YouseeaCMajor7thchord,butthat'sreallyjustasuggestion.It'stellingyouthatyouneedtoplayachordinthefamilyofCMajor7th,butyouarefreetoextenditasyouseefit.CMajor7thcouldjustaseasilybeCMajor9th,it'suptoyou.Thisisoneofthenicefreedomsaffordedtoyouasajazzmusician.It'salsotrueinreverse;ifyouseeaverytallchord,youhavethechancetoreduceittoitssmallestpart.IfyouseeanF13thchord,youcansaytoyourself,“OK,it'sjustanextendeddominant7thchord,Icanreducethat

chordtoF7.”Doingsoisn'twrong;actually,it'sprettycommon.Theonlything to ponder is why you would see such a tall chord. Sometimescomposersputtheminthereforaverygoodreason.Oftenachordexistsbecause it supports a particularmelody note (themelody is the 13th).You should try to learn to play every chord you see, but that's anotherstory.Reducingisfine,withonenotableexception:alterations.ChordAlterationsAchordalteration,asdiscussedearlier,istamperingwiththefifthorninthofthechordinsomeway.Youtypicallyseethisisonadominantchord,althoughyoucouldseeitanywhere.Chordalterationsarenotsomethingthatyoucan typically ignore.Theyarealways there foragood reason.Usuallyit'stosupportamelodynoteofsomesort.Here are some conditions to keep in mind when dealing with alteredchords.

Whenindoubt,playthemaswritten!Alterationstothefifthmustbeplayedastheyaffectthecoretriad.Alterationstotheninthdon'thavetobeplayedaslongasyoureducetoa7thchordandleavetheninthsoutaltogether.It's probably not a good idea to extend an altered chord any higher thanwritten. Altered chords can have funny extensions that are not clear andexpected.Whenindoubt,playwhatyouhave.Alwayslookatthemelodythatgoeswiththealteredchord.Isthemelodynotethereasonforthealteration?Ifnot,whyalterthechordatall?Maybeit'salteredforharmoniccolorandbeautyandnotnecessarilyfunction.

These tipswillassistyou inyourunderstandingofwhyyouseealteredchords,whentousethem,andhowtoplaythem.Lotsofdominantchordsarealteredbecauseasdominantchords, theytypically functionasVchords in jazz,so theywill resolve to I.BecausetheyareVchordsandtheyresolvetoIstronglyanyway(becauseofthepull between the 3rd and the 7th) composers and players like to alterthem as the alterations have little effect on the V chord's proclivity to

resolve!Yousimplyendupwithamorecolorful chord,which isa veryjazzything.

BluesForms

Now that youhaveheardabout chordsandharmony, it's time tocovertheblues,abasic ingredient in jazz.Jazzgrew from thebluesandstillreliesonthebluesasastandardformandsongstyle.Thebluesis justplaincool.Everybody'sgotthebluesatonepointoranother!Jazzfolkshave the blues pretty often. In addition to the standard AmericanSongbook tunes that everyone knows and loves, the blues remains averyimportantformforjazzplayers.Everyself-respectingjazzcomposerhaswrittenabluestuneor twoor threeor four.Thebluesexists in twovarieties:minorbluesandmajorblues.Eachbluessongisexactlytwelvebars(ormeasures) long.Bluessongsfollowastrict repeatingharmonicformula,soit'seasytotransposethemintoanykey,andingeneral,theyareeasytolearntoplay.12-BarMajorBluesThe12-barblues is taken from the “traditional”bluesyoumighthear inthebluesclubsorbysomeonelikeB.B.King,butthejazzplayershaveadaptedtheharmonyjustalittlebit.Takealookatwhatatraditional12-barbluespiecelookslike:

Now,contrastthatwiththebluesthatmostjazzplayersplay.

The last five measures are where you see a change. Instead of thetraditional blues V–VI–I ending, the standard jazz ii–V–I progression isthrown in. Preceding that ii chord, a V/ii is thrown in to set up theprogressionandmakelifeabitmoreinterestingfortheimproviser.Notice how the Roman numeral harmony, chord symbols, and guitarchords are given for each example. This way, you can transpose thechords into any key youneed to. TheBbblues is definitely oneof themostused,standardjazz/blueskeys,soit'saverygoodonetostartwith.Here'salistofjazztunesthatarebasedonthe12-barmajorblues:

“Now'stheTime”(CharlieParker)“BlueMonk”(TheloniousMonk)“Straight,NoChaser”(TheloniousMonk)“Billie'sBounce”(CharlieParker)“TenorMadness”(SonnyRollins)

There are a million more, but this will get you started. Make sure totranspose them into different keys! If you don't play harmonies, learnsomemelodies(allthejazzblueshave“heads,”solearnthose).12-BarMinorBlues

Thefinalvariantofjazzbluesiscalledtheminorblues,andyouguessedit,it'sinaminorkey!Takealookattheminorblues.

Youseesomebasicharmony,suchasyouriandivchords,theexpecteddominantVchordthatyouneedforminorkeys.Thechordthatisslightlyoff isthebVIchordthatprecedestheVchordinbarnine.That'ssimplywhat makes a minor blues work the way it does; a definite differencebetweenthemajorandtheminor.

ExtraCredit

Ifyou'relookingforjazztunestoplay,checkouta“realbook,”whichisatakeoffonthe“fakebooks”thatincludemelodies,basicchords,andlyricssomusicianscanimprovisewithanysong.Therearetonsofrealbooksavailableonthemarket,andeachisarepositoryofhundredsofjazzleadsheets withmelodies, words, and chord changes. It's a great place tostudyandlearnsomegreatmusicwhileyou'reatit.Also, you'll notice a turnaround in the last bar of aDmin7b5,G7. Thisturnaroundsets the ichordup inbaroneso the tunecan looparound.The progression is the “minor” version of a ii–V–i progression, as youlearnedearlierinthechapter.Thatwrapsupyourgeneraloverviewofjazzharmony.Sure,there'smoreto look at, but this will get you more than started. If you have a realinterestinjazz,thataresomegreatbooksthatdealwithjazzharmonytoreadandstudy;eitherthatorconsultagoodjazzteacher!Eitherwayyoulookatit,nothingbeatslisteningtoasmuchmusicashumanlypossible.

16

TranspositionandInstrumentation

Oneofthemostconfusingandmalignedaspectsofmusictheory isthenature of transposing instruments. Few topics frustrate students morethanthis.Transposingisn'tdifficult,onlymisunderstood.Whenyoulearnabouttheinstrumentsandtheirtranspositions,youalsocanlearnabouttheirmusicalrange,howtowriteforthem,andhowtoanalyzemusicthatcontainsmixturesof transposingversusnontransposing instruments.Totrulystudymusic,youhavetoknowthatwhatyouseeisn'talwayswhatyouhear.

WhatIsTransposing?

SupposeJoshplaysthealtosaxophoneandBillplaystheclarinet.Theyget together and jam one day. Joshwrites a shortmelody on the sax,notates it, and hands it to Bill to play along with. To their shock andamazement,theresultingsoundisterrible.Whatwassupposedtobetwoinstruments playing the same melody in concert ended up as acacophony! Confused, they set out to understand why alto sax andclarinet can't read the same melody. What they discover is thattransposingandthenaturalkeysofinstrumentshascausedthismusicalcalamity.Alltheirlives,JoshandBillweretaughtthatCisCandDisDand so on. Unfortunately, this is not always true; it depends whichinstrumentyouarelookingat.ConcertPitchThepitchofanynoteisamathematicalevent.Notesexistasvibrationsof air. The speed at which they vibrate can be measured and isexpressed in hertz (Hz). This is the only true measure of a note, itsfrequencyinhertz.Alargegroupofinstrumentsexistthatplayin“concert

pitch,”meaningthatwhentheyplayorreadanoteonthemusicalstaff,theyaregettingthe“mathematicallycorrect”answer.WhenapianoplaysamiddleC,it'splayinganotewithafrequencyof261Hz—it'sanexactthing; the piano is playing concert pitch. There are a large number ofinstruments thatplayconcertpitch.Here isa listofpopular instrumentsthatplayconcertpitch.ThesearealsocalledCinstruments.

Violin,viola,cello,bassPianoHarpGuitar/bassFlute/piccoloOboeBassoonTromboneEuphoniumTubaPitchedpercussion(exceptglockenspiel)

The entire list above plays in concert pitch. There are someexceptions:Guitarandbass transposeanoctavedown inorder tokeeptheirmusicinthestaff,buttheyarestillconsideredconcert.Thepiccoloand glockenspiel read an octave lower than they actually play. This isalsomeanttokeeptheseveryhigh-pitchedinstrumentswithintherangeofthestaffforreadingcomfort.WhatDoesTransposingMean?

Hereisalistofthecommoninstrumentsthattranspose:

ClarinetSoprano,alto,tenor,andbaritonesaxophoneFrenchhornTrumpet,baritonehornEnglishhorn

Thereareothertransposinginstrumentsoutthere,butthesearetheonesyouwillseemostoften.

INTIME

Agreatexampleofaconcertpitchisanorchestraltuningnote.Whenasymphonyorchestra tunesup, theoboeplayer playsa concertAnote.The rest of the orchestra tunes up to this concert A note. MostmetronomesthatprovideatuningpitchalsoprovidethesameconcertA(A=440Hz).Atransposinginstrumentreadstheexactsamemusicaseveryoneelse.Theonlydifference is thatwhenatenorsaxplaysawrittenC, thenotethatcomesoutof thetenorsaxwouldnotregisterasaConatunerormatchaConapiano.Anentirelydifferentnotecomesout!AconcertBbis heard when a trumpet plays a written C. This is what is meant bytransposition. Look at an example. If you play a short melody for thetenorsaxonthetopstaff,whatyouactuallyhearisthebottomstaff!

Nowyoustarttoseethepossibilityforconfusion.Ifyoudidn'tknowaboutthis, youmight be very confused. Just think about poor Josh and Bill.Amazingly, this isn't always taught in the study of an instrument. Moststudentsjustlearntoreadthenotesinfrontofthem.Butyouarehereformorethanjustplaying!Youwanttounderstandwhatyouarelookingat,and ifascorehasmultiple instrumentson it, youcan't trust youreyes!Youhavetoknowwhatyou'rereallylookingat.WhyDoesThisHappen?Good question. Why can't we all just get along—er, play in the samekey?Therearetwopossiblereasonsthatcertain instrumentstranspose

andothersdon't.Thefirstishistory.Brassinstrumentsrelyheavilyontheovertoneseries tomake theirnoteshappen.Brass instrumentsused toadd“crooks,”whichwereadditionalpipes,totheirinstrumentsinordertoplay indifferent keys.TheFrenchhornwasagoodexampleof this. Intime, as the instruments evolved and valves were added to the brassinstruments, the additional crooks were no longer necessary. Certaininstrumentsevolvedintocertainkeysandstayedthere.It'snowbeensolong and there has been somuchmusic written that it would be verypainfultochange.

INTIME

Thinkyou'reimmunetothis?Playinarockband?Imaginethis:Youplayinabluesbandandyoubringinasaxortrumpetplayertoexpandyoursound.Whenitcomestimetoteachthemelodies,whatareyougoingtotellthemusiciantoplay?IfheorshewantstosoloontheEbluesyourguitarplayerissofondof,exactlywhatwillyousay?Youneedtoknowhowtranspositionworks.The second reason is best shown in the sax family. There are foursaxophones in common use today: soprano, alto, tenor, and baritone.Eachof the foursaxophones transposesdifferently.Thereason that it'sdonethiswayhaslesstodowithhistoryandmoretodowiththeeaseoftheplayer.Eachofthefoursaxophones,whilephysicallydifferinginsize,has the exact same system of keys that Adolphe Sax invented in the1800s. The sax transposes four different ways so that any sax playertrainedonanyoneoftheinstrumentscouldplayanyofthesaxophoneswithout having to relearn anything. Each saxophone reads the sametreble clef melody and the composer makes sure that each part istransposed correctly on paper for the proper sonic result. Some otherinstrumentsalsodothis.

TransposingChant

For too many years, students have been baffled, perplexed, andgenerallyconfusedastohowtotransposecorrectlyforinstruments.Butyoucanlearnachantthatwillhelpyoumakesenseofit.Theanswerliesinknowingtwothings:Youhavetoknowthefullnameoftheinstrumentandyouneedtoknowthechant.Eachinstrumenthasakeyname.Butatrumpetisn'tusuallycalledaBbtrumpet, is it?Trumpet usually suffices.Knowing the full nameof eachinstrumentisonekeytounderstandinghowittransposes.Theotherkey

isthechant,whichgoeslikethis:Theinstrument'skeynameisthenotethat youhear in concertpitchwhen that instrument reads itswrittenC.(Thank you, Scott Lavine.) Now put that to use, using the Bb trumpetagain,whichhasakeynameof“Bb.”Tounderstandhowthechanthelps,add this information into your chant: The instrument key name (in thiscase Bb) is the note you hear in concert pitch when that instrument(trumpet) reads itswrittenC.Simply,whena trumpetplaysawrittenC,youhearaBb.

Thismeansthatwhatevernoteornotesarewrittenfortrumpetwillcomeoutexactlyonewholestepbelowwhatiswritten.Sowhatcancomposersdotofixthis?Simplywritethetrumpetpartupawholestep,inawrittenD.ThetrumpetplayerwillreadandplaytheD,yetaperfectCwillcomeoutinconcertkey.Sounddown,writeup.Formosttransposinginstrumentsthisisthecase.Thereareacoupleofzanyexceptions,butyoudon'tneedtoworryaboutthem right now. For themost part, you write parts up and they sounddown.Justrememberthechant.

BbInstruments

ThereareafewcommoninstrumentsthatexistinthekeyofBbtogetherandthustransposetheexactsameway.TheBbinstrumentsincludetheBb trumpet, Bb clarinet, and Bb soprano saxophone. Each of theseinstruments follows the same rule: Whatever they read comes out awholestepdown.

There isanother instrument that iscalledaBb instrument: theBbtenorsax.It'salittlebitdifferentthantheothers—ittransposesanoctaveandawholestepdown.WhenatenorsaxplaysaC,youindeedhearaBb,butit'safulloctavelowerthantheotherBbinstruments.Towritepartsthatsoundcorrect,youhavetowritethepartupawholestepinthecaseofclarinet,trumpet,andsopranosax.Inthecaseoftenorsax,writeitupanoctave and a whole step (or a major 9th). The other instrument thatfollowsthissametranspositionistheBbbassclarinet.

EbInstruments

TherearetwocommoninstrumentsthatareinthekeyofEb.Thefirstisthe Eb alto saxophone, and the other is the Eb baritone saxophone.BeinginthekeyofEbmeansthatwhentheseinstrumentsreadawrittenC, an Eb concert pitch is heard. The Eb alto saxophone transposes a

major sixth away from where it's written. This means that a melodywritten in concert pitchwouldhave tobe transposedupamajor6th inordertosoundcorrectonthealtosaxophone.

Thebaritonesaxophone isalso in the keyofEb; theonlydifference isthatthebaritoneisafulloctavebelowthealtosax,soittransposesattheintervalsofamajorsixthandanoctave(oramajor13th).Inorderforamelodywritteninconcertkeytosoundcorrectlyonabaritonesax,itmustbewrittenamajor13thup!Remember, it soundsdown,but itmustbewrittenup.

FInstruments

Two instruments transpose in the key of F: the French horn and theEnglishhorn.BoththeFrenchhornandtheEnglishhorn(whichisatenoroboe) transpose in the same way, exactly a 5th away. If a composer

writesamelody inconcertkeyandwants theFrenchhornandEnglishhorntoplaythemcorrectly,hemustwritethemelodyupaperfect5thinorderforittosoundcorrect.

OctaveTransposes

Theguitarandbassareuniquetransposinginstruments.Boththeguitarandthebassplayinconcertkey.Thatis,whenguitarandbassplaythenoteC,anelectronictunerwouldregisterthenoteC.Buttheguitarandbass“octavetranspose”; that is, thepitchtheyread isanoctavehigherthan the sound that comes out of their instruments. This is a slightlyunusualpractice.Thereasonforthismakesperfectsense!Ifguitarandbassdidnot transpose like this, theirmusicwouldbeextremely lowonthe staff—most of the notes they played would be many ledger linesbelowthestaff.Andyouknowhowannoyingitistoreadthatway.Guitarandbass raise theirnotesanoctavehigher tokeep themajorityof thenotesonthestaffforeaseofreading.Youcouldgoyourwholelifeneverknowingthisandyoumayneverevennotice! If you ever have towrite a unison line for guitar or bass, you'llknowexactlywhattodo.Thereareotherinstrumenttranspositionsthatyouhaven'tlearnedabouthere.Thereareclarinets inAandtrumpets inD,andFrenchhornscanbe inalmostanykeypossible.As longasyou realize that thenameofthe instrument is the note you hear (in concert pitch) when it plays awrittenC,youwillknowhowtoreadandunderstandthatinstrument.

AnalyzingScores

At this point, you've gotten pretty far into chords and theory and canmakeyourwaythroughmyriadmusicalsituationswithconfidence.You'veanalyzed your favorite pop songs andmorewith ease and now you'vedecidedtostepup.You'vedecidedtogotothelibraryandcheckoutthescoreofasymphonyorchestra.YouwentGerman!YoucheckedoutoneofBeethoven'sninesymphonies.Now,you'dliketoknowwhat'sgoingonin Beethoven's head; he is a genius after all. So you crack open thescorefortheNinthSymphonyandseethattherearealotofinstrumentsinit.Here'swhatyouseeinthescorelistingofrequiredinstruments:

PiccoloFluteOboeClarinet(inBb,C,andA)BassoonContrabassoonFrenchhorns(inD,Eb,Bb,andbassBb)

Trumpet(inBbandD)TrombonesPercussion,includingpitchedpercussion(timpani)ViolinViolaCelloBassFour-partchoir

Well, that'squitea list.What'sevenworse is that thereare instrumentstherethatyouhavenotevendealtwith.What'sanAclarinet?HornsinD,Eb,Bb,andbassBb?Youwonderwhatisgoingon.Welcome to a full symphony score of the nineteenth century! Aconductor/ composer would only view scores like this: transposingscores.Youseeexactlywhat theplayers readon theirmusicstands. Ifyouwanttofigureoutwhatisgoingon,you'llhavetotransposethepartsinto concert pitch to figure out what's there, and you'll have to do itbasicallyat“firstsight.”Beginbypickingafewsinglechordstoanalyzeinthefourthmovement.(The fourthmovementcontains the famous “Ode toJoy”parteveryoneknowsand loves.)Now, theNinthSymphony isvery long,sowe're justgoingtoanalyzetwomeasuresofit.(ThispartisinthekeyofDminor.)You have the full listing of instruments above, butBeethoven does notuse themall at thesame time.Thesectionyouare lookingat featuresonlyflute,oboe,clarinet,bassoon,contrabassoon,horn inD,horn inB,trumpet in D, timpani, violin, viola, cello, and bass. Take a look at theexcerpt. (On theCD, the voices are playedwith a synthetic symphonyorchestra.Listeningtoa“real”recordingofthismonumentalpiecewilldoyousomegood.)Pretty impressive-looking, right?Thechords inquestionarehighlightedonthestaff.Inordertostart,youneedtofigureoutwhichinstrumentsare

in concert key andwhich ones need to be transposed. This is actuallyeasierthanyouthink.Rememberthelistingofinstruments(whichisalsoon the score excerpt)? If the instrument isn't concert pitch (that is, ittransposes),itwilltellyouinitsname,suchasBbclarinetandsoon.

So, lookat the transposing instruments aloneand figure outwhat theyarereallyplaying.

Wesegregatedtheclarinet,Frenchhorns,andthetrumpet.Nowgoovertheir transpositions one by one so you know what to do to eachinstrumenttobringittoconcertkey.

ClarinetinBb.Everythingiswrittenawholestephigherthanconcertpitch.Transposethenotesdownawholestep.HorninD(thehorninBisn'tusedinthisexample).Everythingiswrittenawholestepdown.Toreaditinconcertpitch,transposethenotesupawholestep.TrumpetinD.Thisis thesameastheFrenchhorninD;transposeitupawholesteptogettoconcertpitch.

Nowyouneed toadjust thosenotesso that they read inconcertpitch.Hereiswhattheylooklikeinconcertpitch:

Now throw themback in the score in concert pitchand you canget toworkanalyzing.Hereisthefullscoreinconcertpitch:

Nowallyouhave todo isstart reading from thebottomupandputtingsomechords together.Remember that thebassand thecontrabassoonare the lowest-soundingpitches, so you canget your roots from there.Amazinglyenough,whenyouanalyzethepiece,youcometothesethreechords:

Bb,Gminor,andAtriads!Triads!What,wereyouexpectingmore?Sure,you have somany instruments in an orchestra, you'd figure that therewould bemanydifferent notes, right?Wrong. Thebasic foundations ofharmonydon't change.Beethovenwasa tonal composer, and in thosetimes, tonal meant triadic and seventh chords. So, all in all, it's just amatter of taking a three-note chord and voicing it throughout a hugeorchestra, doubling notes in different instruments to create the sound.When you analyze thismusic, you can still break it down to the small

parts and thankfully figure out what's going on—as long as you knowwhatnotestheinstrumentsareactuallyplaying!Realizing that a full orchestra is playing only fairly simple triads andseventhchordsisabitofarevelation.Forsome,itcanmaketheactofsymphoniccomposing less impressive.Haveno fear; therealgenius inwritingforlargegroupsisnotwhatchordsarepresent,aschordsarejustthe culmination of melodies that intersect vertically. The brilliance is inwriting for the different groups of instruments andmaking them soundcohesive.

InstrumentRanges

Aslongasyou'restudyingtheseinstrumentssodeeply,youmightaswelllearn the ranges of the instrument families. You might be looking totheory for help in your compositions, and there is nothingmore usefulthanunderstandingwhatyoucanandcan'twriteforcertaininstruments.Thefollowingchartsshowtherangesforjustabouteveryinstrumentyoushouldhaveahandleon.Youcanseetheirrangesfromtheextremetoptotheextremebottom.Realizethatnochartwillevertrulytaketheplaceofstudyingscoresandreadingsomegreatorchestrationbooks,butitwillsaveyoufrommakingsomesillymistakes(likewritinginthewrongkeyorwritingcompletelyoutofaninstrument'srange).Herearethechartsforyourreference.

17

EtudeThree:AdvancedHarmony,JazzHarmony,andTransposition

SpelltheFollowingChords

SpelltheFollowingBorrowedChords

UsingtheSpaceProvided,WriteaMelodyandHarmonizeItUsingAnyCombinationOf:Diatonic,Secondary,andBorrowedChords

SpelltheFollowingJazzChords

SpelltheFollowingAlteredJazzChords

NametheFollowingJazzChords(ExtendedandAltered)

TransposetheNotestoConcertKey

TransposetheConcertNotestoTransposing

TransposeThisMelodySoEachInstrumentPlaysinUnison

AppendixAGlossary

44timeAlsocalled“commontime”andisabbreviatedbythissymbolc;denotesthatfourbeatsarefoundineachmeasure12-BarMajorBluesA set progression of chords that takes twelve bars or measures tocompleteandresolvestoamajorordominantchord12-BarMinorBluesA set progression of chords that takes twelve bars or measures tocompleteandresolvestoaminorchordAeolianModeAmajorscaleplayedfromitssixthnote(alsotheminorscale)ArpeggioThenotesofachordplayedonenoteatatimeAugmentationDotAlsocalledadot;increasesthedurationofthedottednotebyonehalfAugmentedIntervalAnyintervalthatisonehalfsteplargerthanmajororperfectBassClefAsymbolusedforinstrumentsthathavealowerpitch,commonlycalledtheFclefBorrowChordsA chord that exists in the parallel major or minor key that you can“borrow”inyourpresentkeyCClefAclefthathastwosemicirclesthatcurveintothemiddleofthestaffandpointtowardmiddleCChordThreeormorenotessoundedsimultaneouslyChordAlterationsChordsthathavefifthsorninthsthathavebeenalteredChordProgressionThemovementofchordsfromonepointtoanotherChordSubstitutionWhenonechordcantaketheplaceofanotherchord

ChordTonesMelodicnotesthatarecontainedwithinthesupportingharmonyCircleofKeysAvisualorganizationofallthepossiblemusicalkeysClefAsymbol that sits at the beginning of every staff ofmusic that defineswhichnoteiswhereCommonChordsChordsthataresharedbetweentwodifferentkeysCompoundMeterMeterthatbreaksitselfintogroupsofthreenotesConcertKeyInstrumentsthatadheretothephysicaldefinitionsofpitch(i.e.,A=440Hz)ConcertPitchInstrumentsthatplayinconcertkeyDeceptiveResolutionA substitution when one chord resolves to an unexpected resolution,typicallywhenthetonicisexpectedandnotheardDiatonicUsingthenotesfromonlyonescale/keytomakechordsormelodiesDiminishedIntervalAnyintervalthatisonehalfstepsmallerthanaminororperfectintervalDiminishedScaleA symmetrical scale built on repeating intervals, always half steps andwholesteps.Therearetwovarietiesofdiminishedscales:onethatstartswith the patternwhole step, half step intervals, and one that uses halfstep,wholestepintervalpatternsDominantThefifthchordortoneofascaleDominantSeventhChordAmajortriadwithaminorseventhintervaladdedDorianModeAmajorscaleplayedfromitssecondnoteEighthNoteArythmnthatreceiveshalfofonecount;itsdurationisonehalfofabeatEnharmonic

WheretwonotessoundthesameyetaredifferentnotesonpaperExtendedChordsChordsthatcontain9th,11th,or13thintervalsinthemFirstInversionWheneverthethirdofthechordisinthebassFullyDiminishedSeventhChordAdiminishedtriadwithadiminishedseventhintervaladdedGrandStaffWhenthebassclefandthetrebleclefaregroupedtogether;oftenusedforpianoHalfDiminishedChordAdiminishedtriadwithaminorseventhintervaladdedHalfNoteArhythmthatreceivestwocounts;itsdurationistwobeatsHalfStepThesmallestintervalHarmonicMinorAminorscalewiththe7thnoteraiseduponehalfstepHarmonicRhythmThespeedatwhichtheharmonyprogressesfromchordtochordHarmonizationUsingchordsandmelodiestogether;makingharmonybystackingscaletonesastriadsInstrumentRangesThelowestandhighestnotesaparticularinstrumentcanphysicallyplayIntervalThedistancefromonenotetoanotherInvertedChordsAnychordortriadwheretherootisnotthelowest-soundingpitchIonianModeThemajorscaleKeyDefinesthebasicpitchesforapieceofmusicKeySignatureUsedto indicatethatacertainnoteornotes isgoingtobesharporflatfortheentirepieceLeadSheet

SimplifiedshorthandforamusicalpiecefoundinjazzLeadingToneTheseventhnoteofamajorscale—atonethatpullsheavilytothetonicLocrianModeAmajorscaleplayedfromitsseventhnoteLydianModeAmajorscaleplayedfromitsfourthnoteMajorIntervalsIntervallicdistancesofseconds,thirds,sixths,andseventhsMajorScaleAseven-notescalebasedontheintervalpatternofWWHWWWHMajorSeventhChordAmajortriadwithamajorseventhintervaladdedMediantThethirdchordortoneofascaleMelodicHarmonizationHarmonizingamelodywithchordsorothermelodiclinesMelodicMinorAminorscalewiththe6thand7thnoteraiseduponehalfstepMinorIntervalsIntervallicdistancesofseconds,thirds,sixths,andsevenths;exactlyonehalfstepsmallerthanamajorintervalMinorScaleAseven-notescalebasedontheintervalpatternofWHWWHWWMinorSeventhChordAminortriadwithaminorseventhintervaladdedMixolydianModeAmajorscaleplayedfromitsfifthnoteModeThenotesofamajorscalestartingfromanynotebuttheexpectedtonicModulationTheartofshiftingthetonalcentertoanotherkeyandstayingthereOrchestrationTheartofarrangingmusicformultipleinstrumentsPassingTonesMelodicnotesthatarenotcontainedwithinthesupportingharmonyPentatonicScales

Ascalethatcontainsonlyfivenotes;canbemajororminorPerfectIntervalsIntervallicdistancesofunison(nointervalatall),fourth,fifth,andoctavePerfectPitchThe natural ability to name a note just by listening to it (also calledabsolutepitch)PhrygianModeAmajorscaleplayedfromitsthirdnotePrimaryChordsTheI,IV,andVchordsofanymajorkeyQuarterNoteArhythmthatreceivesonecount;itsdurationisonebeatRelativeMinorTheminorkeythatissharedwithinamajorkeysignatureRelativePitchThe learned ability to nameand recognize chords and intervals by earcomparatively,notabsolutelyResolutionThefeelingofrestinaharmonyRomanNumeralsAstandardwayformusictheoriststonameandhelpanalyzechordsandchordprogressionsRootPositionAchordthathasitsrootasthelowestsoundingpitchScaleAgroupingofnotestogetherthatmakesakeySecondInversionWheneverthefifthofthechordisinthebassSecondaryChordsTheii,iii,andvichordsofanymajorkeySecondaryDiminishedChordsAnydiminishedchordthatisnotfunctioningasatrueleadingtonechordSecondaryDominantChordsAnydominantchordthatisnotthefifthchordofakey;adominantchordthatresolvestoanychordotherthantonicSeventhChordAnytriadwithanaddedseventhinterval

SimpleMeterMetersthatcontaingroupingsoftwoorfournotesSolarHarmonyThesystemof harmony that revolvesaround the tonic chordbeing themostimportantharmonySubdominantThefourthchordortoneofascaleSubmediantorSuperDominantThesixthchordortoneofascaleSupertonicThesecondchordortoneofascaleTablatureAgraphicalsystemthatguitarplayersuseforreadingnumbersinsteadofnotesTertianHarmonyHarmonybasedonchordsbuiltfromthirdintervalsThirdInversionWhenevertheseventhofthechordisinthebassTonicThefirstchordortoneofascaleTransposingChanging the key of a melody while keeping its intervallic relationshipintactTransposingInstrumentAnyinstrumentthatplaysinakeyotherthanconcertpitchTrebleClefAsymbolthatcirclesaroundthenoteG,commonlycalledtheGclefTriadAthree-notechord,builtwiththirdintervalsTupletsAgroupingofoddgroupsofnotesdividedequallyintooneormorebeatsVoiceLeadingTheartofconnectingchordtochordinthesmoothestmannerpossibleWholeNoteArhythmthatreceivesfourcounts;itsdurationisfourbeatsWholeStepThedistanceoftwohalfstepscombined

WholeToneScaleAsymmetricalscalebuiltentirelywithwholesteps

AppendixBAdditionalResources

Here isa list of important books that youshould knowabout.Someofthese were referenced in this book, and all of them will deepen yourknowledgeofmusicingeneral.

Books

Black,Dave,andGerou,Tom.EssentialDictionaryofOrchestration.LosAngeles:AlfredPublishingCo.Gerou,Tom,andLusk,Linda.EssentialDictionaryofMusicNotation.LosAngeles:AlfredPublishingCo.Harnsberger, Lindsey C. Essential Dictionary of Music. Los Angeles:AlfredPublishingCo.Kennan,Kent.Counterpoint.UpperSaddleRiver,NJ:PrenticeHall.Kennan,Kent,andGrantham,Donald.TheTechniqueofOrchestration.EnglewoodCliffs,NJ:PrenticeHall.Piston,Walter.Harmony.NewYork:W.W.Norton&Company.Roeder, Michael Thomas. A History of the Concerto. Portland, OR:AmadeusPress.Stolba, K. Marie. The Development of Western Music: A History.Madison,WI:BrownandBenchmark.White, John D. Comprehensive Musical Analysis. Metuchen, NJ:ScarecrowPress.

WebSites

wwww.musictheory.netOneofthebestonlineresourcesformusictheory.wwww.sibelius.com Makers of the Sibelius brand of score writing andmusictheorysoftwareforWindowsandMacintosh.wwww.music.vt.edu/musicdictionary/Excellentgeneralmusictheorysite.

Nowallyouneedisamanager.

TradePaperbackwithCD,$19.95ISBN:1-58062-886-9

TradePaperbackwithCD,$19.95ISBN:1-59337-324-4

TradePaperbackwithCD,$19.95ISBN:1-58062-883-4

TradePaperbackwithCD,Media$19.95ISBN:1-59337-529-8

TradePaperbackwithCD,$19.95ISBN:1-59337-652-9

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