Tonal Harmony(Chapter Three)

5/24/2018 Tonal Harmony(Chapter Three)

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38

Capte TreIntroduction to Triads

and Seventh Chords Introduction

In this chapter we begin working with chords, the basic vocabulary o tonal harmony. Wewill not be concerned at this stage with how chords are used compositionally or even whatkinds o chords occur in the major and minor modes, although we will encounter thesetopics soon enough. First we have to learn how to spell the more common chord types andhow to recognize them in various contexts.

TriadsIn o the Student (pp. xixiv), we explained that tonal harmony makes use o tertian(built o 3rds) chords. Te undamental tertian sonority is the triad,a three-note chordconsisting o a 5th divided into two superimposed 3rds. Tere are our possible ways tocombine major and minor 3rds to produce a tertian triad.

M3 M3

M3M3 m3

m3

m3

m3

+5 P5 P55

Te names and abbreviations or these our triad types are given in Example 3-1.

Example 3-1

augmented(+) major(M) minor(m) diminished()Play these triads at the piano and compare the way they sound. You might be able to guessrom listening to them that in tonal music the major and minor triads are ound the mostofen, the augmented the least ofen. Tere are also names (in addition to note names) orthe members o a triad (Ex. 3-2).


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Triads

Example 3-2

fifth

third

root

Study the preceding diagram and examples very careully beore going on.

C H E C K P O I N T

1. Which triad types contain a m3 as the bottom interval? As the top interval?

2. Which triad types contain a M3 as the top interval? As the bottom interval?

3. Which triad types contain a P5 between the root and the 5th? a

5? a+5?

Self-Test 3-1

(Answers begin on page 559.)

A. Spell the triad, given the root and the type. Major triads are indicated by anuppercase letter (G), minor by an uppercase letter ollowed by the letter m (Gm

augmented by a + (G+), and diminished by a

(G

).1. Bm 7. A

2. E 8. Dm

3. G

9. G

4. F

10. B

5. Cm 11. Am

6. D+ 12. Cm

B. Notate the triad, given the root and type.


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40 Chapter Three Introduction to Triads and Seventh Chords

C. Fill in the blanks.

ex. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Fifh F D G B

Tird D A G F C

Root B B C Fype M + m m + M

M

m M

D. Given the chord quality and one member o the triad, notate the remainder o thetriad, with the root as the lowest tone.

Exercise 3-1 See Workbook.

Seventh ChordsI we extend a tertian triad by adding another 3rd on top o the 5th o the triad, the result isa our-note chord. Because the interval between this added note and the root is some kindo 7th (major, minor, or diminished), chords o this sort are called seventh chords. Because it would be possible to use more than one kind o 7th with each triad type, thereare many more seventh-chord types than triad types. However, tonal harmony commonlymakes use o only ve seventh-chord types (Ex. 3-3). Below each chord in Example 3-3 youwill nd the commonly used name or each chord and the symbol used as an abbreviation.Be sure to play Example 3-3 to amiliarize yoursel with the sound o these chords.

Example 3-3

Type of chord:

Symbol:

Construction:

major seventh

M7

major triad

major 7th

major-minor seventh

Mm7

major triad

minor 7th

minor seventh

m7

minor triad

minor 7th


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Seventh Chords

Type of chord:

Symbol:

Construction:

half-diminished seventh

k7diminished triad

minor 7th

(fully) diminished seventh

7

diminished triaddiminished 7th

Quite soon we will begin composition exercises using triads. Although seventh chwill not be used in composition exercises or some time, you will nevertheless begbecome amiliar with them rom an analytical standpoint through examples and anaassignments.

C H E C K P O I N T

1. Which seventh-chord types have a diminished triad on the bottom?

2. Which ones have a M3 between the 5th and the 7th o the chord?

3. Which ones have a m3 between the 3rd and the 5th o the chord?

4. Which ones contain at least one P5? Which contain two?

5. Which one consists entirely o a stack o minor thirds?

Self-Test 3-2


A. Identiy the type o each seventh chord, using the abbreviations given in Exampl(M7, Mm7, m7, k7,7).

Mm7

ex. 1 2 3 4 5 6 7

8 9 10 11 12 13 14 15


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B. Notate the seventh chord, given the root and type.

C. Given the seventh chord quality and one member o the chord, notate the rest o thechord.


This would be an appropriate point at which to begin work on

Counterpoint Unit 1, which can be found at www.mhhe.com/kostka7e.

Inversions of ChordsUp to now, we have been notating all chords with the root as the lowest tone. However, in

a musical context, any part o a chord might appear as the lowest tone. Te three possiblebass positionso the triad are illustrated in Example 3-4.

Example 3-4


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Inversion of Chords

Te bass position that we have been using, with the root as the lowest tone (or inbass), is called root position.You might assume that third position would be the or a chord with the 3rd as the lowest tone, but musical terminology is raught withconsistencies. Instead, this position is called rst inversion.Reasonably enough, seinversionis used or chords with the 5th in the bass. Te term inversionis used he

mean the transer o the lowest note to any higher octave.

Example 3-5

All the chords in Example 3-6 are F major triads in rst inversion. Notice that the u

notes o the chord can be spaced in any way without altering the bass position. Also, athe notes can be duplicated (or doubled) in different octaves.

Example 3-6

Te inversion o seventh chords works just like the inversion o triads, except that inversions (our bass positions) are possible (Ex. 3-7).

Example 3-7

It is important to understand that the inversion o a triad or seventh chord is determonly by what member o the chord is in the bass;any chord members may appear insoprano or in the other voices without changing the inversion.


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Inversion Symbols and Figured BassIn analyzing music we ofen use numbers to indicate the bass positions o chords. Instead ousing 1 or rst inversion, 2 or second inversion, and so on, we use numbers derived romthe Baroque system called gured bassor thoroughbass.During the Baroque period (ap-

proximately 16001750), the keyboard player in an ensemble read rom a part consistingonly o a bass line and some symbols indicating the chord to be played above each bass note. In the Baroque system, the symbols consisted basically o numbers representing inter-

vals above the bass to be ormed by the members o the chord, but the notes could actuallybe played in any octave above the bass. Te system dealt only with intervals, not with rootso chords, because the theory o chord roots had not been devised when gured bass wasrst developed. Te ollowing table illustrates the gured-bass symbols or root position and invertedtriads and seventh chords or a G major triad and a G Mm 7.

Sonority desired

Complete gured5 6 6 7 6 6 6

bass symbol 3 3 4 5 5 4 4 3 3 3 2

Symbol most 6 6 4 4ofen used 6 4 7 5 3 2

How to nd Bass 6th 4th Bass 6th 4th 2ndthe root note above above note above above above bass bass bass bass bass

Te Baroque keyboardist reading a gured bass ollowed the key signature unless told todo otherwise. So a root position triad, or example, might be major, minor, or diminished,depending upon the key signature. I the Baroque composer wanted to direct the keyboardplayer to raise or lower a note, several methods could be used, including the ollowing three.

1. An accidental next to an arabic numeral in the gured bass could be used to raise orlower a note.

7

2. An accidental by itsel always reerred to the 3rd above the bass and could be used toalter that note.

3. A slash or plus sign in connection with an arabic numeral meant to raise that note.

64

3


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Lead-Sheet Symbols

Another symbol that you will occasionally encounter is a horizontal line, usually smeaning to keep the same note or chord. For instance, 53

6over a bass note means to us

same bass note or a root position triad ollowed by one in rst inversion. Example 3-8 illustrates a portion o an actual gured bass part rom the Baroquriod, along with a possible realizationthat would have been improvised by the keybo

ist. Some keyboard players may have added embellishments not shown in this realizaBach included the numeral 5 at several places to remind the player to play a root tion triad.

Example 3-8 Bach, Easter Oratorio,II

6

/0

/0/0

!

6 56

46 5 5 6 5 6

Te realization o gured basses is still considered to be an effective way to learn ceaspects o tonal composition, and we will occasionally use exercises o this kind in the A ew gured-bass symbols have been adopted or use in harmonic analysis. Wethese bass-position symbolsto distinguish them rom gured bass, which is not the

thing. Bass-position symbols are usually used with a roman numeral (as in I6

or Vpart o a harmonic analysis. (Roman-numeral analysis is explained in the next chapNotice that when a seventh chord is inverted, the 7 is replaced by the appropriate bposition symbol.

Bass position Triad symbol Seventh chord symb

Root position (none) 7

Root position 6 65

Second inversion 6443

Tird inversion (none) 42(or 2)

Lead-Sheet SymbolsTere are some intriguing parallels and contrasts between the gured-bass system oseventeenth and eighteenth centuries and the lead-sheet symbols (sometimes calledsymbols) developed or use with jazz and other types o popular music in the twenand twenty-rst centuries. Both acilitated the notation process and served to providecient inormation to allow the perormer to improvise within certain bounds. Howwhereas the gured-bass system provided the bass line with symbols indicating the ch


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that were to be constructed aboveit, lead-sheet symbols appear along with a melody andindicate the chords that are to be constructed below. Example 3-9 illustrates some lead-sheet symbolsor the nine chord types that we havestudied so ar, along with some commonly used alternatives. Other chords and alternatesymbols can be ound in Appendix B in the back o this book.

Example 3-9

E Em Edim or E E+

EM7 or E7 E7 Em7 k7Em75 or E 7Edim7 or E

Te list o symbols in Example 3-9 is incomplete because there are some chords that willbe introduced in later chapters. A special case is the chord with an added sixth, as in C6,which calls or a triad with an added note a M6 above the root. Also, lead-sheet symbolswill occasionally speciy a particular bass note, as in C/G, which calls or a C major triadover a G in the bassa triad in second inversion. Tis is called slash-chord notation. Fi-nally, you may discover that lead-sheet symbols requently differ rom one edition to thenext because editors and arrangers routinely make substitutions, simpliying or compli-cating the harmony as they see t. Te top staff o Example 3-10 is rom the beginning o a typical American standardballad, and it uses ve o the chord types seen in Example 3-9. Te bottom staff shows thechords in close position, but they would be voiced differently by a jazz pianist. Notice thatthe in Fm75 does not literally mean to at the fh o the chord, but to lower it a hal

stepin this case rom C to C.

Example 3-10 Kosma, Autumn Leaves

1

4

cc

&The fall ing- leaves

A7 D7

drift by the win

GM7

dow-?& CM7

the au tumn- leaves,

F7 b5 /C B7

of red and gold.

E

?

w . w w w w ww ww w w

DISC 1 : TRACK 1


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Lead-Sheet Symbols

Lead-sheet symbols can be a very helpul rst step toward a harmonic analysis, anwill occasionally give you practice with them in sel-tests and exercises.

Self-Test 3-3(Answers begin on page 561.)

A. Identiy the root and type o each chord, and show the correct bass-position symbol (

Root

Type

Bps

Root

Type

Bps

65

F

M

BMm7

ex. ex. 1 2 3 4 5 6

7 8 9 10 11 12 13 14

B. Te bottom staff o this recitative is played on bassoon and keyboard, the keyboaplayer (the continuo) realizing the gured bass. Fill in each blank below the basline with the lead-sheet symbol o the chord to be played at that point, using slashchord notation or inverted chords, as in the example. Remember that a numeral itsel is simply a reminder to use a root position triad.

Bach, Easter Oratorio,II

D/F

DISC 1 : TRACK 2


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C. Notate on the bottom staff the chords indicated by the lead-sheet symbols. Notateall chords in root position unless the symbol calls or an inversion. A 6 afer a chordsymbol means to add a note a M6 above the root.

Hendricks and Adderley, Sermonette

!

!

I heard me a

F

Ser - mon - ette,

F6

have

D75/F

you

C/G

heard it yet

C7 Am/C

with

A7/C

that

Dm

soul

F/A

- ful

B

mes

Am7

- sage

Gm7

that

Fdim7

you

G

wont

G7

soon for

C7

- get?


DISC 1 : TRACK 3


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Recognizing Chords in Various Textures

Recognizing Chords in Various TexturesSome students, especially those without much keyboard experience, nd it diffi cult atto analyze a chord that is distributed over two or more staves, as in Example 3-11.

Example 3-11

!

Example 3-12

position

root

One procedure to ollow with the chord is to make an inventory o all the pitch claound in the chord (B, G, and D) and to notate the chord with each pitch class in tuthe lowest note. Te other notes should be put as close to the bottom note as possible

version that consists only o stacked 3rds is in root position. We can see rom Examplethat the chord in Example 3-11 is a g minor triad in rst inversion. Te chord in Example 3-13 contains the pitch classes E, A, C, and G, allowing ourpositions.

Example 3-13

!Example 3-14 tells us that the chord in Example 3-13 is an A major-minor seventh cin second inversion.

* The termpitch classis used to group together all pitches that have an identical sound or that are identical except for the octave or octseparate them. For example, all B

s, Cs and Ds belong to the same pitch class, no matter what octave they are found in.


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Example 3-14

position

root

You might already be able to carry out this process in your head, which will speed thingsup considerably. I not, you will learn to do so with practice.

C H E C K P O I N T

1. What is the symbol or the rst inversion o a triad? O a seventh chord?

2. Explain 42,64, and

43.

3. Which bass position or which chord type requires no symbol?

Self-Test 3-4


A. Label each chord with an appropriate lead-sheet symbol in the space above the chord.Use slash-chord notation or inverted chords. All o the notes in each exercise belongto the same chord.

!

!

1 2 3 4 5

6 7 8 9 10 11


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Recognizing Chords in Various Textures

B. Provide the root, type, and bass-position symbol (Bps) or each chord in the olloexcerpt. Each chord is numbered. Put your analysis o the chords in the blanks beeach excerpt.

1. Fischer, Blumen-Strauss

!

Root

Type

Bps

1 2 3 4 5 6 7 8 9 10 11 12

2. Byrd, Psalm LIV

Te 8under the treble cle on the tenor staff (third staff rom the top) means ththe notes are to be sung an 8ve lower than written.

+

$

%Root

Type

Bps

S

A

T

B

Be

Be

Be

Be

- hold,

- hold,

- hold,

- hold,

God

God

God

God

is

is

is

is

my

my

my

my

help

help

help

help

- er:

- er:

- er:

- er:

( )

1 2 3 4 5 6 7

DISC 1 : TRACK 3

DISC 1 : TRACK 3


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3. Schumann, Wiegenliedchen,op. 124, no. 6

(Note: Chord 14 is missing an A.)

5 ritard.

Root

Type

Bps

dimin.

22

&?

&?

21 3 4 5 6 7

8 9 10 11 12 13 14 15

C. ime signature review. Fill in the blanks.

Beat and

meter type

Beat

note

Division

of the beat

Time

signature

1. Compound duple 2. ..3.

0

4. -.


DISC 1 : TRACK 3


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Variations

Summary

Te undamental sonority o tonal harmony is the triad,a three-note chord consisting o

divided into two superimposed 3rds. Te bottom note o the 5th is the root,and the top note

5th.Te note that divides the 5th is the 3rd.Tere are our triad types: major, minor, dimini

and augmented. A seventh chordmay be thought o as a triad with another 3rd added above the 5th o the

Te added note is a 7th above the root. Although many seventh chord types are possible, onl

occur with any requency in tonal harmony:

major seventh chord(M7): major triad with a M7 above the root

major-minor seventh chord(Mm7): major triad with a m7 above the root

minor seventh chord(m7): minor triad with a m7 above the root

half-diminished seventh chord(k7): diminished triad with a m7 above the rootdiminished seventh chord(

7): diminished triad with a

7 above the root

Root positionis the term or a chord with the root notated as the lowest tone. Any other arr

ment is called an inversion.A chord with the 3rd as the lowest tone is in rst inversion,whone with the 5th as the lowest tone is in second inversion.A seventh chord with the 7th as the

est tone is in third inversion.Tere are symbols or most o the various bass positions:

Bass position Triad symbol Seventh-chord symbol Bass no

Root position none 7 root

First inversion 6 65 third

Second inversion 6443 fh

Tird inversion n/a 4

2

sevent

Inversion symbols are derived rom gured bass,a method o abbreviated notation used i

Baroque era. Lead-sheet symbolsare used in jazz and most popular music to indicate chords

played under a given melody. Both gured-bass symbols and lead-sheet (pop) symbols will be

occasionally throughout much o this text.

Variations

For additional review and practice, please see Chapter 3 on our website atwww.mhhe.com/kostka7e.

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Tonal Harmony(Chapter Three)