Page 1


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FOUR-PART HARMONY Volume Two ! ! !

by David Powell ! ! ! ! ! ! ! ! ©Copyright 2015, David Powell www.vancouvermusictheory.com ISBN: 978-0-9918594-3-6 (PDF)

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Table of Contents

! Harmony and Voice Leading

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1. Keyboard Style ……………………………………………………………..…… 1 2. More About Minor Keys ………………………………………………….…….. 8 3. Diatonic 7th Chords ……………………………………………………….…… 14 4. Secondary Dominants in Major Keys …………………………………………… 20 5. More About Modulation ………………………………………………………

34

6. The Dominant 9th, 11th, and 13th chords …………………………………….. 36 7. Diminished and Half-Diminished 7th Chords ………………………………… 43 8. More Sequences ……………………………………………………………….. 54 9. Figured Bass …………………………………………………………………… 59 10. The Neapolitan 6th Chord ……………………………………………………. 64 11. The Chords of the Augmented 6th …………………………………………… 68 12. Mode Mixture ………………………………………………………………… 73 13. Modulating with Altered Pivot Chords ……………………………………….. 79 14. More About Diminished 7ths ………………………………………………… 83 15. Modulating to III# and VI# …………………………………………………. 90 16. Using the N6 and Augmented 6th Chords to Modulate ……………………… 92 17. Modulating Using the Circle of 5ths …………………………………………. 98 18. More About Augmented 6th Chords ………………………………………… 100 19. New Possibilities for the Cadential 6-4 ………………………………………. 104 20. Plagal and Related Cadences ………………………………………………… 107

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Forms

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21. Minuet and Trio Form ………………………………………………………. 113 22. Rondo Form ………………………………………………………………… 117 23. Sonata Form ………………………………………………………………… 122

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! ! Melody Writing

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24. 8-Bar Melodies ……………………………………………………………… 133 25. 16-Bar Melodies …………………………………………………………….. 139

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Appendix

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Summary of Triads in 2nd Inversion ……………………………………………. 149 Doubling in Minor Keys ………………………………………………………… 152 Common Progressions in Major and Minor Keys ……………………………….. 153 Summary of Techniques for Remote Modulation ……………………………….. 155 Some Excerpts from Bach’s Minor Key Chorales ……………………………….. 160

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Review Exercises ……………………………………………………………… 167

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Preface

This volume is primarily written for students preparing for harmony exams such as the Intermediate and Advanced Harmony exams of the Royal Conservatory of Music (Toronto). Volume One covers the material for the Introductory and Basic exams.

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Studying four-part harmony will be more meaningful for students if they have some awareness of the historical context of this subject. Roughly speaking, four-part harmony texts such as this one teach the harmonic language of the 18th and early 19th Centuries. In broader terms, they teach the principles of tonal harmony and chord progressions. These principles apply not only to classical music, but also to jazz, rock, folk, and other styles.

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We begin with the simplest of pieces: hymns and chorales for SATB choir. They are the least elaborate music we can write; they have to be easy because they are written to be sung by people with little or no musical training. So, the lines move by step and small leap, and the voices move mostly in the same rhythm. Chromatic chords such as the N6 and the augmented 6th chords are generally not used in hymns or chorales (being too complex for congregations to sing), but would be found in most other types of music of this era. The remote modulations covered in this book are mostly a 19th Century phenomenon, and would have only occurred rarely in the 18th Century.

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Exercises are provided for all material in the book except form analysis. For practice with forms, I recommend analysing the piano sonatas of Mozart, Beethoven and Haydn (see A Companion to Beethoven’s Pianoforte Sonatas: Analysis, by Donald Francis Tovey, for excellent analyses of Beethoven’s sonatas). I also recommend using commercially available practice exam compilations when preparing for exams. Finally, harmony exams often contain counterpoint questions. Please see my separate volume A Counterpoint Handbook for counterpoint lessons and exercises.

! Copying !

Permission is granted to copy homework sections for ease of marking. Otherwise please respect my copyright and refrain from copying this book.

! !

David Powell Vancouver, Canada January 2015


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Harmony and Voice Leading 


Unit 1 ~ Keyboard Style We usually write hymns and chorales in two staves, with the soprano and alto in the top staff, and the tenor and bass in the bottom staff. We also need to learn to write hymns and chorales in keyboard style, that is, in a way that is easier for a keyboard player to read and play. In keyboard style, the bass part is written alone in the bass clef and follows the normal rules for stem direction: if the note is higher than the middle line (D), the stem goes down. If it's lower than D, the stem goes up. The stem on a D itself can go either way. We write the rest of the notes in the treble clef, in close position. Close position means that the notes of the chord are as close to each other as they can be. In close position the right hand will not have to stretch more than an octave, and there are no gaps in the chord into which one could put another chord note. The opposite of close position is open position. Compare the following:

Close position:

Open position:

&

bb

w ww

&b

b ww w

Here is a measure written in chorale style:

Here are the same chords written in keyboard style:

b œ b & œ

b & b œœœ

? b b œœ

œ œ œ

œ œ œœ

œœ œ œ

? bb œ

œœ œ œ

œœ œ

œœœ

œ

œ

1


The stem on the chord in the right hand will follow the direction of whichever note is furthest from the middle line. Compare these two chords:

˙˙ ˙

b & b ˙˙˙

Sometimes one of the 'voices' in the right hand will have a different rhythm from the others. If this happens it will have its own stems. Study the following examples:

b & b 42 n œœœ œ œœœ In the above, the stems on the D and F go down even though these notes are below the middle line. If they went up they would be harder to read.

b b & œœœ œ œœœ You still have to avoid consecutives in keyboard style. Here the 'soprano' and 'tenor' have consecutive 5ths:

b & b œœœ

œœœ

If two notes a second apart appear in the right hand then they are placed on opposite sides of the stem. The lower note goes on the left, and the upper note goes on the right of the stem.

b & b œœœ

2

œœœ

œœœ

œœœ


Usually there should be 3 notes in the right hand, even if two voices aresharing the same note. In the following example the alto and tenor are both singing the same F:

b ˙ b & ˙ You may have two voices only in the right hand if you have a series of consecutive 1st inversion chords. Note that the two upper voices move in parallel 4ths throughout the passage.

b & b œœ

œœ

œœ

œœ

? bb œ

˙˙

œ

œ

œ

˙

3


Homework for Unit 1 ~ Keyboard Style In the blank measures provided on the next page, rewrite this hymn in keyboard style:

# c & ˙˙

œœ œœ œ œ œœ œ œœ œ

? # c ˙˙ # œ œ & œ œ œœ œ œ ? # œœ œœ œœ œœ &

#

˙˙

?# ˙ ˙

4

,

˙ ˙ ˙˙

˙ ˙ ˙˙

˙ ˙ ˙ ˙ œœ œœ œœ

œœ

˙˙

˙˙

œœ œœ œœ œœ

˙˙

œœ ,

˙˙

˙˙

˙˙ œœ

œ œ œ œœ . œ œ J œœ

˙ ˙

˙ ˙

˙˙

,

˙ ˙

˙

˙˙

œœ œ œœ œ œ ˙œ ˙ ˙ œ ˙ ˙ œ . Jœ ˙

˙ ˙

˙˙ ˙˙ ˙ ˙

˙˙ ˙ ˙


&

#

˙˙ ˙

?# ˙

&

œœ œ œ

œœ œ

œ

œœ œ

œ

œœ œ

œ

#

?#

&

#

?#

5


Rewrite this hymn in keyboard style. I've done measure 5 for you as it was tricky. Carefully compare measure 5 on the next page with measure 5 on this page.

# 3 & 4 œ œ ? # 34 œ œ

# œ & œ œœ . œ # œ J ? # œ œœ œœ œ &

#

&

˙

˙˙

œœ

˙˙

œ œ

œœ

œœ œœ œœ œ #œ œ œ œœ œ œ œ œ œ œ œ œ

œœ œœ œœ

œœ œ œœ

œœ œœ œœ œœ œ œœ œ

œœ œœ œœ

œ œ œ œ œ œ

˙˙

œœ œ œ œ œ

œ œ œœ œ

? # œœ œ œ œ œ 6

œ œ œ œ œ œ

œœ œœ œœ

œœ œœ # œœ

? # œœ œœ œœ #

˙ ˙

œœ œœ œœ

œ œ

,

˙ ˙ ˙ ˙

˙ ˙

œœ # œœ œ œ

˙˙

˙˙

œœ

˙ ˙

˙

œ œœ œœ # œ

,

,

œ œ œ


# 3 & 4 œ œœ ? # 34 œ

œœ œœ œœœ œ œ

œ œ œ

# œ & œœ œœ œœ # œ œ œ œ ?# œ œ œ &

#

?# &

#

?# 7


Unit 2 ~ More About Minor Keys Modulating in Minor Keys As mentioned in volume one (unit 19), if a piece is in a minor key, it very often modulates to the relative major. Modulation to the relative major is quite simple. The tonic triad of the relative major is the mediant triad of whatever minor key you are in. For example, if you are in C minor, the tonic triad of the relative major is the mediant triad, E b - G - B b. It's quite simple to get there. One easy way is to sound the nVII, which is the dominant of the relative major, and then just stay in the new key. If you think about it, you will realize that this involves actually removing an accidental, rather than adding a new one ( no more Bn). Here is the very simplest possible modulation from c minor to E b major: Study carefully the use of Bn and B b.

b & b b c œœ n œœ ? b b c œœ b c: i b E:

œ œ

viio6

œœ b œœ œ œ œ œ œ i vi

V-4 2

œœ .

˙ ˙

œœ J œ œ œ œ œ I6

V

˙ ˙ I

Finding the pivot Finding the pivot chord of modulations such as this can bea little more difficult that in major keys. In major keys, we have the benefit of an added accidental to tell us when we are going to the new key. In minor keys we do not. This is because the relative major has the same key signature as the minor key you are in, and so no new accidentals are required to go there. For the purposes of writing your chord symbols, you can consider the dominant of III (either V/III of VII/ III) to be the first chord of the new key, and the chord before it is therefore the pivot. In the above example, the B b major triad on the 4th beat is functioning as V of E b, so you can think of that as the first chord of the new key. Therefore, the chord before it is the pivot. 8


Here's another example. In this one, we have VII6 of the new key, which is a dominant chord, so the chord before it (iv) is the pivot.

œ œ œœ œ œœ œ œœ œ œ œ œœ œ œ œ œ

b c œ b & œ ? b b c œœ g:

i

iv ii viio6 I

B b:

V6

Bach

œœ œ œ œ œœ J J œ œ œ œ œ œ œ œ

etc.

Closely related keys in minor keys In Volume One we talked about closely related keys in the context of major keys. Closely related keys are keys that are no more than one sharp or one flat away. C minor's closely related keys are: E b major

f minor

g minor

A b major

B b major

Notice that d minor is not included, as the key signature is two flats away from C minor. Here are some example modulations:

bb œ b & œ ? bb c:

b

œœ

VI f:

œœ

œœ

œœ

V6 5

i

œœ n œœ iv i

œœ

From c minor to f minor

9


b b œ œœ œ œ b & œ œ œœ œ œ œ œ ? bb œ b œ œ œ c: I E b:

bb œ b & œ ? b b œœ b c:

i g:

VI IV

œœ œ œ i6 iv6

V- 7 I

œœ # n œœ œ œ

œ œ

i6 4

V#

bb ˙ b & œ œ b œœ œœ ? bb

œ œ œ œ b œ œ œ œ c:

i6 iv b A : vi

V6 5

œ . ? b b ˙œ œ œ œ b 10

i B b:

i6 ii6

V

From c minor to g minor

From c minor to A b major

I

b œ & b b ˙ œ n œ˙ œ

c:

From c minor to E b major

I

From c minor to B b major


Progressions for Harmonising the Melodic Minor Scale In minor key pieces you will often see the top 3 or 4 notes of the melodic minor scale, either going up or down. Very often these notes occur in the same voice. Below are some examples which show the notes both in the bass and in the soprano. They could equally well appear in the alto or tenor.

bb 3 b & 2 ˙˙ n ˙˙ n ˙˙ ˙ ˙ ˙ ? b b 23 ˙ ˙ ˙ b IVn

i

n viio 6

n ˙˙ ˙˙ ˙˙

ww . . w. w.

˙ ˙ ˙ ˙ n˙ n˙

Vn

i

IV6 V6

w. w. ww . . i

In the first example above, the An could also be harmonized with iin5 (but IVn seems to sound better). The Bn could be harmonized as Vn. In the 2nd example above, IV6 is the only chord you could use to harmonize the An.

b & b b ˙˙ ? bb

˙˙ b i

˙ ˙

˙ ˙

v

VI

˙ ˙

˙˙

w. w.

˙˙

˙˙

˙˙

III

i

v6

iv6

w. w.

˙˙

˙˙

˙ ˙

w. nw . ww . .

Vn

The 3rd example shows one way to harmonize a descending melodic minor in the soprano. Here are 3 more: i - III6 - VI - i6

i - III - iv - V #

I - III6 - iv - V #

The descending scale in the bass is often harmonized as I have shown above. This is a very common progression. VI could be used in place of the iv6. These progressions use 'v', the 'natural' dominant. This chord is not used as much as the dominant with the raised 3rd. Because the leading note is not raised, v does not have the same pull to the tonic chord that V # with a raised third does. For this reason, don't use it at cadences (see volume one, unit 18).

11


Homework for Unit 2 ~ More About Minor Keys Write the following modulations. Use the examples in unit 2 as a guide. You can do them all in four chords: first tonic, pivot, new dominant, new tonic. 1. f minor to A flat major 2. g minor to d minor 3. a minor to d minor 4. e minor to D major 5. e flat minor to a flat minor 6. b minor to G major

7. a flat minor to e flat minor 8. g minor to B flat major 9. f sharp minor to A major 10. c sharp minor to B major 11. f minor to D flat major 12. d minor to F major

Show functional chord symbols.

bbb œ œ b & œ œ œœ œœ œ œ œ œ ? bb b œ œ œ b œ bbb b & ? bb b b

12

f: i A b:

VI IV V

I


bbb b & ? bb b b Harmonize these soprano and bass lines - note that they use the notes of the melodic minor scale going either up or down. Show root/quality chord symbols.

&b œ œ œ œ

bbb œ œ œ œ

##

?b

bbb

##

œ #œ #œ œ

### œ #œ #œ œ &

nnn

? ###

nnn

bbbb œ nœ nœ œ

b b &

#

##

? bb œ œ œ œ

# œ #œ #œ œ

## œ œ œ œ

œ œ œ œ

bbbb

13


Unit 3 ~ Diatonic 7th Chords We already know two seventh chords: ii7 and V7. In fact, one may add a seventh to any triad. As we already know, the seventh is a dissonant interval, and must resolve. It generally resolves by falling a step.

&c ?c

fig. 1

˙ ˙ ˙˙

˙˙ ˙ ˙

V7

fig. 2

˙˙ ˙ ˙ ii7

I

˙ ˙ ˙˙ V

Look at figures 1 and 2. They show the progressions V7 to I and ii7 to V. In both cases, the same thing happens: the seventh of the first chord falls a step to become the 3rd of the next chord. In both progressions, the root of the first chord is a P4 below (or P5 above) the root of the second chord. In figures 3 and 4, we see the same principal applied to two new seventh chords: iii7 and vi7. Just as in the above examples, the seventh of the first chord falls a step to become the third of the next. Also, the root of the first chord is a 4th below (5th above) the root of the second. The progression IV7 - vii(6) is also possible. The progression vii7 - iii would probably not be used (since vii tends to go to I) unless it is part of a sequence (see next page).

&

? 14

fig. 3

˙˙ ˙ ˙

˙˙ ˙ ˙

iii7

iv

fig. 4

˙˙

˙ ˙ ˙˙

vi7

ii

˙ ˙


Figure 5 shows the Do-Fa-Ti-Mi (a.k.a descending 5ths) sequence that you learned about in volume 1. As before, the root of each chord is a 4th lower (5th higher) than the root of the next one, and the seventh of each chord resolves to the 3rd of next chord. The third of each chord remains to become the seventh of next chord. Every 2nd chord is written without a 5th, because this gives smoother voice leading. During this sequence, the leap of an aug 4th is permitted. The leading note may also be doubled. fig. 5

& ˙œ œ ˙˙ ˙ ? ˙ ˙˙ I7

V-7

˙˙ ˙˙

˙˙ ˙ ˙

˙˙ ˙˙

IV7

vii7

iii7

˙˙ ˙ ˙

˙˙ ˙˙

vi7

˙˙ ˙ ˙

ii7

V7

˙˙ ˙˙ I

Figure 6 is the same thing in c minor. In minor keys, use the diatonic version of these chords in this sequence. Actually, you mainly find this sequence in music for instruments, especially in the Baroque and Classical eras. In a chorale or hymn you would probably never have such a long sequence: three or four chords in sequence would be enough. fig. 6

bb ˙ b & ˙ ? b b ˙˙ b i

˙˙ ˙ ˙

˙˙ ˙˙

˙˙ ˙ ˙

˙˙ ˙˙

˙˙ ˙ ˙

i7

iv7

VII7

III7

VI7

˙˙ n ˙˙ ˙˙ ˙ ˙

ii7

V

˙˙ ˙˙ i

These progressions may be found in inversions. Exactly the same rules apply.

&

?

˙˙ ˙ ˙ I6 5

˙˙ ˙ ˙ IV4 2 15


Up to now the 7ths of our 7th chords have usually resolved to the *3rd* of the next chord, e.g. when V7 goes to I, the 7th falls to the 3rd of I. Now as long as the 7th falls a step, it doesn't have to fall to the 3rd of the next chord. It could fall to the root, 5th, or even 7th of the following chord. Check out these examples:

& ˙˙ ? ˙ ˙

˙˙ ˙ ˙

& ˙˙ ? ˙ ˙

˙˙ ˙ #˙

˙ & ˙ ? ˙ ˙

˙ ˙

16

˙ ˙

The 7th (F) resolves by step to the 5th of vi (a deceptive cadence). We have seen this already in volume one. Similar progressions include IV7 - V and iii7 - IV

The 7th (F) resolves by step to the root of V7/vi (E).

The 7th (G) of vi7 resolves by step to the 7th (F) of V7. Parallel 7ths are bad, so use inversions to avoid them: in this example we went from vi7 to V6, not to V7. 5


Homework for Unit 3 ~ Diatonic 7th Chords Write these progressions: 1. iii7

- vi

in A major, B major and D major

2. vi7

- ii

in A major, D major and G major

3. I7

- IV

4. I7

IV7

vii7

iii7

vi7

ii7

V7

i7

iv7

VII7 III7

VI7

ii7

V7

5. 6.

in B major, E major and F major I

in B major, C major, A major i

I6 - IV4 - vii6 - iii4 - vi6 - ii4 - V6 - I 5 2 5 2 5 2 5

1.

&c

in d minor and f minor in A major and E major

2.

?c

&

3.

4.

? 17


&

? &

5.

? 6.

&

? Resolve these seventh chords, and add chord symbols.

& b ˙˙ ? b ˙˙ &

bbb

? bb 18

b

˙˙

#

˙˙ ˙ ˙

### ˙ ˙

˙ ˙ ˙˙ ˙˙

˙˙ # ˙˙

# # # ˙˙

˙ ˙ ˙ ˙ ˙ ˙ ˙˙


Complete these progressions:

b b & ? bb B: V7

I7

IV7

vii7

iii7

vi7

III7

VI7

ii7

V7

I

b b & ? bb g-: i

iv7

VII7

ii7

V7

i

&

? C: I6 5

IV4 2

vii6 5

iii4 2

vi6 5

ii4 2

V6 5

I

19


Unit 4 ~ Secondary Dominants in Major Keys A secondary dominant is a dominant chord that is borrowed from a different key from the one we are writing in. We already know one secondary dominant, V/V. Just as we can borrow the dominant from the key of the V triad, we can borrow the dominants of other triads, too. Consider the supertonic triad, ii. In C major, ii is a d minor triad. The dominant of d minor is A, C #, E. We may use this chord in C major, and call it V/ii. See figure 1. fig. 1

# www

ii

V/ii

& www

Just as V/V goes to V, V/ii goes to ii: fig. 2

& ˙˙ ˙ ? ˙

# ˙˙ ˙ ˙

˙˙ ˙ ˙

˙˙

˙ ˙

˙˙ ˙˙

Just like regular dominants, secondary dominants contain the leading note of the key to which they belong. For example, figure 2 shows V/ii, which contains C #, the leading note of d minor. You should treat this note just as you would any other leading note: normally it would rise when the secondary dominant goes to its tonic. However, if necessary, it may fall to take the fifth of the next chord, provided that it's in an inner voice. Never double the chromatically altered note.

20


Figure 3 shows the vi triad in C major, and V/vi, which is the dominant of a minor.

w & ww fig. 3

# www

vi

V/vi

fig. 4

&

˙˙ # ˙˙

˙˙

˙ ˙

?

˙ ˙

˙˙

˙˙ œ˙ œ ˙˙ # ˙˙

ww

ww

Figure 5 shows V/iii. fig. 5

&

www iii

fig. 6

& ˙˙ ? ˙ ˙

# # www

V\iii

œ . # œj #œ . œ Jj # œœ . œœ . J

from Mendelssohn

œ˙ œ œœ œ œ ˙˙ œ œ ˙

˙˙

˙ ˙

V\viio does not really exist. This is because vii is a diminished triad, and therefore cannot be the tonic triad of any key. Only a major or minor triad can be a tonic, and therefore only a major or minor triad can have a dominant. 21


So, we have now seen V/V, V/ii, V/iii, and V/vi. And we know that V/vii doesn't exist. There's one more possibility, and that is V/IV. V/IV is a bit different from the others. Think about C major. IV is an F major triad. The dominant triad in F major is C-E-G. But in C major, that is simply the tonic triad. Therefore, to make a real secondary dominant, we must use V7 of IV, not just V.

&

www

www

fig. 7

IV fig. 8

& ˙˙ ? ˙˙

b www w

V7\IV

V\IV=I

b ˙˙ ˙ ˙

˙˙ ˙˙

˙˙ œ˙

œ

ww

w w

The secondary dominants I have shown so far have been simple dominant triads or 7th chords in root position. There are several other possibilities: for example, if we wish to place a secondary dominant before ii we could use V\ii, V6\ii, V7\ii, or any inversion of V7\ii. All of these chords have a dominant function. Treat them in the normal way: the leading note rises, the seventh falls, etc. You can also use vii6 as secondary dominant. Figure 9 shows viio6/ii. Use the same doubling you'd use for the regular viio6 - double only the 3rd. fig. 9

& ˙˙ ˙ ? ˙ C: I6

22

# ˙˙ ˙ ˙

viio6/ii

ww

w w ii


Chains of Secondary Dominants Sometimes, a secondary dominant resolves onto another secondary dominant. In the following example we have a V7/ii chord : A - C# - E - G. We would expect this chord to go to ii: D - F - A. Instead, we modify the ii chord by raising the 3rd (F to F#) and adding a 7th. This turns the ii chord into V7/V. This chord then resolves to V7.

& ˙˙ ? ˙˙ C: I

˙˙

# ˙˙

#˙ ˙

n ˙˙

˙ ˙

V7/ii

˙ ˙

V7/V

V7

ww w w I

There are a few things to note about doubling and voice leading in this progression: 1. The leading notes do not rise. Instead, they each fall a chromatic semitone to become the 7th of the following chord: C# - C, F# - F 2. In chains like this, leave the 5th out of every 2nd chord. In our example the V7/ii has a 5th, the V7/V does NOT have a 5th, and then the V7 has a 5th. This helps us to have smooth voice leading and avoid consecutives. 3. The 7th of each chord goes down a step to become the 3rd of the next chord.

Here is the same progression using inverted chords:

˙ & w ? # ˙˙

˙

n # ˙˙

w˙ ˙˙

˙ ˙ ˙ 23


You can use this progression to go completely around the circle of 5ths. You probably wouldn't use this entire progression in a piece (although Bach went half way around it in his Fantasy in G minor for organ, BWV 542) However, it's a good exercise to try to play it at the piano without the music in front of you. (Note that at some point you have to make an enharmonic respelling. In this example I have respelled the F flat chord on the downbeat of bar 3 to an E chord.)

œœ b œœ b œœ b œ b & œ

b œœ b œœ bb œœ ∫b œœ

? œ œœ b œ b œœ

# œœ n # œœ #n œœ n œ œ

b œ b œœ b œ œ bœ

œ œœ œ œ œ

w w w

Compare this progression to the "Do-Fa-Ti-Mi" sequence of diatonic 7ths in unit 3. How are these progressions similar? How are they different?

Chromaticism and Voice Leading In general, if you have a note in one chord and then a chromatically altered version of that note in the next chord, it's best to keep those two notes in the same voice. Consider the two following examples. Both examples have a chord with Cn going to a chord with a C #. In the first example the C and C # are in the same voice. This is the way to do it. In the second example the Cn is in the soprano and the C # is in the tenor. This is not so good, so avoid it where possible.

& ˙˙ ˙ ? ˙

# ˙˙ ˙ ˙

Good

24

ww

w w

˙˙

˙ ˙

˙ ˙

#˙ ˙

w w

w w

Not so good: avoid if possible


Secondary Dominants in Minor Keys In minor keys, different secondary dominants are available. V/iv is quite often used. Notice that the third of the tonic chord must be raised to create the leading note of iv.

bb ˙ b & ˙ ˙ ? bb ˙ b

n ˙˙ ˙ ˙

V7/iv

i

˙˙ ˙˙

˙˙ n ˙˙

iv

V7

n ww w w

In

Another possibility is V/VI, as below. Notice the D b, which belongs to the key of VI (A b)

bb ˙ b & ˙ ˙ ? bb ˙ b i

b ˙˙ ˙ ˙

V7/VI

˙˙ ˙˙

˙˙ ˙ ˙

˙˙ ˙ ˙

VI

ii6 5

i6 4

n ˙˙ ˙ ˙

V7

w w w w i

V7/III is the same as VII7. It doesn't contain any accidentals.

b & b b ˙˙ ? b b ˙˙ b i

˙ ˙ ˙ ˙

˙ ˙ ˙˙

˙ ˙ ˙˙

˙ ˙ ˙

V7/III

III

iio6

i64

or VII7

n˙ ˙ ˙ ˙ Vn

w w ww i

25


You may also use V/V or V7/V, as in major keys. Notice that V/V has 2 accidentals.

bb ˙ n˙ b & ˙ #˙ ˙ ˙ ? bb ˙ ˙ b c-: i

26

V/V

n ˙˙ ˙ ˙ Vn

˙˙ ˙ ˙ i


Homework for Unit 4 ~ Secondary Dominants Write each of the following progressions in two different major keys each: 1. V\ii - ii

7. V7\iii - iii

2. V7\ii - ii

8. V6\vi - vi

3. V6\ii - ii 5

9. V4\vi - vi6 2

4. V4\ii - ii6 2

10. viio6\vi - vi

5. viio6\ii - ii

11. V7\IV - IV

6. V\iii - iii

12. viio6\IV - IV

2

1

&c ?c 3

4

&

?

27


5

6

&

? 8

7

&

? 9

10

&

? 11

&

?

28

12


## ˙ & ? ## ˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

w

˙

˙

?b ˙

˙

˙

˙

w

&b ˙

˙

˙

˙

˙

w

˙

˙

˙

˙

˙

w

&b ˙

?b ˙

w

Write this progression in keyboard style:

& ˙˙˙ b ˙˙˙ ? ˙ ˙ I V6/IV 5

IV

V4/ii 3

ii

V6/vi 5

vi

V6/V 5

I6 4

V

I

29


Write this progression in 12 different major keys, as in the example in unit 4.

&c

œœ ? c #œ œ V7/ii

# œœ nœ œ

n œœ œ œ

V7/V

œœ œœ V7

I

& ? &

? Do this last line in keyboard style and write root/quality symbols above:

&

? 30


Add the missing voices to these. These are all in major keys.

& ˙ ˙ ? ˙ #˙

#˙ n˙

w w

### ˙ ˙

˙ ˙

w

## ˙

˙ ˙

b ˙ ˙ &b ? bb ˙ n˙ bb b & ? bb

###

b ˙ ˙

˙ ˙

˙

w

˙

˙ ˙

w

#˙ n˙

w

˙ #˙ ˙ ˙

## ˙

w

˙ ˙

bbbb ˙ ˙

˙ ˙

w

#˙ n˙

w

n˙ b˙

w

bbbb

Complete this circle of 5ths progression. Every chord is a dominant 7th chord, except the last one. Leave the 5th out of every other chord. Note that the 8th chord is respelled from F b to E.

œœ bœ ?b œ &b

b œœ œ œ œ œ bœ bœ

bœ bœ bœ œ

œ œ œ œ

w 31


1. Write the V/V chord in a-, d-, g-, c-, f-, b b-, e b- and a b-

2. Write the V7/iv chord in a-, e-, b-, f #-, c #-, g #-, d #-, and a #-. 1.

& # ww ? # ww

&

?

&

?

32

2.


Write these progressions. Make sure the note values you choose make rhythmic sense. 1. i - VI - V6/iv - iv - I # in d minor and e minor 5 2. i - V4/VI - VI6 - V6 - I # in f minor and b minor 2 3. I - iv - V6/VII - VII - V6 - I # in g minor and c # minor 5 5 1.

&

?

&

2.

?

&

3.

?

33


Unit 5 ~ More About Modulation Modulation without pivots In both major and minor keys, up to now we have always used a pivot to modulate. It is possible, however, to modulate without a pivot chord, in both major and minor keys. Take a look at the following example. The first chord of the new key is the F # - A - D chord on the 4th beat of the first bar. The chord right before it is F - A - D, which does not exist in G major, and so cannot be a pivot chord. Study the chord analysis.

bb c œ b & œ ? b b c œœ b c: i

œœ œ œœ n œœ œ œ œœ œ # œœ œ no pivot i6

iio6 g: V6

œœ œ n œœ # œ œ œœ œ œ œ œ œ œ i

i6

˙˙ ˙ ˙

iio6 V7

i

Here is the same progression in C major:

œ & œ ? œœ

œœ œ œœ œœ œ œ œ œ œ œ #œ œ no pivot

34

œœ œ œœ # œ œ œœ œ œ œ œ œ œ

˙˙ ˙ ˙


Modulation or Secondary Dominant? Sometimes you will have to decide whether a chord with an altered note is the start of a modulation or if it's simply a secondary dominant. Look at this 4-bar phrase, which consists of two 2-bar phrases:

œ & œ ? œœ C:

I

œ œ œ œ

œœ œ œ

œœ œœ

viio6 I6 vi

œ œ œ œ œœ # œœ

U ˙ ˙ ˙

u

ii6 V/V V

œ œœ œ œ œ œ œ œœ œœ œœ œ œ I

U œœ # œœ ˙˙ œ œ ˙ œ œ ˙ u

V 4 I6 V6 vi6 3 G: ii6 V

I

Now, both cadences have D - F # - A going to G - B - D. However, we will analyse the first one as V/V - V and the 2nd one as G: V - I The first cadence has a motion towards G major with the F #, but that motion is not strong enough to qualify as an actual modulation. This is because the D-F #-A chord is in first inversion (weaker than root position) and it's also on a weak beat. The same bar has Fn on the strong beat, so here the Fn is more important than the F #. Also, there is no dominant approach chord. At the second cadence the D-F #-A chord is in root position, and there is a good dominant approach chord, ii6, right before it. This will sound like a strong cadence in G major and is therefore labelled as a modulation.

35


Unit 6 ~ The Dominant 9th, 11th and 13th Chords To make 7th chords we took a triad and added a 3rd on top, which created a 7th. It's possible to continue piling up the 3rds to create 9th, 11th and 13th chords (V13 actually contains all 7 notes of the scale!) We can use these added notes to vary and enhance the sound of the dominant. The Dominant 9th fig. 1

fig. 2

& www ? ww

ww ww

The dominant 9th is formed by adding the 9th from the bass. See figure 1. Since we only have 4 voices, the 5th is always left out - see figure 2.

V9 generally resolves to I, and the 9th itself resolves downward by step. It's probably best to approach the 9th by common tone - see figure 3 - or by step - see figure 4. It can be used in both major and minor keys. The 9th is usually in the soprano. For now, just use the chord in root position.

& ˙˙ ? ˙ ˙

fig.3

œ œ œ œ

fig. 4

˙˙ . . ˙˙ ..

œœ œ œ

˙˙ ˙ ˙

˙˙ .. ˙. ˙.

Figure 5 shows V #9 in c minor. Don't forget to raise the leading note when you use V9 in minor keys. You can also have V9/V: see figure 6.

bb b & œœ œ nœ ? b b œœ œ b œ fig. 5

36

œœ œœ

n n n ˙˙ ˙ nnn ˙ fig. 6

œ #œ œ œ

˙ ˙ ˙˙

œ œ œ œ


The Dominant 11th chord This is rather strange and unusual chord, because the 11th is the tonic note, and it's odd to have the tonic note in the dominant chord. Again since we are limited to four voices and V11 contains 6 notes, we must leave two notes out: the 9th and the 3rd. "Why do we leave out the 3rd?", I hear you ask. There is no 3rd because it would create a harsh dissonance with the 11th. As with V, keep the 11th in the soprano and use the chord only in root position. See figure 7. Now, depending on how it resolves, V11 can look a lot like V7 with a suspended 3rd. So my guideline is this: if the 11th resolves down a step, label the whole thing as V7 with a 4-3 suspension. See figure 8. If the 11th stays put, i.e. a stationary resolution, label it V11. See figure 9. Approach the 11th by common tone, as in figure 9. Note also that in order to have a complete tonic chords, you need to let the 7th rise. There's nothing wrong with this: the tenor is 'covering' for the alto and singing the note the alto is supposed to sing. The alto is moving up by step, i.e. smoothly, and in parallel 3rds with the tenor, so this will sound fine.

fig. 7

& ww w ? w

fig. 8

˙˙ ˙˙

V

7 4

w w w w

˙˙ ˙˙ -

3

fig. 9

˙˙ ˙ ˙

˙˙ ˙˙ V11

ww w w I

Historical note: the progression in fig. 9 wasn't used much in the 18th Century, and you wouldn't find one in a chorale or 18th Century English hymn. You would be more likely to find one in 19th Century music. So don't use this if you are harmonizing in Bach chorale style.

37


The Dominant 13th chord This is also more of a 19th Century sound than an 18th Century one, and is not found in traditional 18th Century hymns or chorales, so again, don't use it if you are harmonizing in a Bach chorale or hymn style. The V13 is formed using the root, 3rd, 7th, and 13th. Keep the 13th in the soprano and use the chord only in root position. The usual soprano line to use with this is 3 - 1. It can be used in major keys - see figure 11 - or in minor keys - see figure 13. V13/V is possible. See figure 12. fig. 11

˙ & ˙ ? ˙˙

V13

˙ ˙ ˙˙ I

fig. 12

˙ ˙ œœ

# œœ œ œ œ œ V13 /V

V

˙˙ .. ˙. ˙.

fig. 13

bbb

˙ ˙

n ˙˙ b bb c: V13 n

˙ ˙ ˙˙ i

Note that in this progression the leading note does its typical 'cheat' and leaps down a 3rd to sing the 5th of I. Otherwise you end up with 3 roots and no fifth.

38


Homework for Unit 6 ~ V9, V11 ,V13 1. Write V9 - I in C+, G+, F+, B b+, D+, A+, E b+ and A b+ 2. Write V9- i in a-, g-, f-, e-, b-, and c-

&

1.

?

&

2.

?

&

?

39


Complete these using V9

&

##

œ œ

œ

? ## œ

? bb ˙ bb b & ? bb

˙

˙

b

bbbbbb œ

˙

˙

#

˙

˙

˙ bb ˙

˙

˙

˙

bbbbbb

# ˙ ˙

œ œ

b Œ œ

˙

˙

b b &

b Œ œ

˙

˙ ˙

˙

bb

Do these in keyboard style:

&b ?b I

40

V9

I

IV

V9

I

ii6

V9

I


1. Write the progression V13 - I in A+, E b+, D b+, F+, C+ and B+. The melody must always have 3-1. See unit 6 figure 11. 2. Write V13 - i in f #-, c #- e b-, g-, d-, and a-.

### c ˙ & ˙ ˙ ? ### c ˙ 1.

ww w w

&

? &

2.

? &

? 41


Complete these using V13

˙

&

˙ ˙

?

˙

w

˙

&b œ œ ˙ ?b

n ˙

w

n

Write I - ii7 - V11 - I in G+, A+, B+ and D b +

&

#

w˙ ?# ˙ ˙ &

#

?# 42

˙ ˙ ˙

w ˙ ˙˙

˙ ˙ ˙

w

w

œ œ ˙

w

(this one's in a minor)

˙

w


Unit 7 ~ Diminished and Half-diminished 7th chords You can build a seventh chord on the 7th scale degree (leading note) in major and minor keys. If you build a 7th chord on the leading note in major keys, it will be half-diminished. These chords have a -3, o5, and -7 above the root. See figure 1. If you build one in a minor key, it will be a diminished 7th chord. These chords have a -3, o5 and o7 above the root. See figure 2.

www &c w fig. 1

fig. 2

bbb

www nw

viio7

viiØ7

The symbol for the half-diminished 7th is a circle with a line through it. See figure 1. The symbol for the diminished 7th is just a circle. See figure 2. Please note carefully that the viio7 chord in minor keys is built on the raised seventh degree; therefore, in minor keys, the root of this chord will alway have an accidental next to it. These chords belong in the chart on level 2. They are like dominant chords: they like to go to the tonic. They will not go anywhere else. As with all 7th chords, the 7th falls a step into the next chord. Notes on voice leading in minor keys Usually the voice leading is stepwise. Study the following examples of the diminished 7th going to the tonic in c minor:

bb ˙ b & ˙

fig. 3

? bb

˙˙ n b

fig. 4

˙˙ ˙˙

˙˙ ˙ n˙

˙˙ ˙ ˙

fig. 5

˙˙

n ˙˙

fig. 6

˙˙ ˙˙

˙˙

n ˙˙

˙ ˙ ˙˙ 43


Figure 3: The soprano and alto have a diminished 5th going to P5. This is acceptable. Figure 4: The top voices from figure 3 have been inverted to create parallel 4ths. This is preferable to figure 3. Figure 5 shows another possible voice leading, with a doubled 3rd in the tonic. This is OK too, since the two 3rds are being approached by step in contrary motion. Figure 6: This is another possible voice leading: it avoids the consecutive 5ths of fig. 3 and the doubled 3rd of fig. 5. One part leaps.

Voice leading in major keys Here are the same progressions, but now in C major, with the half-diminished 7th chord: fig. 7

& ˙˙ ? ˙ ˙

fig. 8

˙˙ ˙˙

˙˙ ˙ ˙

˙˙ ˙ ˙

fig. 9

˙˙ ˙˙

fig. 10

˙˙ ˙˙

˙˙ ˙˙

˙ ˙ ˙˙

The only bad one here is the first one, figure 7, because now these are true consecutive perfect 5ths between alto and soprano. The other three examples are all OK, as in C minor above.

44


Inversions of viio7 Here are some examples of the inversions of viio7: fig. 11

bb ˙ nœ b & ˙ œ ? b b ˙˙ œœ b

œœ

fig. 12

œœ

i - viio6 - i6 5

fig. 13

˙˙ n œœ œœ ˙ œ œ ˙ œ œ

n ˙˙ ˙ ˙

i - viio4 - i6 3

fig. 14

œœ œ œ

viio4 - i6 2 4

œœ œ œ

˙ ˙ ˙ ˙ n ˙œ œ ˙ ˙ viio4 - V 2

In viio7 every note is in a tritone with another note. The bass and soprano notes should generally resolve correctly 'à la tritone'. So for example ... ... in fig. 11 the bass has a D, which is a tritone away from the A flat in the tenor. The bass D should definitely rise to E b, and it's probably best (and smoothest) for the A b to fall to G. ... in fig. 12 the bass has an F, which is in a tritone with the soprano B. These notes should BOTH resolve in the standard way, with F going to E flat and B going to C. ... in figs. 13 and 14 the A flat in the bass is not only in a tritone, it's also the 7th of the chord and therefore simply falls a step. Inversions of viiØ7 Probably the best of the inversions of the half-diminished 7th is the 2nd inversion. It sounds very good, especially if you can arrange your voice leading to have parallel 3rds (or more likely 10ths) betweeen the outer voices, like so:

& œœ œ œœ ? œœ

œœ œœ

œ œœ œ œ œ œ

œ œ œœ

œ œ

œ œ

˙˙ ˙˙ 45


Applied vii7 Chords The diminished and half-diminished 7th chords can be used as secondary (applied) dominants in both major and minor keys. Here are some examples: 1. Borrow the viio7 chord from V: fig. 15

b b ˙ n ˙˙ b & ˙ ? bb

˙ # ˙˙

b

C-:

i

viio7/V

w w n ww Vn

2. Borrow the viiØ7 chord from V: fig. 16

˙ & ˙ ?

˙

C+: I

˙˙

# ˙˙ viiØ7/V

w w ww

Note the leap in the alto. We leap to avoid parallel fifths with the soprano.

V

Note carefully the spelling and structure of these chords: Figure 15: F # An, C, E b. Note that this chord has been borrowed from G minor (B b, E b), which is the minor dominant of C minor. Why use the minor dominant? Because diminished 7ths are built from notes of the harmonic minor scale. Figure 16 : F #, A, C, E ( a half-diminished seventh chord), built using notes from G major.

46


Figure 17. Borrow the viio7 chord from vi:

˙ & ˙ ˙˙ ?

C: V

˙˙

˙˙

viio7/vi

vi

# ˙˙

˙˙

Figure 18. Borrow the viio7 chord from ii:

& ˙˙

b ˙˙

? ˙˙

# ˙˙ viio7/ii

C: I

˙˙

Note that in both figs. 13 and 14 the viio7 chord is resolving by step and the 3rds of ii and vi are doubled.

˙˙ ii

Figure 19. Borrow the viiØ7 chord from IV:

˙ & ˙

˙ ˙

? ˙˙

˙ b˙

˙˙ ˙ ˙

Note the use of the 2nd inversion here, which sounds very good.

These applied vii7 chords can of course all be inverted. Here's the 1st inversion of viio7/V

bb ˙ b & ˙ ? bb

b

˙ i

˙ #˙ n ˙˙

viio6/V 5

˙˙ n ˙˙

V6

˙˙ ˙˙

i 47


Homework for Unit 7 ~ viio7 and viiØ7 Write the following exercises in 10 keys. Do these in the major: viiØ7 - I viiØ7/V - V then do these in the parallel (tonic) minor: viio7 - i viio7/V - V # (or Vn)

Here's the first line in G major and g minor, as an example:

# c ˙ ˙ & ˙ ?# c ˙ G+: viiØ7

&b

b

? bb

48

˙˙ ˙˙ I

˙˙ ˙ #˙

˙˙ ˙˙

viiØ7/V V

b b ˙˙ ˙ bb #˙ g-: viio7

˙˙ ˙˙

n ˙˙ # ˙˙ ˙ ˙ #˙ ˙

i

viio7 /V V


&

?

&

?

&

?

&

? 49


&

? &

?

&

? &

? 50


Write the following progressions. For 1 and 2, use one bar per progression: 1. i - viio6 - i6 in d, a, e, and b b 5 2. iv - viio4 - i6 in c, a b, f, and e b 3 For number 3, use 2 bars per progression. 3. VI - viio4 - i6 - V - 7 - i 2 4

&

1.

&

2.

&

3.

in c #, d #, f #, and a #

?

?

? &

? 51


Write the following exercises in 8 major keys: 1. I - viio7/ii - ii (double the 3rd of ii) 2. V - viio7/vi - vi (double the 3rd of vi) 3. i - viiĂ˜7/iv - iv (double the root of iv)

&c ?c &

? &

?

52


&

?

&

?

&

?

53


Unit 8 ~ More Sequences In volume one we learned about the so-called 'Do-Fa-Ti-Mi' sequence, also known as the descending 5ths sequence. In this sequence the first pair of chords is repeated down a 2nd each time, which results in going around the circle of 5ths (diatonically, not chromatically). Here's the major key version:

& b ˙˙ ˙ ?b ˙ I

˙˙ ˙ ˙

˙˙ ˙˙

IV

vii

˙˙ ˙ ˙

˙˙ ˙ ˙

˙˙ ˙˙

iii

vi

˙˙ ˙ ˙

˙˙ ˙˙

ii

V

I

and here's the minor key version:

b & b b b ˙˙ ˙ ? bb b ˙ b

˙˙ ˙ ˙

˙˙ ˙ ˙

˙˙ ˙˙

˙˙ ˙˙

˙˙ ˙ ˙

˙˙ ˙ ˙

n ˙˙ ˙˙

The Pachelbel's Canon Sequence This one is also known as "Do - Sol - La - Mi". The pattern here is that the first two chords are repeated down a 3rd each time.

b ˙˙ b & w˙ ? bb

54

˙˙ ˙

˙˙ w˙

˙˙ ˙

˙˙ w˙

˙˙ ˙


Here's another, where the original progression is moved up a 2nd each time. This is do-fa-re-sol

& ˙˙ ˙˙ w ? ˙ ˙ I

IV

˙ ˙ w ˙

ii

˙

˙ ˙ ˙ ˙

˙˙

vi

IV

V

˙

˙ ˙ w ˙

˙˙

V

iii

˙˙

w w

˙˙

w w

7

I

Sequences have such a lot of power and momentum that the strength of the pattern can sometimes make odd progressions sound perfectly OK. For example, the above sequence contains the progression V - iii, which is somewhat unusual. Here, the pattern of the sequence make it sound logical and natural.

This one is a"do-sol-re-la" or rising 5ths.

˙ & ˙ ˙ ? ˙ I

˙˙ ˙˙ V

˙ ˙ ˙ ˙

ii

˙˙ ˙˙ vi

˙ ˙ ˙ ˙

iii

˙ ˙ ˙˙ IV

˙ ˙ ˙˙ I6 4

˙ ˙ ˙ ˙

V

w w ww I

So the momentum of the sequence makes some progressions sound fine which on their own would sound strange. Here are some other things you can get away with in a sequence: 1. You may double the leading note during a sequence. 2. The vii triad may appear in root position. 3. The x4 leap is allowed, and o5 leaps are allowed without having to resolve stepwise inwards.

55


Exam questions often provide you with a soprano or bass, to which you must add the other three voices. When you are studying the given part to decide how to harmonize it, be on the lookout for opportunities to use sequences. If you see a melodic sequence, check to see if a harmonic sequence would be a good way to harmonize it (it may or may not). For example, take a look at the following bassline. It's a melodic sequence because the first two notes rise a 4th, and then this short pattern is repeated up a step. It so happends that the progression I - IV - ii - V is a good one, so this would be a good place for a Do-Fa-Re-Sol sequence:

? œ

56

œ

œ

œ


Homework for Unit 8 ~ Sequences Write the Do - Fa - Ti - Mi (descending 5ths) sequence in F major, E b major, e minor and a minor. Remember to use sequential voice leading in all voices. Show functional and root quality symbols

& b c ˙˙ F

? b c ˙˙ F: I

Bb

˙˙ ˙ ˙

IV

& ? & ? & ? 57


Complete these and add chord symbols à la the examples in unit 8.

# ˙ &

˙

˙

?# ˙

˙

˙

˙

˙

˙

˙

bb b & b ˙

˙

˙

˙

˙

˙

˙

˙

? bb b b ˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

&b

b

? bb

58

˙

˙

˙

˙

˙


Unit 9 ~ Figured Bass In the Baroque era, ensembles generally included something called the 'basso continuo', 'continuo group', or simply 'continuo'. The continuo consisted of a keyboard instrument such as an organ or a harpsichord, and a bass instrument such as a cello or bassoon. The keyboard part would consist of a bassline with numbers written underneath it. These numbers tell the performer what notes to play above the bass: for example, a '7' written below the staff means there's a 7th above the bass note. This tells you what the chord is and what inversion it's in. Playing the right hand chords is called 'realizing' the figured bass. The numbers are essentially the same ones you are already using with your Roman numerals in the functional chord symbols. For example: 3 (or no number) = Root position triad 6 = 1st inversion triad 7 = root position 7th chord 6 = 1st inversion 7th chord ... and so on. 5 Here's an example. This bassline:

?c ˙

˙

˙

˙

6

4 2

˙

6

˙

˙

6

6 4

˙ 7

w

˙˙˙

ww w

Would be realized like this: • chord 1 has no number so that means it's a root position triad • chord 2 has a 6 underneath it so it's a 1st inversion triad • chord 3 has nothing, so it's a root position triad • chord 4 has 4 2 under it, so it's a 3rd inversion 7th chord • chord 5 has a 6 under it, so it's a 1st inversion triad and so on ... here's the realization:

˙ & ˙˙ ?˙

˙˙ ˙ ˙

˙˙ ˙

˙

˙˙ ˙ ˙

˙˙ ˙ ˙

˙˙ ˙

˙˙ ˙

˙

˙

˙

w 59


If a chord has an added accidental (e.g. in the case of a secondary dominant), then the added accidental is shown in the figured bass. If you see an accidental on its own, it applies to the third above the bass. If something other than the 3rd is altered, then you get the accidental plus the number: So this bassline ...

? bb œ b 3

œ n

œ

œ 6

œ

n5 #

œ 7 n5 #

˙ n

... is realized like this: • The first chord has a 3 under it, which means root position triad • The 2nd chord has a n under it, which means root position triad with a raised 3rd (raised with a n) • The 3rd chord has nothing under it, which also means root position triad • The 4th chord has a 6 under it, which means a first inversion triad • The 5th chord has a #, which means the third from the bass has a sharp next to it. It also has n5, which means there's a natural next to the fifth above the bass • The 6th chord is the same as the 5th chord, but with a 7th added • Finally the 7th chord has a natural under it, which means it's in root position, with a raised third.

Here is the final result: a modulation to g minor, with a Picardy third.

b œ & b b œœ n œœœ œœœ œœ ? bb œ œ œ b œ

60

# œœ œœœ n ˙˙˙ n œ œ œ ˙


Sometimes the bass will move but the chord above will stay the same. We use a line to denote this. This bassline has an F with a 3 below it, meaning an F major triad in root positioon. The line means that we keep that F chord while we play the E, meaning that the E is simply a passing note.

œ 3

œ

œ

____

6

œ

Here is the realization:

& œœœ

œœœ

œ

œ

œœ œ

œœ œ

œ

œ

61


Homework for Unit 9 ~ Figured Bass

# 3 & 4

? # 34 œ &

œ œ œ

3

#

3

6

?# œ œ œ &

#

3

6

7

?# œ œ œ &

#

3

6

#

?# œ œ œ 3

62

6

3

#6 4 3

3

˙

˙

œ

œ œ œ

3

6

3

6

3

3

œ œ œ

˙

œ œ œ

œ œ œ

˙

3

3

œ

3

6

3

6

œ œ œ 6

3

3

#

6

6

3

3

#6 3

3

œ œ œ

˙

3

3

3

3

œ

˙

3

œ #

œ 6


In this one I've indicated a root position chord with a blank, i.e., if there's nothing under a chord, it's in root position.

n c &

?n c œ

œœœœœ œ

œ. œ œ œ J

____ 6

&

œ œ œ œœ œœ œ œ

6

7

#

6

œ. œ œ œ J

#œ . œ œ #œ J

œ #œ œ œ

? œ. œ œ œ J

œ. œ œ œ J

œ #œ œ œ

?

6 5

&

b7

6

#

#

#6

6 #

6 5

6 5

6 4

4

#

œ œ œ œ

#6

6

6 4

3

6 4

#

œ . Jœ œ

7

63


Unit 10 ~ The Neapolitan 6th Chord This chord is called 'Neapolitan' because it was popular with the Neapolitan School of Italian opera composers. It is a modification of ii6 in minor keys, and functions as a dominant approach chord.

b & b b www

Here is ii6

To form the neapolitan 6th chord, simply lower the root by a chromatic semitone:

b bw & b b ww

This is generally analysed as 'N6', although it could also be analysed as bii6. The N6 chord usually goes to V, or to the cadential 6 4. The best note of the N6 to double is the 3rd (the bass note). The lowered root is usually in the soprano part, which then goes down a diminished 3rd to the leading note:

bb b˙ n˙ b & ˙ ˙ ? b b ˙˙ ˙ b

b ˙˙

w w

˙ ˙

ww

w w w w

˙˙ n ˙˙ ˙ ˙ ˙ ˙

Composers often slipped a viio7/V in between the N6 and the V. This is very effective notice the stepwise chromatic lines in the outer voices, which are moving in contrary motion.

bb ˙ b & ˙

b œœ

˙ ? bb œ b

œ

œ œ

c-:

6

N6

64

i

n œœ œ #œ

œœ . ˙œ

nœ œ J

˙ ˙ ˙ ˙

viio7/V

V

-

i

œ

7


Homework for Unit 10 ~ The Neapolitan 6th Chord 1. Write the N6 chord in each minor key. Name the key and write the correct key signature. On the next page, write these progressions in 6 minor keys each. 2. N6 - V - i 3. i - N6 - i6 - V - i 4 4. i - VI - N6 - viio7/V - i6 - V - i 4 Make sure that the cadential 6-4 chord is always placed on a strong beat. See the examples. 1. example:

& c b ww w ?c w a-

& ?

65


2. example:

& b œœ œ ? œ

˙˙

# œœ

˙ ˙

œ œ

& ? 3. example:

& œœ œ ? œ & ?

66

b œœ œ œ

œœ # œœ œ œ

œœ

ww

w w


& ? 4. example:

& ˙œ ?œ

œ b œœ # œœ œ œ

œ œ œ #œ

œœ # œœ ˙˙ œ œ ˙ œ œ ˙

& ?

& ?

67

Four-Part Harmony Volume Two - sample  

These books cover the material for harmony exams such as those set by the RCM in Toronto. Vol. One covers the material for Introductory and...

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