SOLUTIONS MANUAL for Tonal Harmony, 9th Edition by Stefan Kostka

SOLUTION MANUAL

SOLUTION MANUAL

Part I: Fundamentals Chapter 1: Elements of Pitch Chapter 2: Elements of Rhythm Chapter 3: Introduction to Triads and Seventh Chords Chapter 4: Diatonic Chords in Major and Minor Keys

Part II: Diatonic Triads Chapter 5: Principles of Voice Leading Chapter 6: Root Position Part Writing Chapter 7: Harmonic Progression and the Sequence Chapter 8: Triads in First Inversion Chapter 9: Triads in Second Inversion Chapter 10: Cadences, Phrases, Periods, and Sentences Chapter 11: Two-Part Tonal Counterpoint Chapter 12: Nonchord Tones 1 Chapter 13: Nonchord Tones 2

Part III: Diatonic Seventh Chords Chapter 14: The V7 Chord Chapter 15: Other Diatonic Seventh Chords

Part IV: Chromaticism Chapter 16: Secondary Functions 1 Chapter 17: Secondary Functions 2 Chapter 18: Modulations Using Diatonic Common Chords Chapter 19: Some Other Modulatory Techniques Chapter 20: Larger Forms

Part V: Chromaticism 2 Chapter 21: Mode Mixture and the Neapolitan Chapter 22: Augmented Sixth Chords Chapter 23: Enharmonic Spellings and Enharmonic Modulations Chapter 24: Further Elements of the Harmonic Vocabulary Chapter 25: Tonal Harmony in the Late Nineteenth Century

Part VI: An Introduction to Twentieth-Century Music Chapter 26: Materials and Techniques Chapter 27: Post-Tonal Theory Chapter 28: New Directions

CHAPTER 1 Elements of Pitch Most of the material in this chapter will already be familiar to the typical college music major. Nothing should be taken for granted, however, and scales should get special attention. Students should be strongly encouraged to practice all of the scales on their instruments and to relate the patterns they have learned through such practice to problems in the theory class. It is essential that vocalists practice scales on the piano in order to begin internalizing patterns that many of the instrumentalists will know already. (All scales may be played two-handed, using a 54322345 fingering.) In addition, class scale-singing drills using letter names or chromatic fixed-do solfege can be very productive.

The last third of the chapter, dealing with scale degree names and intervals, will be less familiar to many students.

They should understand that mastery of this basic material is essential for all further study and that fluency requires the ability to spell and construct intervals very quickly. Various kinds of speed drills are easy to devise, and the class time spent on them will be well invested.

In-class drills should be a frequent activity as students work their way through Chapters 1-4. Speed and accuracy should be the goal, but at least some of the drills must be designed so that students who are having more trouble are given the time to come up with correct answers. A struggling student who has just begun to ponder a question learns little by hearing a colleague call out the answer.

Answers to Selected Exercises Exercise 1-1 A. 1.

A1

2.

F2

3.

D3

4.

A4

5.

E5

6.

G6

7.

C8

B.

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Chapter 1

Exercise 1-2 A.

B.

1. D

2. Fm

3. Db

4. Bb

5. B

6. A

7. Cb

C.

D.

1. 5 flats 6. A 11. D

2. 1 sharp 7. 7 sharps 12. Eb

E.

1.

2.

3.

4.

5.

6.

4# D Bb A F#

2b 6b

¶

3. B 8. Cb 13. 6 flats

4. 3 flats 9. 1 flat 14. Fm

5. Bb 10. 4 sharps

G#

§ ∞

B

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Chapter 1

Exercise 1-3 A.

B.

C.

1. melodic minor

2. harmonic minor

3. harmonic minor

4. major

5. melodic minor

6. natural minor

1. d

3. b

2. c

4. bb

5. gm

6. fm

7. am

D.

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Chapter 1

E.

1. fm

2. 6 flats

3. 4 sharps

4. bb

5. (none)

6. f

7. am

8. 2 flats

9. b

10. ab

11. 1 sharp

12. d

13. 3 flats

14. 5 sharps

Exercise 1-4 A.

1. 3

2. 5

3. 2

4. 1

5. 6

6. 4

7. 8

9. 5

10. 2

11. 6

12. 1

13. 8

14. 4

15. 3

8. 7

Exercise 1-5 A.

B.

1. P

2. __

3. P

4. __

5. P

6. P

7. P

8. P

9. __

10. __

11. __

12. P

13. P

14. __

15. P

16. P

17. P

18. __

19. __

20. __

1. M

2. m

3. M

4. M

5. M

6. M

7. m

8. m

9. M

10. m

11. M

12. m

13. M

14. M

15. m

16. M

17. M

18. m

19. m

20. M

21. M

22. m

23. m

24. M

25. m

26. m

27. M

28. m

29. m

30. M

C.

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Chapter 1

Exercise 1-6 A.

B.

1. o4

2. +6

3. P4

4. +5

5. m6

6. o3

7. +4

8. +2

9. o5

10. o5

11. +4

12. +2

13. o8

14. +5

15. o4

16. +6

17. +3

18. o5

19. m6

20. o7

5. m7

6. o5

1. M6

2. o4

3. m3

4. +2

7. P4

8. M2

C.

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Chapter 1

D.

E.

1. m3

2. o5

3. o4

4. m2

5. +4

6. m2

7. M2

8. M2

9. P4

10. P5

11. m2

12. m6

13. o4

14. m2

15. +1

16. m3

17. P8

18. M6

19. +1

20. P1

21. o5

22. o4

23. m3

24. P5

1. c

2. d

3. d

4. c

5. c

6. d

7. d bass

8. c

9. d

10. c

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Chapter 1

_______________________ (section)

______________________________ (name)

Chapter 1 Quiz #1 A. Name the pitches in the blanks provided, using the correct octave register designations.

___

___

___

1

2

3

middle C

___

___

___

___

4

5

6

7

B. Notate the indicated pitches on the staff in the correct octave. Include accidentals where appropriate.

Fm5

Bb1

A3

D4

G3

Bm4

E4

Cb3

C. Notate the specified scales using accidentals, not key signatures. The melodic minor scale should be written both ascending and descending.

1.

f melodic minor

2.

fm harmonic minor

3.

d natural minor

D. Notate the specified key signatures.

1. A

2. Db

3. B

4. g

5. a#

6. bb

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Chapter 1

________________________ (section)

______________________________ (name)

Key for Chapter 1 Quiz #1 A. Name the pitches in the blanks provided, using the correct octave register designations.

E1

C2

B2

1

2

3

middle C

G4

F5

E6

D7

4

5

6

7

B. Notate the indicated pitches on the staff in the correct octave. Include accidentals where appropriate.

Fm5

Bb1

A3

D4

G3

Bm4

Cb3

E4

C. Notate the specified scales using accidentals, not key signatures. The melodic minor scale should be written both ascending and descending.

1.

f melodic minor

2.

fm harmonic minor

3.

d natural minor

D. Notate the specified key signatures.

1. A

2. Db

3. B

4. g

5. a#

6. bb

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Chapter 1

___________________ (section)

_____________________________ (name)

Chapter 1 Quiz #2 A. Label what each interval becomes when it is inverted.

1. M6 becomes ______

3. +4 becomes ______

5. o3 becomes ______

2. P5 becomes

______

4. m7 becomes ______

6. P4 becomes ______

M6 1

m2 2

P4 3

+6 4

M3 5

M7 6

E. Fill in the blanks.

Key signature

Name of key

Key signature

Name of key

1. three sharps

___ major

4. six flats

___ minor

2. ________

Db major

5. ______

g# minor

3. two flats

___ minor

6. ______

E major

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Chapter 1

Key for Chapter 1 Quiz #2 A. Label what each interval becomes when it is inverted.

1. M6 becomes

m3

3. +4 becomes

o5

5. o3 becomes

+6

2. P5 becomes

P4

4. m7 becomes M2

6. P4 becomes

P5

M6 1

m2 2

P4 3

+6 4

M3 5

M7 6

E. Fill in the blanks.

Key signature

Name of key

Key signature

Name of key

1. three sharps

A major

4. six flats

eb minor

2. 5 flats

Db major

5. 5 sharps

g# minor

3. two flats

g minor

6. 4 sharps

E major

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CHAPTER 2 Elements of Rhythm Most music students have a practical understanding of durational symbols and time signatures, although some confusion over compound time signatures can be expected. Practice with aural identification of beat and meter types is helpful, "drop the needle" exercises being very efficient in this regard.

At the same time, the scales and intervals from Chapter 1 must be kept fresh in the students' minds. Mastery of this material requires much time and effort, and the students should not be allowed to backslide here.

Answers to Selected Exercises Exercise 2-1 A.

B.

C.

1. 2

2. 4

3. 5

4. 4

5. 2

6. 2

7. 8

8. 3

9. 8

10. 2

11. 6

12. 4

13. 2

14. 6

15. 7

16. 8

1. Quadruple (duple)

2. Triple

3. Duple (quadruple)

4. Triple

5. Quadruple (duple)

1. d

2. F#

3. £

4. f#

5. F#

6. Bb

7. Ab

8. ™

9. Eb

10. ­¶

11. D

12. D

13. £

14. e

Exercise 2-3

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Chapter 2

B.

Exercise 2-4 A.

B.

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Chapter 2

Exercise 2-5 A.

B.

C.

D. The second measure of No. 4 might also be eighth-quarter-eighth.

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Chapter 2

E.

F.

G.

H.

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Chapter 2

_______________________ (section)

_________________________________ (name)

Chapter 2 Quiz A. Fill in the blanks.

Beat and meter type

Beat value

Division of the beat

Time signature

q q

1. simple quadruple 2. compound duple

qk

3.

ek

4. simple duple

q

5.

6.

B. Each measure below is incomplete.

Add one or more rests to complete the measure.

q q q C. Provide an appropriate time signature for each measure. In some cases more than one correct answer may be possible.

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Chapter 2

Key for Chapter 2 Quiz A. Fill in the blanks.

Beat and meter type

Beat value

Division of the beat

1. simple quadruple

h

q q

2. compound duple

qk

3. compound triple

ek

4. simple duple

q

5. simple triple

e

6. compound quadruple

h.

B. Each measure below is incomplete.

Add one or more rests to complete the measure.

Time signature

q q q C. Provide an appropriate time signature for each measure. In some cases more than one correct answer may be possible.

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CHAPTER 3 Introduction to Triads and Seventh Chords In this chapter the student learns to spell and recognize the four triad types and the five common seventh chord types. These are treated as individual sonorities, isolated for now from the context of major and minor keys. This allows the development of some fluency in spelling and recognizing chords before adding in the complications of tonal contexts.

Useful in-class activities include board drills ("Make each note on the board the third of a dominant seventh chord," and so on) and "quick thinking quizzes" (read aloud with a pause of 10-15 seconds between questions). Recognizing chords in various textures can be practiced by means of transparencies or an anthology. This chapter also introduces two related concepts: figured bass and lead sheet symbols. Live performances of works using figured bass and lead sheet symbols will be sure to impress upon the class the close relationship between theory and practice.

Answers to Selected Exercises Exercise 3-1 A. 1. G Bb D 2. Eb G Bb 3. D F Ab

4. A C Eb 5. F Ab C 6. Db F Ab

7. C E G# 8. A# C# E 9. E G# B

10. F# A C# 11. B D# Fx 12. Eb Gb Bb

B.

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Chapter 3

C. 1

2

3

A# F Db

F#

D

4

5

6

7

8

Eb

Gb

D#

Bb

D

B

G

Cb

B

C

9

10 C

G Gb

E

F#

D.

Exercise 3-2 A. 8. m7

1. ø7

2. ø7

3. M7

4. o7

5. o7

6. ø7

7. o7

9. Mm7

10. Mm7

11. M7

12. M7

13. m7

14. Mm7

15. m7

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Chapter 3

B.

C.

Exercise 3-3 A.

B.

1.

2.

3.

1. F# o 6

2. A m 6

3. G Mm7 y

4. A ø7 r

5. D m7 t

6. F M w

7. E o7 7

8. F# m7 t

9. C# ø7 t

10. B M7 y

11. D M 6

12. C m

13. A# o7 y

14. C Mm7 7

15. B m w

16. F Mm7 r

1. F

2. Bo/D

3. C

4. C7/Bb

5. F/A

6. Gm

8. Bb

9. F/A

10. Bb

11. Gm

12. C7

13. F

1. D

2. Bm7

3. E7

4. A

5. D/F#

6. A7/C#

7. D

8. A

9. F#m

10. Bm

11. Bm7/A 12. E/G#

13. A

14. Bm7/D

15. E

16. A

1. Bb

2. F/A

3. Gm

4. Bb/D

6. Ao/Eb

7. Bb

8. F

9. Bb

10. Bb

11. Gm/Bb 12. Gm

13. F/A

14. F

15. Gm

16. BbM7

17. C

18. F

20. F/A

21. F7

5. Eb

19. F

7. F/A

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Chapter 3

22. Bb

23. Gm/Bb 24. D/F#

25. Gm

26. D7

27. Gm

28. D

29. Gm

30. Gm

31. F/A

32. F7

33. Bb

34. Bb/D

35. Eb

36. Bb/D

37. Cm

38. Bb

39. F

40. Bb

3. Db /F

4. A#ø7

5. Do7

6. A7

C.

Exercise 3-4 A.

1. C#o7/E 2. A

B. 1.

1 G m

2 G m

3 D M 6

4 G m

5 D M

6 Eb M

7 A o 6

8 D M

9 D M

10 D m

11 G m7 7

12 F Mm7 r

13 Bb M

14 Eb M

15 G m w

16 D M

17 G m

18 D M

19 G m

20 F M 6

21 Bb M

22 G m

23 C m7 r

24 F M

25 Bb M

26 Bb M

27 F# o 6

28 G m

29 A ø7 r

30 D M

31 Eb M

32 G m w

33 D M

1 C# ø7 7

2 F# Mm7 7

3 B m

4 B m 6

5 C# ø7 7

6 F# Mm7 7

7 B m

8 B m 6

9 E ø7 7

10 A Mm7 7

11 D M7 7

12 G M7 7

13 A# o7 r

14 B m 6

15 C# o 6

16 E# o7 7

17 F# M

18 F# Mm7 y

19 B m 6

2.

7. Em7/G 8. Bb/F

9. Em/G

34 G M

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Chapter 3

3.

1 Eb m

2 F ø7 r

3 Bb M

4 Eb m

5 F ø7 7

6 Eb M 6

7 Ab m

8 A o7 7

9 Gb Mm7 r

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Chapter 3

_____________________ (section)

___________________ (name)

Chapter 3 Quiz A. Given the triad or seventh-chord quality and one member of the chord, notate the rest of the chord.

3rd Mm7

5th m

7th o7

3rd o

5th m7

B. Identify the type of triad or seventh chord, using the abbreviations introduced in this chapter.

_____

_____

_____

_____

_____

C. Fill in the blanks above this example with lead sheet symbols that correspond to the figured bass. Use slash chord notation, as in C/E, for inverted chords. ___

___

___

___

___

___

___

___

4+ 2

6

6 4

6 #

#

6

Q

___

D. Identify the root and type of each chord, and show the correct bass position symbol (bps). All the notes in each example belong to the same chord. The lowest note in each example is the bass note for the purpose of analysis.

Root

___

___

___

___

___

Type

___

___

___

___

___

Bps

___

___

___

___

___

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Chapter 3

Key for Chapter 3 Quiz

A. Given the triad or seventh-chord quality and one member of the chord, notate the rest of the chord.

B. Identify the type of triad or seventh chord, using the abbreviations introduced in this chapter.

__o7__

__o__

__ø7__

__M__

__M7__

C. Fill in the blanks above this example with lead sheet symbols that correspond to the figured bass. Use slash chord notation, as in C/E, for inverted chords. p Em

E7/D

Am/C

Em/B F#/A#

B

Em/G D#o/F#

4+ 2

6

6 4

#

6

6 #

Em

Q

D. Identify the root and type of each chord, and show the correct bass position symbol (bps). All the notes in each example belong to the same chord. The lowest note in each example is the bass note for the purpose of analysis.

Root

F

E

Ab

B

G#

Type

m7

+ (or Aug)

M

Mm7

m

Bps

7

6

w

t

___

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CHAPTER 4 Diatonic Chords in Major and Minor Keys This chapter begins by attempting to dispel the notion, so often held by students, that a tonal composer chooses from a menu of three scales before beginning a piece in the minor mode. The fact is, of course, that diatonic minor mode music is more complicated than diatonic music in the major mode because of the variability of § and ¶. It is fair to say that in minor most melodic pitches conform to the melodic minor scale and most harmonic pitches belong to the harmonic minor scale, but exceptions are so common as to render such a "rule" useless.

These complications are encountered when triads and seventh chords in minor are presented. Instead of following the simpler but misleading system of forcing chords to conform to the harmonic minor scale, we include as norms three chords from outside of that scale: III, i7, and IIIM7.

Class activities should include a great deal of drill, especially involving triads. Brain twisters like "F is the 5th of a vi chord in what major key?" and "F# is the bass note of a Vt in what minor key?" will challenge even the best students and help to develop skills essential for analysis.

Answers to Selected Exercises Exercise 4-1 A. 8. G#0 viio

B.

1. Cm vi

2. Bm iv

3. D#0 vii0

4. Bb/F IIIw

5. C V

6. Em/G vi6

9. E III

10. F/A V6

11. Eb VI

12. Bbm vi

13. Ab VI

14. C#/G# 15. A Vw IV

3

4

Cb: 70 (¶)

G: 70 (¶)

c: (£)

10

11

12

1

2

ab: (™) 8

20

9

f: (¶)

v20

Cm: (£)

3

gm: (§)

^

Db: (¢)

IV

5

III

fm: (∞)

6

7

e: VI (§)

F: (£)

13

14

15

Bb: ii (™)

D: (§)

Fm: (™)

V

ii

C. 1.

I 1

Vq 2

IVq 3

V 4

Iq 5

vii0q 6

I 7

IV 8

2.

I 1

vii0q 2

Iq 3

iiq 4

vi 5

Iw 6

V 7

I 8

vi

7. Fm/C ivw

iii

Eb: 70 (¶)

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Chapter 4

D.

1.

G#

2.

Eb

3.

F# %w

4.

5.

g

6.

G

Exercise 4-2 A. The instructions did not call for slash chord notation, but it would not be incorrect if the student included them.

1. CM7/G IV9t

2. D#-7 iiø7

8. A7/C# Vr

9. G#m7 iii7

10. E-7/Bb 11. Bm7 vii-t ii7

1

2

B.

$9e

Bb: (¢) 8

3. Bbm7 iv7

3

F: (¡)

9

10

E: (¢)

$9e G: (™)

!9e

2e

4. Gm7/F viy

5. GM7 III9e

6. AbM7 I9e

7. EbM7 VI9e

12. Fm7/Ab 13. A#07 iir viio7

14. EbM7 III9e

15. Bm7 vi7

4

5

b: (£)

#9e fm: (™)

11

12

13

cm: (∞)

Ve f: (∞)

Ve

3e

Eb: (£)

2-e

6

A: (¶)

7

7-e g: 70e D: (¶) (§) 14

vie

15

2-e

e: (™)

c: (¡)

ie

C.

1.

I

Vr

Ve

I

Iq

iir

Ve

I

2.

I

Vq

vi

I9t

IV

Iq

V7

I

Ab: (§)

6e

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Chapter 4

______________________ (section)

________________________ (name)

Chapter 4 Quiz A.

Name the triad type (M, m, o, or +) that is usually found on each scale degree in major and minor modes.

Major: ____

____

____

____

____

____

____

Minor:

____

____

____

____

____

____

____

Degree:

1

2

3

4

5

6

7

B. Name the seventh chord type (M7, m7, Mm7, ø7, or o7) that is usually found on each scale degree in major and minor modes.

Major: ____

____

____

____

____

____

____

Minor: ____

____

____

____

____

____

____

2

3

4

5

6

7

Degree:

1

C. Given the key and a chord, supply the roman numeral below the staff. Be sure that your roman numeral is the correct type and includes a bass position symbol if necessary. Finally, provide an appropriate lead sheet symbol above the staff (you do not need to use slash chord notation).

1. _____

2. _____

3. _____

4. _____

F: ____

b: _____

d: _____

A: _____

5. _____

6. _____

7. _____

8. _____

c#: _____

g: ____

Db: _____

E: _____

D. Analysis. Put roman numerals in the spaces provided, making sure each roman numeral is of the correct type and includes a bass position symbol, if needed.

___ 1

___ 2

___ 3

___ 4

___

___

5

6

___ 7

___ 8

___ 9

___ 10

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Chapter 4

Key for Chapter 4 Quiz A. Name the triad type (M, m, o, or +) that is usually found on each scale degree in major and minor modes.

Major:

M

m

m

M

M

m

o

Minor:

m

o

M

m

M

M

o

Degree:

1

2

3

4

5

6

7

B. Name the seventh chord type (M7, m7, Mm7, ø7, or o7) that is usually found on each scale degree in major and minor modes.

Major:

M7

m7

m7

M7

Mm7

m7

ø7

Minor:

m7

ø7

M7

m7

Mm7

M7

o7

Degree:

1

2

3

4

5

6

7

C. Given the key and a chord, supply the roman numeral below the staff. Be sure that your roman numeral is the correct type and includes a bass position symbol if necessary. Finally, provide an appropriate lead sheet symbol above the staff (you do not need to use slash chord notation).

1.

C7

2.

GM7

3. Gm

4. AM7

5. D#-7

6.

D

F:

%t

b: ^9e

d: 4w

A:

!9r

c#: 2-y

g: %q

7.

Fm

8.

D#0

E: 70q

Db: iii

D. Analysis. Put roman numerals in the spaces provided, making sure each roman numeral is of the correct type and includes a bass position symbol, if needed.

%q

!

$

%

6

6y

2r

!w

%e

!

1

2

3

4

5

6

7

8

9

10

27 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

CHAPTER 5 Principles of Voice Leading This chapter serves as an introduction to the composition (partwriting) exercises that begin in Chapter 6. After some guidance in the composition of simple melodies in chorale style, the student learns spacing conventions and the proscriptions regarding parallels.

It is extremely important to emphasize the historical context of what may at first appear to be arbitrary and fussy "rules." The students should understand that when we study a style (if tonal music may be broadly termed a "style"), we learn the stylistic norms -- those practices that are appropriate to the style because they conform to stylistic norms. Parallel fifths are not unstylistic in all musical styles, and they are not bad in and of themselves, but they are not stylistic in tonal music.

Sometimes this point can be better understood by a comparison to other styles. The style of Dixieland jazz, for example, is easily recognized, but a Dixieland cornet player certainly would not fit in stylistically with a progressive jazz group, because the cornet player would have the wrong timbre, employ the wrong rhythms, and stay too close to the harmonies in improvisation. No doubt the class can think of similar examples in country music or rock.

Answers to Selected Exercises Exercise 5-1 A. 1.

a. There is not a single focal point. b. The ascending sixth is not approached from above. c. The leading tone does not resolve.

2.

a. The C4 does not belong to the i chord. b. Two augmented intervals occur (F#-C, C-D#). c. The ascending sixth is not approached from above.

3.

a. The second B4 does not belong to the I chord. b. The contour is uninteresting.

Exercise 5-2 A.

I O

iiq C

V C

I O

IV C

iiq O

Ve C

B.

a. Bass and alto cross in m. 2 b. Soprano and alto are too far apart in mm. 2-4.

Vy C

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Chapter 5

Exercise 5-3 A. 1. Bass/Soprano

o

c

c

2. Bass/Alto

c

o

c

3. Bass/Tenor

o

c

c

4. Tenor/Soprano

st

p

p

5. Tenor/Alto

o

o

s

6. Alto/Soprano

o

o

s

B.

V

I

IV

I

V

C.

D.

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Chapter 5

________________________ (section)

____________________________ (name)

Chapter 5 Quiz A. Criticize this melody in terms of the rules for simple melodies discussed in this chapter. List your comments below the example, clearly identifying the portion of the excerpt to which you are referring.

B. Find and label the following errors in this passage: 1. Direct 8ves 4. Spacing error

2. Parallel 5ths 5. Parallel 8ves

3. Contrary 5ths 6. Chord with no third

C. Analyze the chords with roman numerals (and bass position symbols where needed). Below each roman numeral write a "C" or and "O" to indicate close or open structure.

30 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 5

Key for Chapter 5 Quiz A. Criticize this melody in terms of the rules for simple melodies discussed in this chapter. List your comments below the example, clearly identifying the portion of the excerpt to which you are referring.

1

Unresolved leading tone

2

No change of direction after 5th

3

Augmented interval

4

Melody note not in chord

5

No single focal point

6

Consecutive leaps should outline triad

B. Find and label the following errors in this passage: 1. Direct 8ves 4. Spacing error

2. Parallel 5ths 5. Parallel 8ves

3. Contrary 5ths 6. Chord with no third

C. Analyze the chords with roman numerals (and bass position symbols where needed). Below each roman numeral write a "C" or and "O" to indicate close or open structure.

Bach: “Jesu, der du meine Seele” (simplified)

g:

1 O

1q O

% C

1q C

70q O

1 C

2-r C

% C

1 C

1

2

3

4

5

6

7

8

9

31 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

CHAPTER 6 Root Position Partwriting This chapter deals with partwriting root position triads in four- and three-part textures, presented in that order. Many instructors prefer to restrict their students to four-part textures only, and this may certainly be done using this text.

However, others find that the three-part textures offer the student variety and encourage a more creative approach to theory exercises.

The pedagogical approach taken is to classify all root movements into one of three categories, and conventional voice leading strategies, a total of five in all, are explained for each root movement.

If board space is available, it is very useful to have some students work out short exercises at the board while others work the same problems at their seats. After everyone is seated again, the class can critique the board work, not for the purpose of embarrassing their classmates, obviously, but for the very positive learning experience that can result.

Another worthwhile classroom activity divides the class into teams of two to four students each for the purpose of solving a partwriting problem.

To emphasize the musical side of their exercises, one or more instrumental trios or quartets can be formed by class members, with exercises composed for them and parts written out in advance. This is valuable especially for those who have had no close exposure to strings or to transposing instruments. The last few pages of the chapter introduce the student to instrumental ranges and transpositions to facilitate such activities. Exercises may be sung as well, of course—even the most ordinary partwriting exercise can be effective when well played or sung.

Some instructors find that the information on instrumental transpositions and ranges to be more than students can absorb at this point, and that part of the chapter may certainly be omitted. However, being able to decipher a score seems to us to be easier to master than composing for transposing instruments. A silly but effective formula is this: “An instrument called the Honk is in the key of X; when the Honkist sees a C, we will hear an X.” This will work for every instrument except for brasses in bass clef, although it does not tell us whether the pitch will be higher or lower than a concert C. Answers to Selected Exercises Exercise 6-2 In these and similar exercises, we supply the most likely correct student responses. Other solutions are possible.

A.

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Chapter 6

Exercise 6-3 A.

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Chapter 6

Exercise 6-5 A.

C.

G:

%

!

!w %y !q $q

!

%e

!

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Chapter 6

_________________ (section)

_______________________ (name)

Chapter 6 Quiz A. Demonstrate three good ways to partwrite this progression. The soprano line should be different in each solution, and each chord should contain two roots, a third, and a fifth.

F:

I

IV

I

IV

I

IV

B. Complete the examples below, using a 4-part texture in the first one, and a 3-part texture in the second.

e: V

i

VI

iv

V

VI

Bb:

I

vi

ii

V

I

C. Supply the concert (sounding) pitch or the written pitch, whichever is missing.

35 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 6

Key for Chapter 6 Quiz A. Demonstrate three good ways to partwrite this progression. The soprano line should be different in each solution, and each chord should contain two roots, a third, and a fifth.

F: I

IV

I

IV

I

IV

B. Complete the examples below, using a 4-part texture in the first one, and a 3-part texture in the second.

e: V

i

VI

iv

V

VI

Bb:

I

vi ii V

I

C. Supply the concert (sounding) pitch or the written pitch, whichever is missing.

36 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

CHAPTER 7 Harmonic Progression and the Sequence This chapter begins with an introduction to melodic and harmonic sequences, using this topic as a means to explain the norms of tonal harmonic progressions. We take the root movement of the descending fifth as the starting point from which to develop diagrams of normative root movements in major and minor modes. It is worthwhile emphasizing that the harmonic "functions" of tonal harmony developed slowly and were the result of contrapuntal, acoustical, and historical factors, among others.

The chapter continues with further discussion of harmonic sequences, discussing some of the more common root patterns and their variants, and it ends with a brief tutorial on harmonizing simple melodies.

The material in this chapter should be reinforced aurally as much as possible, probably by playing progressions at the piano. Most students are able to recognize the harmonic clichés of tonal music, and those who cannot need to become more sensitized to them. It is also important to keep up regular practice with chord spelling and partwriting as this chapter is studied. A useful exercise is to lead the class in the composition of a chorale phrase, from progression (avoiding ii0 and vii0 for now) to melody to four-part setting, which should then be sung by the class.

To illustrate (and to introduce) what is meant by a harmonic function, it might be worthwhile to play the F7 chord shown in Example 3 of "To The Student," which precedes Chapter 1. Play the chord (but not its resolution), arpeggiate it, then isolate individual pitches and ask what those notes "want" to do. Try to generate a sense of amazement that these vibrating piano strings seem to have wills of their own. How is that possible? Would someone brought up in a culture with no music at all recognize the goal that this chord seems to seek?

Answers to Selected Exercises Exercise 7-1 A. 1. V or vii0 2. IV B. 1. [ iv VI V ] C.

3. vi or IV

2. [ ii IV ]

4. IV 3. (none)

5. I

6. IV

4. [ V viio ]

1. The IV6, sandwiched between the two dominant chords, serves to prolong the dominant function while at the same time providing an effective predominant chord on a metrically strong beat.

A

D G#o A E

D

E7 A

D A Bm7 E

A

A: ! | $ 70q ! [%q | $q] %r ! !q | $q ! 2r % | ! | 2.

D

Eb

Cm

D

Gm Cm Gm

D

Gm

g: V | VI | ivq | V | i | iv iq | i V | i |

J.

1. iq

2. iie

3. iii

4. III

5. Vw

6. vii-r

7. vii-e

8. ii0q

9. VI

10. iii6

11. Iw

12. IIIq

13. ivw

14. iiy

15. IV9t

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Chapter 7

_____________________________ (section)

____________________________ (name) Chapter 7 Quiz

A. Define the following terms. sequence

diatonic sequence

circle-of-fifths progression

B. Fill in the blanks with the chord or chords that would be likely to follow the given chord in a minor key. Be sure each roman numeral reflects the quality (major, minor, diminished) of the chord. ii0

____ or ____

V

____ or ____

III

____ or ____

VI

____ or ____

iv

____ or ____ or ____ or ____

vii0

____

VII

____

C. Analyze the chords specified by this figured bass, and add inner voices to make a four-part texture. Bracket all circle-of-fifths progressions, even those that contain only two chords.

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Chapter 7

Key for Chapter 7 Quiz A. Define the following terms. sequence A pattern that is repeated immediately in the same voice (or voices), but beginning on a different pitch class. diatonic sequence A sequence that stays in one key. circle-of-fifths progression A progression in which the root descends by a 5th (or ascends by a 4th).

B. Fill in the blanks with the chord or chords that would be likely to follow the given chord in a minor key. Be sure each roman numeral reflects the quality (major, minor, diminished) of the chord. iio

_V__ or _70_

V

_i__ or _VI_

III

_iv_ or _VI_

VI

_iv_ or _20_

iv

_ i_ or _20_ or _V__ or _70_

vii0

_i__

VII

III

C. Analyze the chords specified by this figured bass, and add inner voices to make a four-part texture. Bracket all circle-of-fifths progressions, even those that contain only two chords.

39 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

CHAPTER 8 Triads in First Inversion Combinations of root position and first inversion triads should result in a much higher degree of musicality in composition exercises. The introduction to soprano/bass counterpoint that is the final portion of the chapter is intended to carry over into the composition exercises throughout the remainder of the text. In general, a more musical result will be achieved if the student first composes a good soprano/bass framework before providing the inner parts. Students should also be strongly encouraged to do all theory exercises at a piano—especially those exercises that call for some degree of creativity and judgment.

We point out three reasons (aside from bass arpeggiation) for using a triad in first inversion, although these are not mutually exclusive: to improve the contour of the bass line, to provide the bass a greater variety of pitches, and to lessen the weight of non-cadential tonic and dominant chords. A special case is the series of first inversion triads in parallel motion. Our doubling rules are less strict than those that are based upon the Bach chorale style and are more generally applicable. Essentially, the only proscribed doubling is that of the leading tone. Any other doubling can be appropriate, depending upon the circumstances.

This is the first chapter to include Workbook composition exercises that are drawn from music literature (8-1B and 8-1F). Similar activities done as a cooperative classroom exercise or in team competition are invariably successful, and the student solutions may on occasion rival the model.

Answers to Selected Exercises Exercise 8-1 A. 1. The sixth-chord passage begins in the middle of m. 59 and lasts through m. 64. The voice leading resembles Example 8-10.

2.

Vq (a)

I

Iq (a)

IV

Ve

3.

Gm Cm/Eb F

Bb

Eb A0/C D Gm

[i

III

VI

ivq

VII

Vq (a)

ii0q

I

V

i]

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Chapter 8

B. The second phrase (included below) may be used for an in-class exercise. It includes a good example of a sequence that demonstrates how an unusual progression (in this case V to iii) can sound perfectly acceptable in a sequential passage. Notice also that Mozart doubles the third in three of the four root position IV chords in these two phrases.

F and G. The original Beethoven excerpt (below) is obviously far beyond the capabilities of the students at this point, but it can serve as an interesting example for analysis and as an early introduction to the concept of secondary dominants (or as a "microtonicization" of E minor).

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Chapter 8

_______________ (section)

__________________ (name) Chapter 8 Quiz

A. Fill in each blank with the appropriate term.

1.

"Parallel

chords" is a term used for a passage that contains a series of first inversion triads in

parallel motion.

2.

Name three reasons for using first inversion triads: (1) _________________________________________________________________ (2) _________________________________________________________________ (3) _________________________________________________________________

3.

In part writing first inversion triads, it is acceptable to double any part of the triad unless it is the ___________________________

4.

A good definition of "counterpoint" is __________________________________________________________________________________________ ________________________________________________

B. Supply alto and tenor lines for the following passages.

C. Analyze with roman numerals the harmonies specified by this figured bass. Then compose a simple soprano line, and fill in alto and tenor parts.

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Chapter 8

Key for Chapter 8 Quiz A. Fill in each blank with the appropriate term.

1.

"Parallel

sixth

chords" is a term used for a passage that contains a series of first inversion triads in

parallel motion.

2.

Name three reasons for using first inversion triads: To improve the contour of the bass line To provide a greater variety of pitches in the bass line To lessen the weight of non-cadential I and V chords

3.

In part writing first inversion triads, it is acceptable to double any part of the triad unless it is the _leading tone.

4.

A good definition of "counterpoint" is __the combining of relatively independent musical lines______________________________ _____________________________________________________________________

B. Supply alto and tenor lines for the following passages.

C. Analyze with roman numerals the harmonies specified by this figured bass. Then compose a simple soprano line, and fill in alto and tenor parts.

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CHAPTER 9 Triads in Second Inversion Today's students often have a difficult time accepting the notion that a triad is dissonant (unstable) simply because it occurs in second inversion. We have found it useful at this point to emphasize that we are studying a restricted style—an important style, but restricted nonetheless—and that this style depended to a large extent upon historical precedents (see the Introduction to Chapter 9 in the text).

Our analytical symbols for six-four chords are not standard and attempt to reflect the embellishing nature of this sonority. Those who find our symbols too fussy (the parentheses and so forth) may simply ignore them. In the case of the tonic six-four followed by a dominant harmony, we have attempted to convey the essentially dominant function of the chord-pair, while avoiding the confusion with a Vw chord that can result when w - a appears over a V symbol. Instructors who disagree with our solution are free, of course, to use whatever approach they prefer.

To the usual list of six-four types we have added those six-fours created by bass arpeggiations and by the melodic bass, both frequent sources of confusion in analysis.

Answers to Selected Exercises Exercise 9-1 A. 1.

There are two cadential six-four chords and one pedal six-four chord (in m. 5).

5

F: I | -- | Iw V | I | (IVw) | I | Vy Iq a | Iw V | { { V V 2.

Both six-four chords are passing six-fours.

45

e: 1 | 4 (1w) | 2-t | % | 1 q | 4 (1w) | 2-t | % |

3.

The IVw is a pedal six-four. The first Iw is a passing six-four, and the second one is a cadential six-four.

38

G: I (IVw) | I | V y Iq a | V y Iq a | IVq (Iw) | IV Iq | Iw Ve | I

{ V

4.

The IVw is a pedal six-four.

112

116

121

A: ! | -- | -- | -- | ($w) | ! | % | ! | -- | -- | $ | ! | % | !

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Chapter 9

5.

The Vw is a passing six-four. Notice that the first 8 measures take the melody line from ¡ through ™ to £ over a ¡ – ∞ – ¡ bass, while the next 8 measures of the melody consist essentially of a descent from § to ¡.

5

10

C: I | -- | I %q ! %e | ! % | -- | -- | % !q (%w) ! | %e ! | $ | !q | 15

%r | ! | 2q | %y !q | 2q %e | !

F. This exercise is drawn from music literature. Haydn's original makes use of arpeggiated and cadential six-four chords. The cadential six-four appears on the normally weak second beat, as is common in triple meter in this style. (The “M.D.C.” at the bottom stands for “Menuetto da capo” and directs the musicians back to the beginning of the movement.

Haydn: String Quartet, Op. 3 No. 5, III, mm. 37-44.

___________________

______________________ 45

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Chapter 9

(section)

(name)

Chapter 9 Quiz A. Besides six-four chords that arise through bass arpeggiation or melodic bass lines, list three other types of sixfour chords discussed in Chapter 9.

1.

2.

3.

B. Show with roman numerals a good harmonization of the bass line below, being sure to include a good example of one of each of the six-four chord types that you listed above, and show where each one occurs.

a: C. Analyze this excerpt with roman numerals, and identify the types of any six-four chords that are used.

D. Add three upper parts to each example to create a good four-part texture, and identify the types of six-four chords that are used.

g:

4q (1w)

20q

%

^

D:

!

($w)

!

$q

%q

!

46 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 9

Key for Chapter 9 Quiz A. Besides six-four chords that arise through bass arpeggiation or melodic bass lines, list three other types of sixfour chords discussed in Chapter 9.

1. cadential 2. passing 3. pedal B. Show with roman numerals a good harmonization of the bass line below, being sure to include a good example of one of each of the six-four chord types that you listed above, and show where each one occurs.

1 (%w)

a:

1q 20q

%

2

(1w)

%

^

4

1w % { V

3

1

1

C. Analyze this excerpt with roman numerals, and identify the types of any six-four chords that are used.

This excerpt, from “Wenn mein Stündlein vorhanden ist,” provides a good example of a plagal half cadence.

G: !

$q (!w) %y

!q

a

q

$

D. Add three upper parts to each example to create a good four-part texture, and identify the types of six-four chords that are used.

g:

4q (1w)

20q %

^

D:

passing

!

($w)

!

$q

%q

!

pedal

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CHAPTER 10 Cadences, Phrases, Periods, and Sentences This chapter introduces the student to formal analysis. The emphasis here is on the phrase and on small structures that combine phrases, in contrast to the details of harmony and voice leading that are the concern of most of the chapters in this text. The Self-Test and Workbook examples should lead to some healthy disagreements over phrase lengths and labels. Our preference is to accept any analysis that is reasonable and that is applied consistently to the passage in question.

Some instructors may be unfamiliar with the sentence, a formal unit introduced in this chapter. If a more exhaustive discussion is desired, please refer to William Caplin’s Classical Form (New York: Oxford University Press, 1998).

It is essential that this material be reinforced aurally. The examples and exercises should be heard, of course, but the student should also get some practice at diagramming formal structures aurally without seeing the score. Many of the themes of Classical symphonies and quartets, as well as piano sonatas, etc., work well for this.

An invariably successful activity is a performance by class members of the Mozart song (Ex. 10-11), with the left hand of the piano doubled by a cello or bassoon. If time allows, the students would benefit from further analysis of any of a number of the examples and exercise excerpts. For instance, Workbook Exercise B.5 (Mozart Sonata, K.545) can serve as an excellent illustration of how a masterful composer embellishes a simple contrapuntal framework.

At the same time, short drills on everything from intervals to voice leading should be kept up. A few minutes a day spent on these areas will help to keep them fresh in the students’ minds.

Answers to Selected Exercises Exercise 10-1 B. 1.

parallel period a

a’ HC (m.8)

PAC (m.16)

x = mm. 1-2, x’ = mm. 3-4 (phrase 1) x = mm. 9-10, x’ = mm. 11-12 (phrase 2) 2.

parallel double period antecedent a

consequent b

PC (m. 4)

a HC (m. 8)

b’ PC (m. 12)

PAC (m. 16)

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Chapter 10

a.

Mm. 1-8: sentence phrase 1

phrase 2 x'

x

HC (m. 8)

PC (m. 4) Mm. 9-16: sentence phrase 1

phrase 2 x'

x

PC (m. 12)

PAC (m. 16)

b.

The clearest example of imitation between the melody and the bass occurs in mm. 12-13. (One could also hear 8-measure phrases in this excerpt, in which case the form is a parallel period.)

c.

! | !q | $ | !q | 70q | ! | % !q ! | % | !q | ! | $ | !q | 70q | ! !q | 2q % | !

3.

The descending chords in mm. 3-4 and 7-8 can be understood as a harmonic sequence of first-inversion triads. Note that they help to smooth the connection between the cadential chords in each of these phrases. sentence x

x' HC (m. 4)

4.

IAC (m. 8)

PAC (m. 12)

The two phrases are almost identical rhythmically, although their melodic contours are contrasting.

The progression at "x" is a tonicization of (not a modulation to) G, the relative major. contrasting period a

b HC (m.8)

IAC (m.12)

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Chapter 10

5.

This excerpt is a three-phrase sentence, due to the immediate repetition of the initial two-measure idea. The second phrase features a circle-of-fifths sequence. sentence phrase 1

phrase 3

phrase 2

x

x' HC (m. 17)

IAC (m. 21)

PAC (m. 26)

Whenever possible, it is worth taking the time to demonstrate the close connection between "real" music and partwriting exercises. This excerpt for example, can be heard as an elaboration of the following:

6.

There are really only two aspects at issue here. To start with, is the first phrase 4 or 8 measures long? If the former, then you have to go with (1) or (2). Secondly, is the deceptive progression at m. 16 a cadence or not? If so, then you have to choose (1) or (3). The second issue is the more interesting one and will probably be the subject of the most discussion. Our phrase labels (a, b, and so forth) are also open to debate.

(1)

parallel double period antecedent a

consequent b

HC (m.4)

a HC (m.8)

(2)

b1 HC (m.12)

b2 DC (m.16)

PAC (m.20)

parallel double period antecedent a

consequent b

HC (m.4)

a HC (m.8)

b1 HC (m.12)

PAC (m.20)

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Chapter 10

(3)

parallel period a

a1

b

HC (m. 8)

DC (m. 16)

PAC (m. 20)

This interpretation has a1 and b as two consequent phrases. It would also be possible to hear b as a single (very short) consequent to a and a1, resulting in a contrasting period.

(4) parallel period a

a1 HC (m. 8)

PAC (m. 20)

7. repeated contrasting period contrasting period a

contrasting period b

HC (m.4)

a PAC (m.8)

b HC (m.12)

PAC (m.16)

! %y | !q %q (r) | !

The sequence is found in mm. 5-7: (simplified version)

C.

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Chapter 10

________________________ (section)

______________________ (name)

Chapter 10 Quiz A. On a separate piece of paper, provide a formal diagram of the following excerpt similar to those that appear in the text. Be sure to show phrase labels (a, a', x, x', etc.) and cadence types. Each phrase is 4 measures long. In addition, name the form of mm. 1-8 and the form of mm. 1-16. Notice that the key is C Major.

B. Also provide a formal diagram of the following excerpt similar to those that appear in the text. Be sure to show phrase labels (a, a', x, x', etc.) and cadence types. Each phrase is 4 measures long. In addition, name the form of mm. 9-16 and the form of mm. 1-16. The key here is Bb Major.

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Chapter 10

Key for Chapter 10 Quiz A. This excerpt is from Mozart's Piano Sonata, K. 332, I, mm. 94-109. repeated sentence sentence phrase 1 x

sentence phrase 2

phrase 1

x’

x

HC (m.4)

phrase 2 x’

PAC (m.8)

HC (m.12)

PAC (m.16)

B. And this one is from K. 333, I, mm. 119-134. parallel double period antecedent a

consequent b

IAC (m. 4)

a HC (m. 8)

b’ IAC (m. 12)

PAC (m. 16)

The consequent, mm. 9-16, is itself a contrasting period.

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CHAPTER 11 Two-Part Tonal Counterpoint The introduction to soprano/bass counterpoint included in Chapter 8 is expanded here to provide more detail and context for students practicing the composition of musically sensitive outer-voice textures. Our approach combines elements of traditional first-, second-, and fourth-species counterpoint (the latter two appearing in the next chapter) with a tonal framework, including several of the cadential progressions introduced in Chapter 10.

In this chapter, which focuses on a one-to-one rhythmic relationship between two voices moving by consonant harmonic intervals, students are encouraged to balance tonally idiomatic harmonic progressions with optimal bass contours that combine root position and first inversion triads and that move toward and away from registral focal points. Creative sensitivity is required when writing a contrapuntal voice above a bass line, so issues of contour, variety, pitch repetition, range, and the treatment of leaps are presented as basic principles to take into account.

We can recommend a very productive classroom activity that should keep everyone's interest. After collecting the counterpoint assignments, choose one at random (more or less), without naming the composer. If the student composed both lines, play each line by itself and ask the class to critique each in a constructive manner—its musicality and its conformity with the guidelines for bass and soprano lines. After that, do something similar with the lines played together. Only if the exercise is quite good should you identify the student who turned it in.

Answers to Selected Exercises Exercise 11-1 NOTE: Most of the “answers” shown below are only suggested solutions. Other correct solutions would be possible in most cases.

A.

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Chapter 11

Exercise 11-2 A. 1.

2.

General errors: #6

Exercise 11-3 A.

B.

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Chapter 11

C.

D.

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Chapter 11

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Chapter 11

______________________ (section)

_____________________________ (name)

Chapter 11 Quiz A. There are several counterpoint errors in this example. Find at least five of them. Write a number (1-5) for each error over the measure in which the error occurs. Explain each error in the corresponding blank below the example.

1. ____________________________________________________________________________ 2. ____________________________________________________________________________ 3. ____________________________________________________________________________ 4. ____________________________________________________________________________ 5. ____________________________________________________________________________

B. Compose a good one-to-one counterpoint to the following bass line. Write a PAC as the final cadence. Indicate the harmonic intervals formed by the two voices.

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Chapter 11

Key for Chapter 11 Quiz A. There are several counterpoint errors in this example. Find at least five of them. Write a number (1-5) for each error over the measure in which the error occurs. Explain each error in the corresponding blank below the example.

1. Melodic interval of a m7 2. Direct 5ths 3. Parallel 5ths 4. Root position iio 5. Dissonant harmonic interval (o5) 6. Perfect fourth (in the soprano) not followed by motion in the opposite direction 7. Melodic interval of a +2 (or, improper use of melodic minor) 8. Leading tone not resolving to tonic 9. Scale degree 5 above final i chord in cadence 10. Direct 5th into final chord B. Compose a good one-to-one counterpoint to the following bass line. Write a PAC as the final cadence. Indicate the harmonic intervals formed by the two voices.

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CHAPTER 12 Non-Chord Tones 1 The student will be familiar by this time with the concept of the non-chord tone from many of the examples in preceding chapters. What remains is to categorize them, which we do by means of contour, and to learn to use them compositionally. This chapter defines nine types of NCT but concentrates on passing tones, neighboring tones, suspensions, and retardations. After being introduced, passing tones, along with arpeggiations, are incorporated into counterpoint exercises that now allow for the addition of weak-beat motion distributed in a balanced manner between the two voices. Instructions for adding neighbor tones and suspensions to simple textures follow later in the chapter.

Non-chord tones judiciously employed can greatly improve the musicality of theory exercises. On the other hand, indiscriminate use of NCTs can lead to very unsatisfactory results. A good classroom activity is to begin with a good three- or four-voice example on the board, perhaps composed collectively by the class, to which NCTs and arpeggiations are to be added. Playing each NCT as it is proposed by class members should convince the students that they cannot simply add embellishments wherever they might "fit," but instead they must work at a piano in order to produce musically satisfying results.

Answers to Selected Exercises Exercise 12-1 A.

B. One-to-one version:

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Chapter 12

Embellished version:

Exercise 12-2 A. 1.

2.

m. 6

__p__

m. 7

_7-6_ __p__

m. 1

__p__

m. 11

_7-6_ __p__

m. 8

__n__ __p__

The embellishments do not conceal any voice-leading problems. Assuming that Bach composed the bass line first (against a given melody), he had few options in m.3. It would be possible to put the altos on D4 on beat 2 to avoid the spacing problem, but moving in similar motion into the doubled third does not produce a pleasing effect. This would have allowed the tenor to remain on F3 and the alto on D4 on beat 4, but the effect of the soprano/alto dissonance (Bach's preferred 4-3 suspension treatment) in the next measure would have been lost.

F: $

70q !

%q

%e

!

$

%

(e)

!

Reduction (notice the stepwise descent from D5 to F4)

B. 1.

3.

9-8 (soprano)

2.

4-3 (soprano m.1 or alto m.2)

2-3 (bass)

4.

7-6 (soprano)

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Chapter 12

C. This exercise was drawn from Chorale No. 260.

D. 1.

This bass line comes from Figured Bass Chorale No. 20.

2. And this one comes from Figured Bass Chorale No. 26.

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Chapter 12

G. This exercise is based on Mozart's String Quartet, K.170, III, mm. 44-47.

H. In fact, Mozart did not use Exercise G as the first phrase of a parallel period.

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Chapter 12

______________________ (section)

_____________________________ (name)

Chapter 12 Quiz A. Embellish the one-to-one counterpoint given here. Indicate the harmonic intervals formed by the two voices, then underline the strong-beat labels and put parentheses around all dissonant pitches.

B. Add the best example of a suspension to each of the following, along with one other type of embellishment.

Label the suspensions with numbers (7-6, etc.), and label the other embellishments with the appropriate abbreviations.

C. Label each chord (making sure that both quality and bass position are correct), and label the NCTs. Suspensions should be labeled with the appropriate numbers (7-6, etc.). There is only one chord in the final measure.

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Chapter 12

Key for Chapter 12 Quiz A. Embellish the one-to-one counterpoint given here. Indicate the harmonic intervals formed by the two voices, then underline the strong-beat labels and put parentheses around all dissonant pitches.

B. Add the best example of a suspension to each of the following, along with one other type of embellishment.

Label the suspensions with numbers (7-6, etc.), and label the other embellishments with the appropriate abbreviations.

7-6 2-3 9-8?

C. Label each chord (making sure that both quality and bass position are correct), and label the NCTs. Suspensions should be labeled with the appropriate numbers (7-6, etc.). There is only one chord in the final measure.

e:

1 70q

1q

%q

1

4q

20q

1w

% (e)

1

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Chapter 13

CHAPTER 13 Non-Chord Tones 2 This chapter explains appoggiaturas, escape tones, the neighbor group, anticipations, and the pedal point. This is followed by a brief discussion of some problems that can arise in analysis.

Unfortunately, practice at aural identification of NCT types is often neglected. A good way to begin such exercises is with short examples such as those in Self-Test 12-2-B and Exercise 13-1 B, moving on from there to simple chorale-style phrases, then to melodies with accompaniment.

Making textural reductions is another helpful classroom activity. It is usually most successful if the instructor guides the analysis and summarizes the findings. (For an example, see Exercise 13-1 A.5 below.)

Answers to Selected Exercises Exercise 12-1 A. 1.

m. 1

2.

m. 10

app

m. 13

p

3.

4.

e

e

m. 3

app

m. 11

app

m. 14

app _

p

p

m. 16, violin

9-8

piano

Vl. I m. 23

p

m. 24

app

m. 25

p

Vl. II m. 23

p

m. 26

r

r

n

4-3

p

m.15

9-8 _

r m. 26

app

The vi–I6–ii6 progression can perhaps be best understood as an elaborated (or prolonged) vi–ii6 progression.

G: %t

!

6

!q

2q

!w

%e

!

{ %

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Chapter 13

5.

This example illustrates the limitations of traditional NCT analysis, as discussed in the final pages of the chapter. We have shown multiple analyses for some of the problematic spots. These generally involve interpretations at different levels, as in m. 2, where the A4 is on the surface an appoggiatura but is clearly suspended from the previous measure as well.

F: !

($q)

11

(3q)

(2q)

%e

!q

%t !

!

omit

!

(%q)

%e (!w) %e !

A possible reduction of the previous excerpt is shown below. It points out that the portion of the excerpt that is included in the assignment (mm. 1-7) features an octave descent in the bass harmonized, for the most part, by parallel sixths (13ths) in the melody and parallel thirds (10ths) in the alto. The succession of parallel sixth chords is non-functional in the traditional sense, which is why the roman numerals (above) have been enclosed in parentheses.

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Chapter 13

6.

There are only three non-traditional NCTs in this excerpt, and all of them are unaccented appoggiaturas that occur on a weak part of the beat: the Eb, the Dm, and the Db. The Eb and the Db can both be heard as flat ninths of their respective dominant seventh chords, while the Dm provides a half-step approach to the E. Davis, “Little Willy Leaps”

© 1948, 1979 SCREEN GEMS-EMI MUSIC INC., Hollywood, CA

D. 1.

This exercise is from Figured Bass Chorale No. 5.

2.

And this one is from Figured Bass Chorale No. 12.

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Chapter 13

G and H. This exercise is drawn from the Finale of Act I of the Magic Flute. It is interesting to compare the vocal excerpt with the embellished instrumental version that precedes it.

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Chapter 13

_______________________ (section)

___________________________ (name) Chapter 13 Quiz

A. Define the following NCTs as completely as you can. Where appropriate, be sure to indicate how the NCT is approached and resolved. anticipation

appoggiatura

escape tone

neighbor group

pedal point

B. Put parentheses around each NCT in the excerpts below, and label each NCT.

D: !

%t

A: $q

!w

%e

!

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Chapter 13

Key for Chapter 13 Quiz A. Define the following NCTs as completely as you can. Where appropriate, be sure to indicate how the NCT is approached and resolved. anticipation - An anticipation anticipates a tone that belongs to the next chord. It may be approached by step or leap, and it resolves to the tone that it anticipates.

appoggiatura - An appoggiatura is approached by leap and resolved by step.

escape tone - An escape tone is approached by step and resolved by leap in the opposite direction.

neighbor group - A neighbor group embellishes a single pitch by sounding its upper and lower neighbors in succession (in either order).

pedal point - A pedal point is a stationary pitch that begins as a chord tone, then becomes a NCT as the harmonies change, and finally ends up as a chord tone again.

B. Put parentheses around each NCT in the excerpts below, and label each NCT. (These excerpts are adapted from Mozart's sonatas K. 545, II, and K. 576, III.)

D: !

%t

A: $q

!w

%e

!

{ %

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Chapter 14

CHAPTER 14 The V7 Chord Most theory instructors will probably agree that the resolution of the root position V7 is the most challenging partwriting problem that the student will face in the study of tonal harmony. This might come as a surprise to the student who has heard tales of chromatic harmony to come (like the dreaded German augmented 6th chord!), but the combinations of complete and incomplete V7 chords with complete and incomplete tonic triads, as well as some very stringent procedures concerning the treatment of dissonance and the leading tone, convince us that this is the case.

The V7-vi (or VI) progression must also be mastered. Students have trouble with this, even though the principles are not very different from the V-vi (or VI) progression. An especially challenging problem for class drill is the iv-V7VI progression in the minor mode.

The root position V7 should be well understood before proceeding to the discussion of the inverted V7 in order to avoid an overload of information. Nevertheless, the inverted V7 is easier to manage than the same chord in root position, since both the dominant and tonic chords will almost always be complete in a four-part texture, and the voice leading is usually by step or common tone.

The chapter also includes a discussion of the approach to the seventh of the V7 (root position or inverted). This concept, as well as the downward resolution of the seventh, is important in the study of all seventh chords.

Answers to Selected Exercises Exercise 14-1 A.

B. The first Ve resolves to VI: leading tone and root up by step, fifth and seventh down by step, resulting in a doubled third in the VI chord. The other Ve resolves to i, frustrating the leading tone in the alto in order to obtain a complete tonic triad. “Slash chords” indicating inversions are always an option with lead-sheet symbols, and they are especially appropriate for the cadential six-four, which would be labeled as F#m/C#.

F#m

f#: 1

C#(7) D

Bm

F#m C#

% e ^

4q

1w

F#m

% e 1

{

E#o

F#m

C#

(2-e) 70q 1q

%

V

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Chapter 14

C.

E:

Ve

I

c: Ve

i

D: Ve

i

C: Ve

G: Ve

I

f:

Ve

Eb: Ve

I

f#:

Ve

i

B:

I

I

Ve

Ab: Ve

D: Ve

I

d: Ve

I

I

i

Bb: Ve

I

g:

i

Ve

A: Ve

i

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Chapter 14

F. Mozart's version of this exercise (from The Magic Flute, Act II) is for five voices. Notice that the soprano and first alto cross in m. 4, and the parallel octaves in mm. 7-8

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Chapter 14

G. 1. Bach: Chorale No. 349. We do not label the C#m7 at the end of the first measure because it is not truly a chord (notice the unresolved seventh).

b: 1

%(e) ^

4

1

%

(e) 1

2. Bach: Chorale No. 347. Notice the unaccented appoggiatura in the alto over the !w.

G: !

%q 6

$

!w

%e

!

{ %

3. Bach: Chorale No. 315. The seventh of the optional $9e resolves eventually to the A.

G: % !

q ($9e) !w

%e

!

{ V Exercise 14-2 A.

Db:

Vr

a:

Vt

Eb:

Vy

D:

Vt

c:

Vy

F:

Vr

b:

Vy

E:

Vr

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Chapter 14

B. 1.

The leading tone, in an inner voice, leaps down to the fifth of the tonic triad. The seventh resolves down by step and illustrates the passing tone figure.

F:

2.

!q

$

%

$q

%q

!

%e

!

In both Ve chords the leading tone resolves up by step and the seventh resolves down by step, with a passing tone figure in the Vt, neighbor figure in the Ve.

Ab: !q

%t

!

%q

!

2q

!w

%e

!

{ V

3.

The leading tone resolves up and the seventh down, using an appoggiatura figure.

Bb:

!q

$

%r

!

q

$ (2q)

2q

!w

%

{ %

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Chapter 14

4.

The leading tone in the Vt, in an inner voice, moves down to the fifth of the tonic chord (or the D4 is an escape tone, with the leading tone resolving up to the grace note), while the seventh illustrates the ascending passing tone figure associated with the I-Vt-Iq progression. The leading tone in the Ve leaps down to the fifth of the tonic triad, while the seventh conforms to the appoggiatura figure.

F: !

F. 1.

!q

6

2q

%e

!

Bach: Chorale No. 125. Notice the use of an incomplete IV (or iiq) chord to avoid parallel fifths.

G: !

2.

%t

6

2

%y

!q $ % (2q)

!

Bach: Chorale No. 184. In such cases we would always accept ive and Vy at the beginning and Ve at the end.

a: 4

%

1q %w 1

%r

1

%

1

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Chapter 14

G. Beethoven: Sonata, Op.7, III. The more observant students will notice the parallel octaves between soprano and alto in m.3. The ear recognizes Eb5 as the more important melody note, which mitigates the effect of the octaves.

Eb: !

!w

%e !

$ !q

%r !

% r

!

%

{ %

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Chapter 14

_______________________ (section)

_______________________________ (name) Chapter 14 Quiz

A. The note given in each case is the root, 3rd, 5th, or 7th of a %e chord. Notate the chord in root position, and name the major key in which it would be the %e.

B. Notate and resolve the following chords. Be sure to use complete (c) or incomplete (i) chords where indicated.

If the chord of resolution is not specified, use a tonic triad in root position or inversion, as appropriate. Use four voices in each example.

d:

%e (c)

1 (c)

A:

%e (i)

! (c)

e: %e

^

b: %r

__

Eb: %y

__

F: %t

__

C. All NCTs in the example below are in parentheses. (1) Analyze all the chords in this example with roman numerals. (2) Label all NCTs. Label any suspensions with the appropriate arabic numerals (7-6, etc.). (3) For each %e chord, in root position or inverted, identify the approach and resolution of the 7th (passing tone figure, etc.).

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Chapter 14

Key for Chapter 14 Quiz A. The note given in each case is the root, 3rd, 5th, or 7th of a %e chord. Notate the chord in root position, and name the major key in which it would be the %e.

A

D

Cb

F

B. Notate and resolve the following chords. Be sure to use complete (c) or incomplete (i) chords where indicated.

If the chord of resolution is not specified, use a tonic triad in root position or inversion, as appropriate. Use four voices in each example.

d:

%e 1 (c) (c)

A:

%e (i)

! (c)

e:

%e ^

b: %r _I_

Eb: %y

_Iq_

F: %t _I_

C. All NCTs in the example below are in parentheses. (1) Analyze all the chords in this example with roman numerals. (2) Label all NCTs. Label any suspensions with the appropriate arabic numerals (7-6, etc.). (3) For each %e chord, in root position or inverted, identify the approach and resolution of the 7th (passing tone figure, etc.).

!

1

%r 2

#2 - neighbor tone figure

!

3

%t !q 4 5

$ 6

#4 - passing tone figure

%e 7

!

8

#7 - suspension figure

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CHAPTER 15 Other Diatonic Seventh Chords The unit on diatonic seventh chords concludes with this chapter, which is devoted to all of the diatonic seventh chords other than the V7. The most commonly encountered of these are the ii7 (iiø7) and the viiø7 (viio7) chords. The remaining diatonic seventh chords are presented in the order shown on p. 237 of the textbook, beginning with IVM7 (iv7). They are not found as frequently as are the seventh chords previously discussed, their most natural environment probably being the circle-of-fifths sequence.

The variability of scale degrees § and ¶ in minor results in a large number of possible diatonic seventh chords, most of which are encountered rarely, if ever, in tonal music. However, special cases that should not be overlooked in classroom discussion include the IVe (major-minor seventh) and the #vi-e, both of which occur as passing chords in the minor mode. These are frequently found in Bach’s chorale harmonizations, somewhat less frequently elsewhere in the literature.

The chapter concludes with a discussion of voice leading procedures in circle-of-fifths progressions of seventh chords. Following the usual admonition to alternate complete with incomplete chords in a root position progression of this type, illustrations are provided of the very commonly encountered sequences that involve inverted seventh chords.

Answers to Selected Exercises Exercise 15-1 A.

B. 1. $9e C. 1.

2. 2y

3. &e

4. %r

5. 2t

6. 2e

7. 1y

8. 6e

Neighbor motion is used in all voices into and out of the 70e.

b:

%

$q

%r

1

70e

1

%

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Chapter 15

2.

Both the ii-r and the #vi-e use the suspension figure. The #vi-e is incomplete, perhaps to avoid unequal fifths with the bass. g: 1 | 2-r % m6-e %r | 1 ($t) % e 1

3.

This excerpt contains a circle-of-fifths sequence in a four-part texture. All sevenths use the suspension figure.

3 6e 2e | %e !9e $9e 2q | %y !q $ % | ! |

4.

All of the seventh chords in the excerpt illustrate the suspension figure. Measures 86-92 contain a circle-offifths sequence in a three-part texture. f#: %e | ^ | 4 | &e | #9e | ^9e | 2-e | %e | 1 | ^ | 2-r | %e | _ |

5.

The 7th of the 7-t is approached as a suspension. Notice also the parallel fifths between the Viola and Violin I as the 7-t resolves, disguised by a 4-3 suspension. An alternate analysis would have a %e for the first two 8th notes of m. 59, but we prefer the parallel sixth chords.

55 56 57 58 59 60 61 / ! %r / ! %r / ! !q $ / % ($q / 3q 2q) (r) / 7-t !q / $ 2q / 62 63 / !w %e / !

{ V 6.

The 7th of the ii-y is prepared as a suspension.

This can easily be heard as an elaboration of: 82 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 15

D.

E.

f: 4e

&e

#9e

^9e

2-e

%e

i

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Chapter 15

F. A possible realization:

F: ! $9e 7-e 3e 6e 2e %e !

2r

%

!

$ %e ! %

!

G. A possible realization:

F: !

%q

!

6e 2e

%e

!

$9e 2q %y !q

2e %e !

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Chapter 15

_____________________ (section)

__________________________ (name)

Chapter 15 Quiz A. Notate the following chords in the specified keys. Use accidentals, not key signatures.

d:

1t

e:

^9y

A:

$9r

Eb:

3e

f:

m6-e

B. Notate, introduce, and resolve the specified chords. The seventh of each chord should be introduced as a passing tone, suspension, or neighbor, as indicated. Include roman numeral and lead sheet analyses.

C. Complete these circle-of-fifths progressions, using conventional voice leading.

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Chapter 15

Key for Chapter 15 Quiz A. Notate the following chords in the specified keys. Use accidentals, not key signatures.

B. Notate, introduce, and resolve the specified chords. The seventh of each chord should be introduced as a passing tone, suspension, or neighbor, as indicated. Include roman numeral and lead sheet analyses. (sample solutions)

C. Complete these circle-of-fifths progressions, using conventional voice leading.

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Chapter 16

CHAPTER 16 Secondary Functions 1 We begin the study of chromaticism with a chapter on the secondary V and V7 chords. Our approach is first to treat the spelling and recognition of these chords in the abstract, after which secondary dominants in context are discussed.

Intensive chord spelling drills are essential for Chapters 16 and 17, with speed being an important factor. We frequently use ungraded "quick thinking quizzes" of 10 to 20 questions read at a fairly rapid rate, the rule being that the student must not write the question, only the answer. Oral drill/response games are also effective and fun, with even the quickest students finding a challenge in questions on the order of "D would be the bass note of the chord following a Vy of IV in what major key?"

Those who employ levels analysis, even informally, will want to emphasize that in almost all cases a secondary dominant is harmonically subservient to the chord it tonicizes. Also, it is perfectly acceptable to analyze minitonicizations, as in Exercise 16-2-A-2, in which mm. 21-24 could be analyzed as: | 1 | %r 1 | %y | 1q of ii Answers to Selected Exercises Exercise 16-1 A.

C#7

c#:

Bb

%e/4

Ab:

F#

D:

%t/^

c:

C#7

%q/6

b:

Eb7

Eb:

%q/%

Eb7

%r/4

%e/%

%q/&

%e/2

B7

%/4

g:

A7

C:

%y/2

F:

G

%r/3

A:

D7

%q/#

e:

G#7

B

f#:

D

Bb7

Bb:

%y/4

B. 1. %r/%

2. %e/6

3. X

4. %e/4

5. X

6. %e/2

7. %r/#

8. %y/%

9. %t/3

10. %e/^

11. %r/$

12. X

13. %y/4

14. %y/2

15. %r/6

%y/%

a: A7

G:

%t/%

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Chapter 16

Exercise 16-2 A. 1.

The parallel fifths involve an anticipation above a passing seventh in an authentic cadence.

f:

2.

1

%y/4

4q (1w) (70y)

2-r

%

e

1

The form of this excerpt is a sentence.

C: ! | %r ! | %y | !q %(e)/2 | 2 | %r/2 2 | %y/2 | 2q e | 25

%e | ! %e/6 | 6 %e/$ | $ 2 | !w | %e | _ | I |

3.

The progression is, of course, a long circle-of-fifths sequence, broken just once, at the C7–Am7 progression. As the song continues, the progression is repeated in the key of G. The words for mm. 5-8 appear to refer directly to the interruptions in the sequence: “(I) pick myself up, dust myself off, and start all over again.”

In terms of partwriting, the only tricky spot is at that same C7–Am7 progression. Our solution omits the 3rd from the Am7, although one could omit the 5th instead (at the expense of the soprano line) by having the top line leap down to C5. Taking the Bb, which is the 7th of the C7 chord, up to the C does not seem to be a good solution. Students should be encouraged to include the courtesy accidentals in mm. 4, 5, and 7.

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Chapter 16

4.

F# appears only in the accompaniment, while F appears in both the melody and the accompaniment. This causes cross relationships in m.1, 5, and 13. Measure 15 is especially problematical, with a descending melodic minor scale set over a gradually emerging V7 chord, which results in the questionable analysis of a suspension (G5) resolving to a passing tone. The form is a parallel double period; the antecedent and the consequent are both sentences.

g:

%e

%e

1

%r//#

#

1

4

(^q) %r/#

1

4

%e

1

1

#

4

%q

1

4

%e

1

(^q)

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Chapter 16

5.

The form is a sentence.

Db:

!

!

% 4q/6 %e/6

%t

6

%q/2

2

!

%r

%r

!

!

q

%t

!w

%e !

{ %

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Chapter 16

6.

F: !

2q

$ %r/% !w

!w

%y

{

%y

!q

2q

!w

%y

{

{

%

%

!q

$

!w

%

!

$

!q

%r/$

%

e

%

!q

$q

!w

{

%

!

% C. 1.

V(7)/VI V(7)/iv

2.

V(7)/VII V(7)/III

3.

V(7)/iii V(7)/vi

4.

V(7)/ii V(7)/V V7/iii

5.

6.

V(7)/iv V(7)/VII V7/V

7.

V(7)/V V7/vi

8.

V(7)/V V(7)/III

9.

V(7)/vi V(7)/IV V(7)/ii

10. V(7)/IV V7/ii

D. 1.

V(7)/iv

2.

V(7)/IV

3.

V(7)/III

4.

V(7)/VI V7/iv

5.

6.

V(7)/VI

7.

V(7)/ii

8.

V(7)/vi

9.

V7/III

10. V(7)/V

E. 1.

V(7)/IV V7/V

V(7)/ii

F: I I6 $ %r/% | (!w) %e/2 %e/% %e | ! |

2. f#: 1 %e %r/^ ^ | %t/4 4 %y 1q | 2-e %e 1 |

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Chapter 16

F. 1.

Bach: Chorale No. 107. The wide spacing in the V7/IV is clearly justified by the sweep of the lines, with the texture divided into parallel tenths (soprano and bass) and thirds (alto and tenor). Notice also the leap of the seventh in the bass, after which the parallel tenths continue. The iiq sounds a bit like a IV with a 6-5 suspension.

Eb:

!

IV

%(e)

6 %q %e/$ 2q %r/% !w

%e

!

{ %

2.

Bach: Chorale No. 180. Tonicization of the mediant, rare in the major mode, is common in minor.

d: 1 3.

%(y)/# #q 70r

1q

%(e)

!

Bach: Chorale No. 217. This excerpt is notable in several respects, including, in the second phrase, wide spacing in m. 5 and unusual voice leading in the V-vi progression in m. 6.

C: !

%q a { of vi

6

%e/2 2 !q $9e V

!q 70q !

2r % 6 %r®V

I

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Chapter 16

4.

Bach: Chorale No. 262.

g: 1

%q 1

4q

%r/4

4

1

%(e)

!

G. Schumann: Valse Noble, Op. 9, No. 4

H. Haydn: String Quartet, Op. 54, No.2, III. Notice the C5-C4 stepwise descent in the melody.

C: I

%t/%

%

%y®Vq %t/$

$

%y®$q a

!w %e { V

!

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Chapter 16

I.

Mozart: Piano Sonata, K.311, III, mm. 41-56

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Chapter 16

______________________ (section)

______________________________ (name)

Chapter 16 Quiz A. Notate these secondary dominants in the specified inversions. Include key signatures.

%e/%

e:

Bb:

%q/3

%t/$

G:

b:

%r/^

D:

%y/2

B. Label any chord that might be a secondary dominant with the appropriate roman numeral. Label all other chords with an x .

E:

______

Db:

______

A:

______ f:

______

Ab:

______

C. Label chords and NCTs in this example.

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Chapter 16

Key for Chapter 16 Quiz A.

Notate these secondary dominants in the specified inversions. Include key signatures.

B. Label any chord that might be a secondary dominant with the appropriate roman numeral. Label all other chords with an x .

%t/2

E:

Db:

X

%y/%

A:

%r/4

f:

%e/6

Ab:

C. Label chords and NCTs in this example. [Adapted from Bach Chorale #353]

G:

!

%q

%y/$

$q

%y/2

1

2

3

4

5

2q

%e/%

!w

%

!

11

12

13

14

15

{

2q %r/% % (e) %q/6

6

6

10

7

8

9

%

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Chapter 17

CHAPTER 17 Secondary Functions 2 The unit on secondary functions continues with a discussion of secondary leading-tone chords, this part of the chapter paralleling the approach used in Chapter 16. Intensive chord spelling and recognition drills should be continued in this chapter, including diatonic seventh chords as well as the material from Chapters 16 and 17.

The chapter continues with consideration of harmonic sequences employing secondary functions and the substitution of leading tone chords for diatonic sevenths or secondary dominants in such sequences (Piston's analysis of vii07 as a V09 is especially appealing here). The final two sections concern deceptive resolutions of secondary functions and non-dominant secondary functions, such as VI/vi.

Answers to Selected Exercises Exercise 17-1 A.

70q/3

A:

70r/%

d:

C:

7-y/%

70q/2

F:

G: 70e/6

e:

70q/4

c:

70q/^

E:

70r/$ Ab:

70e/$

70q/6

g:

70e/&

F:

70e/2

Eb:

7-t/%

f#:

70e/#

D: :

70q/%

Bb:

B. 1. vii0r /iv

2. vii0r/V

3. vii0q/vi

4. X

5. vii0q/VII

6. X

7. vii-e/VII

8. vii0e/iii

9. vii0q/ii

10. X

11. vii-e/IV

12. vii0e/VI

13. vii0q/IV

14. X

15. vii0q/V

Exercise 17-2 A. 1.

a.

Occurrences of a:

mm. 59-62, Vla. and Vc.

Occurrences of b:

mm. 59-62, Vn. I mm. 60-62, Vn. II (truncated) mm. 69-72, Vn. I (last measure varied)

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Chapter 17

b.

b is used in imitation in mm. 59-62, Vn. I and Vn. II

c.

a appears inverted in mm. 57-58 , Vc. (two measures only) b is inverted in mm. 65-68, Vn. I and Vn. II (truncated), and in mm. 69-72, Vn. II (last measure varied)

2.

d.

mm. 69-72

e.

!q 1

%r 2

!

3

%e/2 4

%e/% 5

%e 6

Ve/$ 7

!w 9

%e 10

!

11

70r/2 12

2q 13

%e 14

!

15

70e/% 8

The form is a sentence.

D: ! | %r/$ | $ %t/2 | 2 | _ | 2-t | %e (!w) | 70e/6 | 6 | 70e/% | !w %e | ! | %e

3.

g:

(i) Ve | iv i (ivw) ii0q/iv | Vy/iv ivq a Ve i | i h V V/iv | iv vii0t i q | iv iq iv iq | iv vii0e/V V e |

4.

The form is a contrasting period. We offer two analyses of the second measure. A class discussion about this measure might be useful. Is one analysis “better” than the other? How would one make that judgment?

Is it necessary or even useful to decide?

E:

!

!9y

t

$

(9e)

%

y

or vi

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Chapter 17

!q 5.

(9r) $

%

70e/6 6 7-e/% %

e

!

The form is a parallel double period.

G:

!q

!

% $q !

$ %r/%

%q/3

r

%

%

%y/6 %q/2 %y/% sequence

6 4q/6 %/6 %r/2 %/% y (2q)

!

%q

%

!

$q

%r

!

%t

$q ! %y/$ $q (!w) $

2r % e ($9e 2r)

!

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Chapter 17

6.

!

9y

6 (!w) $

$ !

%e

!

A:

%/6 %/6 %e/$ 2-e/6

%e

!

%e

!

%e

! %

$

!

%e

!

9y 6 (!w)

%r/2 (70e/2) 2

2-e/6 (7-e)

!

%e

!

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Chapter 17

C. 1.

2.

A: ! 6 7-e/% | !w %y !q | %r/$ $ %e | ! | a: 1 %y/4 4q %y/# | #q 70r/4 4q 2-r | 1w %e 1 { %

D. 1.

Bach: Chorale No. 68. Notice the crossing of the alto and tenor parts to avoid parallel octaves between alto and bass. (On the 4th beat of the only complete measure there is an optional 6e = 2e/%.)

2.

Bach: Chorale No. 3. The unaccented appoggiatura in the tenor in the final measure is unusual. It might be heard as an "unprepared" passing tone from the bass (D-E-F#). (On the 4th beat of the only complete measure there is an optional 2-y/4.)

3.

Bach: Chorale No. 266. The vii0q-Ve/vi-VI/vi progression is especially interesting.

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Chapter 17

E. 1.

2.

Schumann: Sonata, Op. 22, II. This is an excellent excerpt for class analysis, although the cto7 (see Chapter 24) in m. 7 will have to be explained. The second chord in m.9 is also somewhat problematical. A solution is to label the G# as a passing tone or to hear the chord as a V/vi with an avoided resolution.

Haydn: String Quartet, Op.20 No.5, III

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Chapter 17

F. Registral shifts like the ones we used in mm. 1 and 8 are necessary, or conventional voice leading will drive the right hand into the basement. The apparently unresolved Eb in the 70e/V actually resolves to the D after the “delaying action” by the cadential six-four.

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Chapter 17

______________________ (section)

_____________________________ (name)

Chapter 17 Quiz A. Notate these chords in the specified inversions.

Include key signatures.

A: 7-e/%

Eb: 70q/$

B. Which one(s) of the following progressions could be considered a circle-of-fifths progression? ___ ___ ___

2-e/2

G:

de Ee Fe

Ge c#0e Bbe

C9e De g0e

Fe G9e c0e

C. Label the chords in the two excerpts below. If the blanks are too close together, put some of the roman numerals above the others.

1.

F:

V

___ 1

___ ___ 2

3

___ ___ ___ ___ ___ ___ ___ 4

5

6

7

8

9

10

___ 11

___ 12

2.

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Chapter 17

Key for Chapter 17 Quiz A. Notate these chords in the specified inversions.

Include key signatures.

A: 7-e/%

Eb: 70q/$

G:

B. Which one(s) of the following progressions could be considered a circle-of-fifths progression? _X_ _X_ _X_

2-e/2

de Ee Fe

Ge c#0e Bbe

C9e De g0e

Fe G9e c0e

C. We recommend the use of arrows, as we have done here, when space is limited. [The second excerpt is from Beethoven's Sonata, Op. 14 No. 1, III.] 1.

%

F:

!

%

6

!q 70e®6 %y ® $q 70r®2q

!w

%

1

2

3

4

11

12

5

6

7

8

9

10

2.

{ %

e:

4

2-r

1w

%e

^

1

2

3

4

5

70e/4 4 6

7

2-r 8

{ %

70e/%

%

(1w)

%

9

10

11

12

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Chapter 18

CHAPTER 18 Modulations Using Diatonic Common Chords Modulation is an extension to a deeper level of the tonicizing secondary function, although the distinction between the two frequently cannot be clearly defined. This chapter begins the discussion of modulation by examining relationships between tonalities, after which the concept of the common-chord modulation is explained.

Our approach to the analysis of diatonic common-chord modulations requires the student to listen carefully to the passage to find the point at which the harmony begins to function more directly in the new key than in the old key.

The diatonic common chord, if there is one, should immediately precede that point.

Composing modulating phrases is a more difficult task because it involves both melodic and harmonic considerations. We recommend separating these two issues at first (as in Exercises 18-2 D and E), progressing gradually to freer compositional exercises.

Answers to Selected Exercises Exercise 18-1 A. 1. eb

2. fm

3. G

4. Bb

5. am

6. F

7. dm

8. E

9. f

10. Cb

B. 1.

D

e

fm

G

2.

Gb ab

bb

Cb Db

3.

a

b

C

D

4.

cm

dm

E

Fm gm

5.

g

a

Bb C

d

6.

A

b

cm

E

D

A

e

C. 1. closely related

6. foreign

2. relative and closely related

7. enharmonically equivalent

3. parallel

8. closely related

4. foreign

9. foreign

5. closely related

10. relative and closely related

Exercise 18-2 A. 1.

a

2. b

3. C

4. d

B. 1.

ii F#m i

IV A III

2.

ii Ebm vi

I Db V

5. D IV Gb I

6. g

7. b

8. Ab

vi Bbm iii

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Chapter 18

3.

i Cm ii

III Eb IV

5.

I B IV

iii D#m vi

C. 1.

4.

V F# I

i Fm vi

ii0 G0 vii0

vi G#m ii

6.

III Ab I

iv Bbm ii

iii Cm ii

V Eb IV

VI Db IV

Bb F7 D Bb: ! q | %e %q/6 | Gm Bdim7 Cm Bb/F F7 Bb 6 70t/2 2q | !w %e | ! q | { % F: $ q C7 F Gm F/C C7 F %y | !q 2q !w %e | ! |

2.

Phrases 2 and 4 are very similar melodically. The Em triad (G: vi) is emphasized at the beginning of the fourth phrase.

G:

!

%q ! $q C: !q

% e %q®6 D: ii

%y

$ % ! % G: I

!q 70q !

%e

%® 2 G: vi

6

$q

$

!

q !

(7-e)

6q

q

%

a !q

%

e

!

e

!

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Chapter 18

3.

b. Parallel period. c. Mm. 53-58 (6 measures). Notice that Haydn begins this phrase (mm. 53-54) with 2 measures taken from the end of phrase 1 (mm. 43-44) followed by two measures (mm. 55-56) that seem to refer back to mm.

50-52. And, finally the theme ends with the cadential figure used in mm. 47-48. All of this constituting an interesting example of economy of means.

4.

The Ab and C are the two tones shared by the tonic triads of f and Ab. Notice that they occur in the same register (Ab4/C4) in both keys. f: | i vii0e | i | Vq

5.

r | i | VIq | Vr | I iiq Iw Ve | I | { Ab: vi | IVq V

e: i | i | (ivw) | i | iw | iw | V e | i b: iv

6.

V

The tonality of C is referred to again in the final measures. Tonicization of IV frequently occurs in codettas and codas.

G: I | q vi | ii | % 2 | C: 6 5

Vy/IV | IVq (Iw) iir | Iq iir Iw Ve | ! 6q | { V e: ^ 4q 10

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Chapter 18

15

vii0t/ii | iiq Vt/ii iiq | Vr/V Iw V e | I Vr/IV | { [-------or still in e----] V 20

IV | I Ve/IV | (IVw) | I |

|

7.

Ab:

!q

2q

!w

%e V

70e/%

(1w)

! c: VI

%e

(!w

%)

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Chapter 18

1

(1w) g %

^

d: i Vq (r) | i V e | i

Vq r |

2-r

%(e)

1

g: 4

8.

10

vii0w/V Vq r | I Vr/V | Iw Ve | { V

i C: ii 15

I (vi) Vr/V | Iw Ve | I { V E. 1.

Bach: Chorale No. 181. The B-minor triad in m. 3 temporarily contradicts the expected return to e. The following measure employs the IVe (Mm7) in the minor mode.

e:

1

%r

1

%r

!

2r

%

!

G: vi

%r®6

3

6

$r %q 1

e: i

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Chapter 18

2.

Bach: Chorale No. 303.

F: !

%

!

%

6

2r

%

1

d: i

%/4 4

%y !q

%

!

F: ii

F. a: 1 % ^ | 2-r %y 1q G: 2q %q/% !w %e | ! | G. Haydn: Symphony No. 82, II (mm. 33-40). The two-staff transcription shown below includes most of the doublings with the exception of the contrabasses, which double the notated bass line an octave lower in the forte measures. The details of voice leading are not shown here (the apparent parallel fifths in m. 39, for example, do not occur in the original).

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Chapter 18

H. Beethoven: Violin Sonata, Op. 12, No. 1, II.

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Chapter 18

__________________ (section)

______________________________ (name)

Chapter 18 Quiz A. List the diatonic triads that could serve as common chords between this pair of keys, showing roman numerals on the top and bottom lines and lead-sheet symbols in the middle line. In minor, assume the usual chord qualities: 1, 20, #, 4, %, ^, 70.

First key: D: Triads: Second key: e: B. Harmonize this phrase in 4 voices, modulating from C to G. Include roman numerals.

C. Label the chords in this phrase, which modulates from g minor to d minor.

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Chapter 18

__________________ (section)

______________________________ (name)

Key for Chapter 18 Quiz A. List the diatonic triads that could serve as common chords between this pair of keys, showing roman numerals on the top and bottom lines and lead-sheet symbols in the middle line. In minor, assume the usual chord qualities: 1, 20, #, 4, %, ^, 70.

First key: D:

ii

IV

Triads:

Em

G

Second key: e:

i

III

B. [The excerpt is from Chorale No. 217.]

C: !

q

a

$

%y

!q

%q

(r)

!

%

G: $q C. [The excerpt is from Mendelssohn's Songs without Words, Op. 19, No. 6. Notice how the melodic +2 in the third complete measure clearly signals the modulation.]

1

g:

1q

%e

1 d: iv

4

%

70t

(e)

1

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Chapter 19

CHAPTER 19 Some Other Modulatory Techniques This chapter continues the discussion of modulatory techniques begun in Chapter 18. While perhaps not exhausting the possibilities, these two chapters, along with the modulations discussed in Chapters 21 and 23, certainly account for the vast majority of modulations in tonal music.

The techniques discussed in this chapter include (1) altered chords as common chords, (2) sequential modulation, (3) modulation by common tone, (4) monophonic modulation, and (5) direct modulation. It should be remembered that these methods are not mutually exclusive.

In analysis the importance of modulation to the structure of the composition should be emphasized as much as possible. Chorales and other complete pieces used for analysis should be diagrammed according to their tonal structures: Bach: Chorale No. 39 e i

G III

e i

b v

G III

e i

There is no reason to exclude modulation from ear training drills. Most students can learn to identify modulations in short excerpts, especially if the melody is easy to follow. In longer examples (sonata forms and so on), most students will only be able to tell that a modulation has taken place and to identify the mode of the new key.

Answers to Selected Exercises Exercise 19-1 A. 1.

a.

Ab, f, and Db.

b.

Both are sequential modulations.

c.

The reduction shows the essentially stepwise character of both parts, which proceed, for the most part, in parallel tenths.

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Chapter 19

2.

The wide space between alto and tenor in m.5 could have been avoided easily, but only at the expense of the two sets of parallel thirds in contrary motion. These thirds also account for the relatively unusual root position vii0.

1

a:

1

%q 1

%

1

% y

1

1q

% y

70q

1q

1

%

%

1

70 1 (m6-e)

%/4

4q

d: %

1q

2-y %r

%

a: iv

3.

The two keys are F and Db, distantly related (foreign) keys that are in a chromatic mediant relationship to one another. This common-tone modulation could also be explained through mode mixture, to be discussed in Chapter 21 (F: bVIq = Db: Iq).

25

F: I | Ve/IV | (IVw) (ivw) | I | ¡ | Iq IV | V vii0e/vi | Db: £ vi IVq iiq Iw V | I | { V

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Chapter 19

4.

The NCTs are: m. 15, p; m. 17, e.

15

A: ! | 2r % | ! | 6 %e/% | 6 2 | %e | ! | G: %e/6 5.

The modulation, which occurs in mm. 36-37, resembles the modulation in Exercise 3. Both are common tone modulations involving keys in chromatic mediant relationships: F®Db in No. 3, F®Ab in No. 5.

C. Bach: Chorale No. 155. A very clear example of a phrase modulation. The original has a key signature of one flat.

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Chapter 19

D. Beethoven: Bagatelle, Op. 33, No. 3. Two phrase modulations here.

E. Beethoven: Sonata, Op. 26, II.

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Chapter 19

____________________ (section)

__________________________ (name)

Chapter 19 Quiz A. Analyze the following passages using the blanks provided, and describe each modulation.

1.

2.

B. Continue the soprano line and fill in the inner parts as specified by the figured bass. Analyze the harmonies, putting your roman numerals beneath the figured bass, and describe the modulation.

m

6

6

m

5n

6

r

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Chapter 19

Key for Chapter 19 Quiz A. Analyze the following passages using the blanks provided, and describe each modulation.

1.

2.

E:

[Mozart: Piano Sonata, K. 333, III] Sequential modulation.

c:

1q

70r

t

bb:

!q

70r

t

1q

%q

1q

1

%q

70q

1

1q

70q

%q

1q

%q

1

1

[Beethoven: Piano Sonata, Op. 14 No. 1, II] Common-tone modulation.

!

¡

!

70

!

$

6 r !q 6 2r

%

C: £ B. Direct (phrase) modulation.

m e: %

1

6 %q

1

6 4q

m 5n % G: !

!

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Chapter 20

CHAPTER 20 Larger Forms This chapter continues the study of musical forms that was begun in Chapter 10, where phases, periods, and the sentence were introduced. Here we discuss binary and ternary forms, sonata form, and the rondo.

Binary and ternary forms may be found in formal units as small as individual themes and as large as complete movements. It is well known that the terminology regarding binary and ternary forms is not standardized, as a comparison of treatments of the subject in various popular textbooks will confirm. Our approach regards the terms as referring to a two-part or three-part structure, without regard to tonal design, degree of contrast, or other considerations, although we do include "sectional" and "continuous" as modifiers. Those who wish to follow another approach instead are, of course, free to do so.

We take the position that repetition, unlike return, has no bearing on formal classification. If a performer omits the repeats in a movement in sonata form, for example, the formal classification is unaffected—it is still in sonata form.

Likewise, if we insert repeats into a ternary structure, it does not suddenly become a binary structure. That is, a ternary A B A that becomes |: A :||: B A :| is still ternary, even if some of the repeats are written out. The effect of the repeats (when they are taken) should not be ignored, however, and we attach the term "two-reprise" to such patterns.

Students should be given practice in identifying and diagramming binary and ternary forms aurally. Minuets from Classical symphonies provide a good source for aural examples.

Sonata form should be distinguished from multi-movement sonatas, such as symphonies, string quartets, and solo sonatas. The first movement of a multi-movement sonata is almost always in sonata form, and one or more of the other movements may be as well. Rondos are usually found in the last movement of a multi-movement sonata, although slow movements may also be in rondo form. Both rondos and sonatas are found in other contexts as well, such as in single-movement works and overtures.

Answers to Selected Exercises Exercise 20-1 A. Two-reprise sectional rounded binary. a

:

A HC (m.4)

a1 PAC : : (m.8)

B b

½A a1 HC (m.12)

PAC : (m.16)

1.

Parallel period.

2.

The 70t/% occurs in m. 11, and the 70t/6 is in m. 9.

3.

Quite possibly Mozart wanted to (1) retain the parallel sixths between the violins, (2) use a V7 instead of a V, and (3) have a complete I chord in m. 8. To accomplish all of these goals, it is necessary to go briefly to a five-part texture.

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Chapter 20

B. Sectional ternary (with the first A repeated).

1. Vr/V | Iw | Ve | I | { V 5. Either:

2. Ve/V

a. mm. 1-8: contrasting period

3. vii0e/ii

4. mm. 33-40

mm. 1-16: parallel double period

OR b. mm. 1-8: phrase C. 1.

mm. 1-16: parallel period

It would also be correct to label the “cadence” in m. 20 as F: V/vi, which would still be a half cadence. a F: PAC

a1 F: HC C: PAC (m.8)

(m.4)

a F: PAC (m.12)

a1 F: HC C: PAC (m.16)

:

2.

Two-reprise continuous rounded binary

3.

mm. 16-17 (C®"), mm. 20-21 (A®F), and mm. 24-17 (F®"),

b d: HC

a F: PAC :

codetta F: PAC

(m.20)

(m. 24)

(m.27)

D. Two-reprise continuous binary. a

:

b

a1 D: PAC or IAC (m.13)

HC : : or A: PAC (m.9)

PAC or IAC (m.4)

1.

mm. 14-15.

2.

It tonicizes the dominant.

3.

mm. 10-11 (from mm. 1-2) and mm. 21-22 (from mm. 8-9).

E. 1.

c

d HC

PAC :

(m.17)

(m.22)

Minuet a

:

a1

a

b PAC : : (m.8)

Eb: HC (m.4)

c Bb: HC (m.12)

d PAC (m.16)

Eb: HC (m.20)

a1 PAC : (m.28)

HC (m.24) Trio a

:

a1 Ab: IAC (m.32)

b

HC : : Eb: PAC (m.36)

a

a2

HC

IAC

PAC :

(m.40)

(m.46)

(m.50)

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Chapter 20

2.

Mm. 1-8: Parallel period Minuet: Two-reprise sectional ternary Trio: Two-reprise continuous ternary

3.

Sectional ternary

4.

The return of phrase a in the trio (mm. 41-46) is extended two measures by the insertion of mm. 44-45.

Besides providing a welcome relief from the four-measure phrases, these measures tonicize the dominant and strengthen the cadence in mm. 45-46.

5.

a. 70e/2 b. %q(r)/% c. %e/% d. %e/% e. %y/$

F. Example 1 Secondary Theme. This passage begins and ends in the secondary key of F major (as determined by the Bbmajor key signature and the fifth-relationship between Bb and F). The theme is a sixteen-measure parallel period with an eight-measure antecedent ending with a HC, and an eight-measure consequent ending with a PAC. Example 2 Transition. This passage destabilizes the primary key by modulating from Bb major to F major and ending with a HC in the secondary key (along with five measures that emphasize the cadential goal harmony). It has a restless character with fast-moving and shifting rhythmic values.

Example 3 Closing Section. This brief passage confirms the secondary key F major with short cadential gestures and a tonic pedal.

Example 4 Development. This passage is harmonically more adventurous than the other examples. Beginning in the secondary key of F major, it explores a sequential motive, briefly tonicizing ii and V before moving toward a surprising PAC in F minor (an example of mode mixture) after eight measures. After the cadence, the passage modulates briefly to C minor and Bb major.

Example 5 Primary Theme. This passage begins and ends in the home key of Bb major. It is a sentence: a repeated two-measure idea is followed by a six-measure phrase that moves to a PAC. G. A: mm. 1-20

B: mm. 21-47

A: mm. 48-67

C: mm. 68-87

A: mm. 88-120

The A section is a sectional ternary form.

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Chapter 20

________________ (section)

____________________________ (name)

Chapter 20 Quiz A. Diagram the excerpts below and on the next page at the phrase level, including phrase labels (a, b, etc.), cadences, and measure numbers, and name the form of each example. Put your diagrams below the excerpts or on a separate page.

1.

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Chapter 20

2.

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Chapter 20

B. Describe the characteristic features of the following parts of a sonata form: 1.

recapitulation

2.

secondary theme

3.

development

4.

transition

C. Describe the features that the following pairs of forms have in common.

1.

Sonata and sonata-rondo

2.

Seven-part rondo and sonata-rondo

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Chapter 20

Key for Chapter 20 Quiz A. 1.

[Haydn, Piano Sonata No. 22, III] a

:

E: IAC (m.4)

a1 B: PAC : : (m.8)

b

c PAC : (m.16)

E: HC (m.12)

The form is two-reprise continuous binary.

2.

[Haydn, Piano Sonata No. 40, I] a

:

b HC (m.4)

HC : : (m.8)

c

d HC (m.12)

a HC (m.16)

b1 HC (m.20)

PAC : (m.24)

The form is two-reprise continuous ternary.

B. 1.

recapitulation: This section replays the movement's important themes (from the exposition), usually in the same order, with the modulating material adjusted so that the themes appear in the home key.

2.

secondary theme: In the exposition, this theme establishes the secondary key by beginning and cadencing (with a PAC) in that key. In the recapitulation, this theme reconfirms the home key after a destabilizing transition.

3.

development: The section is more tonally and thematically unstable than the exposition and recapitulation, and may feature development of motives from the exposition, sequential activity, and a succession of keys often distantly related to the home key. Occasionally a new theme may appear in the development section.

4.

transition: This passage destabilizes the home key after the primary theme. In the exposition, it may or may not modulate and moves to a HC in the home or secondary key. In the recapitulation, modulating transitions are adjusted to end in the home key.

C. 1.

Both feature a development section (the C section in the rondo) followed by the return of earlier thematic material (from the exposition in the sonata and the A and B sections in the rondo) adjusted to remain in the home key. Some sonata-rondos feature a modulating B section that is similar to the transition and secondary theme of a sonata.

2. Both feature the return of A material in the home key after each contrasting section (B and C).

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Chapter 21

CHAPTER 21 Mode Mixture and the Neapolitan Because we view § and ¶ in minor as variable scale degrees, we do not categorize IV, v, and VII in minor as examples of mode mixture. In fact, the major tonic triad is the only sonority that we recognize as a chord borrowed from the parallel major. Therefore, almost all of Chapter 21 is devoted to mode mixture from minor into major: the use of b£, b¶, and, especially, b§.

The concept of mode mixture is not a difficult one to grasp, but this seems to be the category of altered chords that students find to be the most forgettable. The instructor should plan constant reminders and drills as the class gets further into chromaticism in order to keep all of the chords studied so far fresh in the students' minds.

If the concept of mode mixture is simple, its compositional application is not. Students tend to toss in the requested example of mode mixture unescorted, unresolved, and unexplained, as in: I bVI iie Ve I Some good advice would be to approach the altered tones by step (chromatically, if possible) and to continue the mode mixture at least until a cadential V or Iw is reached.

The Neapolitan triad is also discussed in this chapter. It is considered by some to be a Phrygian II chord, another example of mode mixture. All of these chords should be included in aural skills drills, and students will usually find the Neapolitan an especially easy chord to recognize aurally.

The discussion of modulations involving mode mixture and the Neapolitan should not be overlooked, as this device puts a number of foreign keys within easy striking distance.

Answers to Selected Exercises Exercise 21-1 A.

B.

A:

2-y

F:

cm:

Nq

Eb:

Bbo F 1. 20q 2. Nq

b

70e

Db:

1w

4q

fm:

I

Ao7 Gb 3. 70e 4. N

Cb 5. bVI

Bø7 Eb 6. 2-r 7. Nq

C:

D:

Ab 8. Nq

b^

b#

E:

20q

G:

Nq

Em D 9. ivq 10. Nq

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Chapter 21

C. 1. The cadence is a plagal cadence.

C: I IV I | IV | I bVI I | bVI | iv | I | – |

2.

135

140

145

g: i | – | – | – | – | Ve/iv | iv | – | – | N | vii0e/N | N | q | vii0e/V Ve | i |

3. At the most foreground level, the tonal structure is: E® e®C®c®C®e®E 215

220

E: ! | —– | q | $ | !w %e | b^ { % C(c): I

| 2q | !w | %e | 1 | 2-r |

{ %

225

| 1w | 70e/6 | 6 | 70e/% | !w | —– | – | %e | ! e(E): 4

%

4. a: 1 4 | &q # | ^q 20 | %q 1 | Nq F: $q %e | ! | %t ! | ($w) ! | %r ! |

41

5.

g: iq 4 | —– | Ve ^ |

| Nq | % | Vr/iv iv |

| 1w | V | i |

{ V

27

6.

c: i | – | 70e | 70y/4 | 4q %y/4 4q | 30

%y/N Nq | – | 70t | 70e/% | 1w %e | 1

10

7.

E: IVq ii-t | (!w) | 2q %r/6 6 | %r/% | %e ! | 1 b: 4 70r %r | i

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Chapter 21

F. Bach: Chorale No.59. This beautiful harmonization should be studied in detail. Bach could have doubled the bass of the passing Iw in m. 5 only at the expense of the good alto and/or tenor lines.

G. Bach, Chorale Harmonization #262. (Bach uses a key signature of one flat in the original.)

I.

Schubert, Impromptu, Op. 90, No.2.

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Chapter 21

___________________

____________________________

(section)

(name)

Chapter 21 Quiz A. Notate these chords in the specified inversions. Include key signatures.

Bb: 2-r

A: b^

f: Nq

B:

4q

Db: 70y

B. Label these chords. Be sure your roman numeral reflects the chord quality and inversion, if any.

A:

______

F: ___

G: ___

D: ______

Ab:

______

C. Analyze the following passage, using the blanks provided.

G:

V

__

__ __

__ __

__ __ __

__

__ __

__

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Chapter 21

Key for Chapter 21 Quiz A. Notate these chords in the specified inversions. Include key signatures.

2-r

Bb:

A:

b^

f:

Nq

4q

B:

Db:

70y

B. Label these chords. Be sure your roman numeral reflects the chord quality and inversion, if any.

A:

2-e

F: 20q

G: 70r

D:

%y/%

Ab:

b#

C. Analyze the following passage, using the blanks provided.

Bach: French Suite #6, Allemande

G:

V

1

b^ !w (%w/4)

4q 4 %e®% %e/$ 2q

!w

%e

!

{ %

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Chapter 22

CHAPTER 22 Augmented Sixth Chords When introducing augmented sixth chords, we take as our starting point the interval of the augmented sixth from which the chord gets its name, demonstrating that it is the result of two "leading tones" to the dominant, one from below and the other from above. The other notes that usually accompany the augmented sixth interval are much less crucial, and certainly none of them function as a root. In fact, we believe the augmented sixth chord to be sonority with a most common bass position but with no true acoustical or even theoretical root.

The presentation of the material in this chapter is brief and to the point. However, three complications that are mentioned in the discussion should be given special attention: (1) the occasional resolution of m¢ to n¢ to provide the seventh of a Ve chord, (2) the enharmonically spelled German sixth, and (3) the problem of parallel fifths in the g–% progression.

A section on other uses of conventional augmented sixth chords is followed by consideration of augmented sixth chords with something other than (b)§ in the bass and chords in which the interval of the +6 resolves to a scale degree other than ∞.

Answers to Selected Exercises Exercise 22-1 A.

C: +6

V

d: +6

V

B. 1. h

2. g

6. f/¡ i 7. f

e: +6

V

Bb: +6

V

a: +6

V

V

Eb: +6

V

g: +6

V

3. IVr (Vr/VII)

4. h

5. g

8. Vt/V

9. f

10. g %q

fm: +6

G: +6

A: +6

V

V

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Chapter 22

C.

D. 1.

Bb:

f

d:

Nq

bb:

g

Ab:

h

B:

2-r

fm:

h

A:

g

c:

f

G:

70e/6

e:

g

The g that begins the waltz sounds like a Ve in Bb. The most obvious additional reference to that key is the Nq chord in m. 12. The m¢ and the b§ both follow the expected resolution to ∞. Parallel 5ths are avoided by moving to a cadential six-four chord before resolving to Ve. a: g | 1w %e | 1 | q | %t | 1 | % | (e) | { V 9

g | 1w %e | 1 | Nq | 1w %e | ^ | 1w %e | 1 | { { { V V V 2.

The g has m¢ (enharmonically spelled) in the bass. In performance, the parallel 5ths are probably not avoided at all.

C: | 2e | %e | ! %r/$ $(add6) g | %e !(add 6) |

3.

There are 9-8 suspensions in mm. 32 and 34. Parallel fifths are avoided in the resolution of the g by arpeggiating £ to ¡, creating a short-lived h. Both m¢ and b§ follow their expected resolutions to ∞.

30

35

| C: ! | %e/2 | 2 | %e | ! 6q

70q/4 | 4 (1w) | g | % e |

e: ^ 4q 4.

In the g (m.4) both m¢ and b§ follow their expected resolutions. Parallel fifths are avoided by means of the iw.

5

d: i iie/VI | Ve/VI VI | g iw | Ve i

{ V

| %e/% %e | (!w) % |

F: vi

10

ii-t V | ii-t

V | 1

2e | %e ! |

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Chapter 22

5.

The other keys are Bb and Ab, the relative major and Neapolitan of the "parent" tonality of g minor. Notice that we have analyzed the modulation to Ab as direct, although it would be possible to identify a common chord. In each of the five f chords the m¢ and b§ resolve to ∞ as expected.

23

25

| g: vii0t/V Vq Vt/V | V | i

f | % ! | f | % Ab: 6 | f |

Bb: vi 30

35

| V I | f | V

97 | 70q/% Vt/V | V | f | V (y 1q %t) | I

g: VI 6.

One might wonder whether the g chord in the 5th measure is a +6 chord at all. Instead, is it a 008 (doubly diminished octave!) chord because the Ab functions as a Gm while the Fm functions as a Gb? Students should be discouraged from labeling the IVy and IVr chords as secondary dominants of VII and should understand that these chords come about through the use of the melodic minor scale. c: ^q | %y/% %q Nq | %y 1q $y | 70r %e ^ | Nq 1w 70r/4 |

4 (1w) g | $r %r 1 | Nq 1w %e | 1 |

{ V 7.

In the h both m¢ and b§ resolve to ∞ as expected. The pitch class Gm/Ab is used in the following ways: %r/6 (m. 3), b^ (m. 6), h (m. 6), n (m. 8), and 70e/6 (m. 9). | C: I vi Vy/ii iiq Vt/ii ii | V y Iq Vt I | vi Vr/vi vi | 5

| Vq/V V Ve/V V | i Vt/bVI | bVI h V |

| I vi Vy/ii iiq Vt/ii ii | V y Iq Vt I | iiq V vii0e/vi vi | 10

| iiq a Iw Ve I |

{ V

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Chapter 22

8.

The 2-3 suspension in the cello in mm. 188 and 189 assumes the C missing from the vii-e.

7-e

Bb:

!

7-e

!

$q 70e® 2 7-t® $q 7-t®

$q 7-t/$

7-e

!

70e/2 2 7-t/$

70e®$

70e/% !w

%e

{ V

!

g/¡

!

g/¡

!

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Chapter 22

9.

Here we have an excerpt similar to Example 22-15 in that the strong tendency of the g to move to V is momentarily dissipated by a dominant of the dominant. The m¢ resolves normally to Fm; the enharmonically spelled b§ resolves to ∞ only after having been diverted to the Gm. 5

| E: ! | 6 | 2e | %e | %r/6

y | 1q %r |

cm: %r | 1 %t 1q

| g %t/% %e | ! |

B: 2q G. Bb: ! %q %y ® $q | f % %r ® %y | !q 70r ® 2q %e | ! | I.

Haydn: String Quartet, Op.74, No.3, II. This marvelous excerpt is certainly worth some class time. Analysis exercise 3 is drawn from the B section of this movement, which is in ternary form.

The ct0e (m. 5) and the V=q (m. 7) are discussed in Chapter 24, but they can easily be explained as NCTs for now.

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Chapter 22

________________ (section)

___

________________________________ (name)

Chapter 22 Quiz A. Label the chords in the excerpts below.

1.

2.

f#:

Eb:

3.

e:

B. Continue these four-part textures.

a: 2-t

g 1w

Nq

%e

1

Eb:

!

%y/$

$q

f

%

%y !q

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Chapter 22

Key for Chapter 22 Quiz A. Label the chords in the excerpts below.

1.

2.

f#: 70q 1q

Nq %

h %

1

Eb:

!q %/2

2 g !w 70e/6 6

3. Chopin: Prelude, Op. 28, No. 4

e: 1w

g

%

1

B. Continue these four-part textures.

a: 2-t

g 1w

Nq

%e

1

Eb: ! %y/$ $q f

%

%y

!q

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Chapter 23

CHAPTER 23 Enharmonic Spellings and Enharmonic Modulations The topic of enharmonicism may be dear to the hearts of many instructors, but to some students it is a difficult hurdle, the one complication too many piled onto the harmonic stack. We try in this chapter to take a systematic and pedagogically sound approach to the subject.

The first part of the chapter explains enharmonicism for convenience so that the student will not confuse this with enharmonic modulation, a pitfall that not all harmony texts have been able to avoid. The ear can serve as the final arbiter: if you cannot hear the enharmonicism, it must be a case of enharmonic spelling for convenience. For example, the modulation from I to iv is easily accomplished through mode mixture. If the keys involved were Ab Major and Db Minor, the composer might choose to notate the second key as C# Minor, but the listener would have no way of knowing about the enharmonicism.

The remainder of the chapter is devoted to enharmonic reinterpretation, which almost always leads to an enharmonic modulation. The chords traditionally used for this are the Mme/g and the diminished seventh chord, although the f and the augmented triad could in theory be employed as well.

Enharmonic modulation and enharmonic spelling for convenience may occur simultaneously, of course. An example is the Chopin excerpt in Workbook Exercise E.1, in which the key scheme fm - E - Gm is notated for convenience as fm - E - Ab, with enharmonic reinterpretation effecting the second modulation.

Since enharmonic modulations can be heard, there is no reason to exclude them from aural training. The easiest to recognize is the Ve or secondary Ve becoming a g.

Answers to Selected Exercises Exercise 23-1 A.

B. 1.

F:

%e

=

A: g (or a:)

Bb:

70e

= G: 70r

| g: i vii0e Vr | i vii0e

g: g

= E: 70t

= Ab: %e D: (or Eb: %e/$, etc.)

= Db: 70y

%e

= cm: g

Fm: %e/$

= Bb: g

Vt | iq vii0q | i |

e: vii0r 2.

| a: iq V e | VI iq | Nq

V e gm: g

| iw Ve | i | { V 140

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Chapter 23

3.

| F: Vy | Iq vii0r/ii | ii vii0e/ii | Iq Vt | I | Db: vii0t

C. 1.

b:

1

%r/4 4

1w g 6

2r

%y

!q

%t

!

1q

2-r %r/% 1w

%

%

C: %e 2.

C:

!

%r %y/$ $q

%e 70e/6 %y

1

eb: 70t

41

E. 1.

45

50

| fm: %r | 1 | %t | 1q | 70e/4 E: 2q

| !w | %e | ! %e/$ | !w |

{

70e/%

%

Ab: g

| %e | ! | %

133

2.

| g: 1 q (%w) 1 70e/% % | 70y % 70t 1q |

135

| 70y % 70t

1w | %e (1w) %e | 1 (70 | 1 etc.)

{ e: 70y

%

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Chapter 23

3.

The F7 chord is heard three times in nine measures, each time in a somewhat different context. In m. 81b, where the listener is still hearing Eb as a tonal center, the F7 probably sounds at first like a Ve/V, but it resolves like a g. We might then expect the F7 chord in m. 85 to resolve again like a g, but here it instead acts as dominant of Bb, the Neapolitan chord in A Minor. It is anyone’s guess what the listener expects of the F7 chord in m. 89 after having already been fooled twice. (We regret the confusion over the measure numbers. To be consistent, renumber 83 as 80b, m. 88 as 85, and 92 as 89.)

73

79

80a

81a

| Eb: !w | %e | ! 1 | 70e/% | % | e | ! 1 | 70y/%

81b

82b

| 70y/% | %e/% | 1w | a: 70r/%

4.

:

c: 70e/%

% 80b

82a

| 1w | %

g

84

|

90

| g | Nq | %e | 1w | %e/N | Nq | %e | 1 and and %e/N g

Note that this is not an enharmonic modulation, but a modulation to the Neapolitan (Cb), spelled as B for the convenience of the performers. The form is a parallel period.

Bb: !

%t

!

%r

!

$9e

2q

%r/%

%

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Chapter 23

1

%t

1q

Nq

2r

(70w)

B: !q 5.

!w

%e

!

%

The first modulation is really to b^ (Bbb), respelled as A for the convenience of the performer. In the second modulation, which is a true enharmonic modulation, the %e/$ in the key of b^ is enharmonically reinterpreted as the g in Db. From the first ending to m. 17 there is a phrase (or direct) modulation back to the key of A. The form is Schubert’s light-hearted take on two-reprise continuous binary, which is what the form would be if you repeated mm. 1-8 and omitted 9-16. The second part would then begin with a Db chord instead of D. | Db: ! |

5

| %q r | a | ! | 10

|

| %e/% | % | ! |

|

15

| %q r | a | ! | b^

| %e |

A: !

| !

:

20

$ |

| ! |

25

| %e/$

| !w | %e | !

|

:

Db: g 143 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 23

____________________ (section)

_____________________________ (name)

Chapter 23 Quiz A. Show the possible enharmonic reinterpretations of the given chords by filling in each blank with the name of a major key.

1.

F: 70e =

: 70r =

2.

Bb: %e =

: g

: 70t =

: 70y

B. Analyze this enharmonic common-chord modulation.

G:

C. Analyze the progression implied by this soprano/bass framework, and fill in two inner voices. Analyze enharmonic common chords where indicated. Do not use identical chords on beats 3 and 4 of the second measure.

d:

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Chapter 23

Key for Chapter 23 Quiz A. Show the possible enharmonic reinterpretations of the given chords by filling in each blank with the name of a major key.

1.

F: 70e =

D : 70r =

2.

Bb: %e = A : g

B : 70t = Ab : 70y

B. Analyze this enharmonic common-chord modulation.

G:

%e

!

%r/2 70e/2

2

%r

!

70e/2

1q 2-r %

e

1

fm: 70r %t

C. Analyze the progression implied by this soprano/bass framework, and fill in two inner voices. Analyze enharmonic common chords where indicated. Do not use identical chords on beats 3 and 4 of the second measure.

d:

1

70q

1q

%r/4

4

%r

1

%e/4

1w

%e

1

fm: g

145 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 24

CHAPTER 24 Further Elements of the Harmonic Vocabulary This chapter is concerned with four topics, none of which are at all exotic or exceptional in music of the tonal era: (1) the dominant with a substituted sixth, (2) the augmented dominant, (3) ninth chords, and (4) the common-tone diminished seventh chord. All of these should be drilled and practiced just as faithfully as the chords introduced in previous chapters were. Added-note chords, discussed briefly in connection with topic (1), and eleventh and thirteenth chords, mentioned briefly in connection with topic (3), are not important elements of the harmonic vocabulary before Impressionism.

Answers to Selected Exercises Exercise 24-1 A.

D:

$99

Fm:

C. 1.

2e

(c)

Eb: (c)

!

b: %e subs 6th

%r

Bb: %=q/$ $

E:

2-t

1

A:

%e

%=e

g: %b9

!

1

The only NCTs are the 9-8 suspension in m. 2 and the anticipation in m. 3. | Bb: %=q/$ | $ %y | 70r/2 2q | !w %e | ! { V

146 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 24

2.

The form is a parallel double period, preceded by a two-measure introduction.

Ab: ! $ 4 | ! | ! (c) ! %e | ! %e ! % | 5

| ! q | % 2-r t %=e | ! (c) ! %e | (or iii) 10

| ! %(e) 1 2-t | %e 1 2r %e(Sub 6) | ! c ! of vi

3.

The form is a parallel double period.

f: %b9

(1w)

%e

1

$q %9(r)

!

of III

Nq

%

%e/4

4addq (2-r)

b9

1w

(1w)

%e

%e

1

^q

%

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Chapter 24

4.

For whatever reason, the common-tone diminished seventh is rarely used as the common chord in a modulation, this excerpt being an interesting exception.

5

| ! | 2e %e | ! $ !q | (c) !q | %e/% | !w %e | ! | 6t 2e %e | { % 9

| ! $ !q | c !q | (c) | 2 %t/2 2q !w %e | ! | { G: 70e/2 % 5.

The first harmonic sequence (it divides into two parts) accomplishes a chromatic ascent of an octave in the bass, connecting the V at the beginning of m. 73 with the V at the end of m. 76. The second sequence reverses direction and makes a quick descent to the V in m.78 by means of parallel first inversion diatonic triads. The melody is independent of the bass in mm. 73-74 and moves parallel with it in mm. 75-78.

73

| g: V g F: Vr I | Bb: V g Ab: Vr I | 75

| Db: V g B: Vr I | E: V g D: Vr I | g: V | (ii0q iq &q ^q | 5q 4q) Ve vii0t V | i h V 6.

The form is a sentence.

90

95

| D: I (ct0e) | I | V9 | I 70e/ii | ii 70e | I 7-e/V | Iw V9 | I

{ V 5

7.

| c: 1 |

| q a | 70t = (c) | %r/% |

subs

| 1w % % 6th | 1 | %

5

8.

| ! |

| (c) |

| ! |

|

10

| %r ! | 2q %q/% | % |

| 2 |

|

15

| (c) |

| 2 |

| %t !q a | 2q %e |

20

| ! |

(!=) | 6q | %e/$ | % e: g

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Chapter 24

_____________________ (section)

__________________________ (name)

Chapter 24 Quiz A. Analyze the given chord, and then notate the first chord in such a way that it leads smoothly into the given chord.

Db:

(c)

fm:

%9

____

____

D:

Ab:

subs

%=/$ ____

g:

%e 6th

____

(c)

F:

V=e

____

____

B. Analyze the chords in this excerpt, and label any NCTs.

G:

____

____

____

____

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Chapter 24

Key for Chapter 24 Quiz A. Analyze the given chord, and then notate the first chord in such a way that it leads smoothly into the given chord.

Db:

(c)

fm:

%9

!

i

D:

Ab:

%=/$

IV

g:

%e

(c)

%r

F:

V=e

subs 6th

i

I

B. [Donizetti: Anna Bolena, "Nel veder la tua costanza"]

G: I

(c)

!

%e

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Chapter 25

CHAPTER 25 Tonal Harmony in the Late Nineteenth Century This chapter describes a number of characteristics of tonal music of the late nineteenth and early twentieth centuries.

The analysis of this music is problematic and presents a challenge even to the experienced theorist, but instructors are encouraged to find a balance between describing features that destabilize the traditional tonal system and features that create or preserve order. Examples of destabilization include (1) the use of a heavily chromatic contrapuntal technique, (2) the employment of modulating and chromatic sequences to move rapidly through contrasting tonal regions, (3) coloristic chord successions, (4) weakening of the principle of concentric tonality, and (5) alternatives to the predominance of circle-of-fifths motions such as chromatic mediant relationships, mediant chains, and chromatic progressions. Examples of order-preserving features include (1) the emphasis on conjunct, linear motion between chords, (2) the continued use of traditional sonorities, combined with a willingness to exploit the entire collection of chromatic pitches in addition to the functional chromaticism that depends on diatonic resolution.

Answers to Selected Exercises Exercise 25-1

Chord: Root int: Total dist.:

1 Cw, Abm M3 3

2 A, Fm6 M3 3

3 A, Fmw M3 11

4 A, Fm M3 13

5 Abw, Ebm P4 4

Chord: Root int: Total dist.:

6 F, Eb M2 6

7 F, Ebq M2 6

8 Ce, Fmt +4 2

9 Ce, Ft P4 4

10 Ce, Eby m3 2

11 Ce, Ey M3 4

Chromatic mediants: #10, 11 Doubly chromatic mediants: #1, 2, 3, 4 5

B. 1.

2.

E: │ I q │ vi (Iw) IVq Iq │ !q $ !q │ ii │ V/V e │ Vy │ Iq a │ V │ a.

m. 10: ii – Iq

b.

The relatively unusual viq chords in mm. 9, 11, and 14. These might also be analyzed as tonic chords with substituted sixths.

c.

The three chords beginning on the last beat of m. 11 might be analyzed in the key of iii: gm: ivq │ Ve │ VI However, in context we hear the latter two chords as Ve/III to I in E.

151

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Chapter 25

3.

The sequential pattern begins with the pickup to m. 17 and modulates by ascending m3 from Em to Gm to Bbm. The pattern is: Em Bm6 Fmw Ve │ i

D

v6 Vw/V │ VII (V in new key)

The relationship between the circled chords (Em, Gm, Bbm) in mm. 17, 19, 21 is that of a chromatic mediant chain involving roots related by m3.

C.

D.

152

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Chapter 25

E. 1.

2.

It uses m¢n, §n, ¶.

I [It+6] C is tonicized by 70e

3.

Measure 13 could be analyzed as: C: Ve/IV vii0y/IV b: vii0r %e

4.

B minor v (minor dominant)

5.

Gm and C Chromatic mediant

F. 1.

Yes G minor.

The ivq - V in mm. 1-2 and the half cadence in m. 3.

2.

Gme, gm-e, Cme

Total voice-leading dist.: 2 2 To allow for the melodic motive of a minor 3rd between Gm and B. 3.

│ V/vi │ Iq iv9e │ IV9e Ve │ I │ Chromatic mediant (roots related by M3).

G.

DMy

Fmt

Ebmt

3

Emy

G0t 2

Cy

G0r

3

Fme

Dmt

f

6

Abmy

A-r

2

Be 2

153

Dby 3

Ge

BbMy 3

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Chapter 25

H. 1. │ B │ │ G │ │ B │ │ Eb │ │ B │ │ G │ │ Ee │ │ Gm(7) │ Eq │ 2.

B major is juxtaposed with both its upper and lower chromatic mediants with roots related by M3 (G and Eb). The E major chords toward the end of the excerpt are juxtaposed with both upper chromatic mediants, one a m3 apart (G major) and one a M3 apart (Gme).

3.

B major is established both through repetition and the symmetrical alternation of surrounding harmonies.

The use of its lower and upper chromatic mediants positions B major as the central harmony of the symmetrical arrangement. There is a hint of traditional motion in mm. 167-72 (I—bVI—IVe) as the alternation around B major gives way to Ee, although the subsequent section (not shown) does not confirm this motion cadentially.

1.

| e: i |

2.

e: mm. 1-11

5

I.

|

|

10

| ii-e | iv | Ve/III | III | ive | ii-e | V |

Ab: mm. 12-20 A: mm. 20-23 3.

mm. 11-12 The e: V resolves to the G/B major third. The ear assumes these pitches to be the 3rd and 5th of e: i, but Eb enters instead, beginning the motion toward the key of Ab. mm. 19-20 Similarly, the Ab: Ve resolves to Ab/C, which is then joined not by its 5th, Eb, but by E, leading toward the key of A.

J. 1.

The “nonfunctional” ii - iii - IV progression in mm. 11-12, which features parallel voice leading. Also, neither tonic nor dominant chords appear until the end of m. 13.

15

2.

| E gm0e | F de | d-e Ge | Ee a | Ce e | 20

| CMe am0e (or cm0e) | G De | Be B+ | E | 3.

The chromatic bass line in mm.16-21 brings the “omnibus” to mind, with the Ge (m. 16) through the e (m.

18) perhaps being most typical.

4.

The unexpected leap to the V+.

5.

The E2 in m. 22 completes the chromatic bass line.

154

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Chapter 25

________________

_________________________

(section)

(name)

Chapter 25 Quiz 1.

You are given the opening measure of a four-measure sequence, as well as the beginning chord of the second measure. Continue the pattern through measures 2-4, ending the exercise on the E-flat major chord that is provided. Using lead sheet symbols, analyze each of the root-position chords in the passage. You should also notice the ascending whole-step pattern represented by the first bass note of each measure.

2.

You are given a series of chord pairs. Notate the inversion of the second chord that connects most smoothly with the first chord as given. Indicate the total voice-leading distance in the space provided. Ignore traditional resolutions (leading tones, sevenths, etc.). There may be more than one right answer. Show all accidentals.

Ebe

Ae

Ct

Ebe

Total voice leading distance: ___ ___

Fy

De

___

Ar

Cme

___

155

Bbe Gbe

G-e Fme

G-e Ce

G-e Ae

___

___

___

___

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Chapter 25

Key for Chapter 25 Quiz 1.

You are given the opening measure of a four-measure sequence, as well as the beginning chord of the second measure. Continue the pattern through measures 2-4, ending the exercise on the E-flat major chord that is provided. Using lead sheet symbols, analyze each of the root-position chords in the passage. You should also notice the ascending whole-step pattern represented by the first bass note of each measure.

2.

You are given a series of chord pairs. Notate the inversion of the second chord that connects most smoothly with the first chord as given. Indicate the total voice-leading distance in the space provided. Ignore traditional resolutions (leading tones, sevenths, etc.). There may be more than one right answer. Show all accidentals.

Ebe

At

Ct

Total voice leading distance: 2 2

Ebr

Fy De 2

Ar

Cme 4

Bbe

Gbr 4

156

G-e Fme

G-e Ct

G-e Ay

2

2

2

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Chapter 26

CHAPTER 26 Materials and Techniques Most twentieth-century composers departed radically from the music of the past. Gone is the great tonal tradition, the harmonic practice that provided a common ground among composers separated by decades and even centuries, no matter how individual their styles. In its place we find a bewildering array of compositional materials and techniques, many of them discarded almost as soon as they were invented in order to satisfy the craving for the new and original. And these developments seem to take place with increasing rapidity, just as in the sciences and in the other arts.

To put all of this into a single unit is impossible, of course. But we feel that the next three chapters provide a solid introduction to the subject, and one that will allow the student to negotiate successfully further readings or more advanced classes in twentieth-century music.

Answers to Selected Exercises Exercise 26-1 A.

B.

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Chapter 26

C. 1.

Ionian, Lydian, Mixolydian

2.

Aeolian, Dorian, Phrygian

3.

Locrian

4.

Ionian, Lydian

5.

Phrygian, Locrian

6.

Ionian

7.

Dorian

8.

Ionian, Dorian, Lydian, Mixolydian

9.

Phrygian, Aeolian, Locrian

10. P4 11. +4 12. +4 13. P4 D.

158 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

E.

F. Enharmonic spellings in this and similar exercises are acceptable.

G. These scales could also use Bb as a starting pitch.

159 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

H. 1.

Whole-tone

2.

G-Dorian

3.

Octatonic

4.

Major pentatonic (black-key)

5.

Phrygian-Dorian

6.

Hirajoshi pentatonic

I.

Dorian, Whole-tone, Mixolydian

Exercise 26-2 A. 1.

Q

2.

Ebmaj7

3.

4.

C Fm E9

5.

Q (inverted)

6.

Q

7.

Q (quintal)

8.

S

B. 1.

Tone cluster (TC)

2.

Split-third chord (ST)

3.

Q (inverted)

4.

Tone cluster (TC)

5.

Split-third chord (ST)

6.

Whole-tone chord (WT)

7.

Whole-tone chord (WT)

8.

Tone cluster (TC)

C. 1.

Quintal chords

2.

Tertian chords

3.

Added-note chords

4.

Polychords 160

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Chapter 26

D. Enharmonic spellings in this and similar exercises are acceptable.

161 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

E.

162 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

F.

G. 1.

Constant repetition of the bass line (passacaglia).

2.

Because of its position as the upper and lower boundaries of the reiterated ground bass, and its metric accentuation, the tone center is probably B. Clearly, however, there is no sense of “function” because of the chromatic saturation caused by the strict planing and dense counterpoint that occurs throughout.

3.

Strong emphasis on quartal melodic construction and prominent dotted rhythm leading up to the high point.

4.

Extensive use of quartal harmonies, especially prominent in mm. 7-12. Occasional use of dotted rhythms.

Brief stepwise figures regularly incorporated.

5.

This motive occurs as beats 2-4 in the opening measure. It recurs in the “alto” voice in m. 5, “tenor” in m.

9, and as closing gesture in m. 17.

163 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

Exercise 26-3 A. 1.

Metric modulation

2.

Nonretrogradable rhythm

3.

Added value

4.

Mixed meter

5.

Displaced accent

6.

Asymmetric meter

B. 1.

a, b, and d are nonretrogradable

2.

C. 1.

Hemiola

9.

metric modulation or tempo modulation

2.

ametric

10. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.

3.

polyrhythm

11. two

4.

Additive

12. golden ratio

5.

dotted

13. polytempo

6.

symmetrical

15. tempo canon

7.

ostinato

8.

isorhythm, talea, color

164 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

_______________________ (section)

_______________________________ (name)

Chapter 26 Quiz A. Notate the following scales starting on the pitch indicated. Be sure to include the octave-related pitch.

B. Describe the structure of the chords shown below by providing the correct symbol: use the symbol "Q" for quartal/quintal chords, "S" for secundal chords, “ST” for split-third chords, and lead sheet symbols for tertian sonorities and polychords.

165 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

C. Which of the following rhythmic procedures—added value, displaced accent, metric modulation, mixed meter, or nonretrogradable rhythm—are illustrated by the following examples:

166 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 26

Key for Chapter 26 Quiz A. Notate the following scales starting on the pitch indicated. Be sure to include the octave-related pitch.

B. 1.

S

5.

F9 (tertian)

2.

Q (quintal)

6.

ST (split-third chord)

3.

Q (quintal)

7.

Eb7 (tertian)

4. G (polychord) Fm

8.

Cmaj9

C. 1.

Nonretrogradable rhythm

2.

Added value

3.

Mixed meter

4.

Metric modulation

5.

Displaced accent

167 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 27

CHAPTER 27 Post-Tonal Theory In this chapter the student is introduced to the elements of post-tonal theory, from pitch-class sets to integral serialism. There are three distinct parts to the chapter, but they are not independent and must be undertaken in the order in which they are presented. (However, we recommend that the two parts of the Chapter 27 Quiz be administered on separate days.)

Basic Atonal Theory. Our approach minimizes the mathematical operations that lie behind pitch-class set theory in favor of an introductory explanation of how these operations can be carried out using notation on the staff. The skills acquired in this section are applicable to a very wide range of post-tonal music, serial or not. If time allows, a good piece for in-class analysis is the third of Anton Webern's Five Movements for String Quartet, Op. 5.

Twelve-Tone Serialism. The importance of serialism in the music of the middle half of the 20th century can hardly be exaggerated, and it still exists as a tool that composers use freely as needed, even if few completely serial works are composed today. A good source for in-class study is Luigi Dallapiccola's Quaderno Musicale di Annalibera, especially Movements 4 and 6. Also, there is nothing like a composition assignment to convince a student that composing a good twelve-tone piece is no more mechanical than composing a good tonal one.

Integral Serialism. Perhaps an inevitable outgrowth of twelve-tone serialism, integral serialism was an attempt to apply the organizational scheme of serialization to other aspects of music, such as duration, dynamics, register, and articulation. We would recommend Milton Babbitt's quite approachable Three Compositions for Piano, No. 1, for an in-class analysis of this genre.

Answers to Selected Exercises Exercise 27-1 A.

4

7

1

0

9

5

1

11

6

2

9

8

4

5

1

x

3

5

1

1

6

2

3

4

1

2

3

4

5

6

7

8

9

10

11

12

B.

168

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Chapter 27

C. The pc sets may be notated in a variety of octave equivalent and enharmonically equivalent ways.

Normal Form

Prime Form

1.

[Eb,E,A]

(016)

2.

[D,F#,A]

(037)

3.

[C#,D#,G#]

(027)

4.

[D,E,G,A]

(0257)

5.

[A,Bb,B,C]

(0123)

6.

[D,Eb,F,G]

(0135)

Prime form

Forte name

Interval-class vector

1.

(014)

3-3

<101100>

2.

(016)

3-5

<100011>

3.

(0147)

4-18

<102111>

4.

(01457)

5-z18

<212221>

5.

(015)

3-4

<100110>

D.

169

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Chapter 27

6.

(0167)

4-9

<200022>

7.

(027)

3-9

<010020>

Sets 6 and 7 are inversionally symmetrical.

E. 1.

Normal form: [C,C#,F#,G] Set class: 4-9 (0167)

2.

L.H./R.H., m. 3, (C,C#,G,F#) R.H., mm. 4-5, (B,Bb,F,E)

3.

Normal form: [F#,G,Bb] Set class: 3-3 (014)

4.

R.H., (Bb,A,C#); L.H., (D,B,Bb); L.H./R.H, (D#,C,B); L.H./R.H., (E,C,C#)

5.

Normal form: [Bb,B,E] Set class: 3-5 (016)

6.

R.H., m. 4, (B,F,Bb); R.H., m. 7, (Bb,Eb,A); etc.

7.

ic1 Yes

8.

Set class: 3-2 (013) R.H., m. 5, (E,G,F#); R.H., m. 6, (B,A#,C#)

170

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Chapter 27

Exercise 27-2 A. These series forms may be notated in a variety of octave equivalent and enharmonically equivalent ways.

I5

B. 1.

2.

I5

I4

I0

I9

I7

I2

I8

I1

I3

I6

I10

I11

P5

F

E

C

A

G

D

G#

C#

D#

F#

A#

B

R5

P6

F#

F

C#

A#

G#

D#

A

D

E

G

B

C

R6

P10

A#

A

F

D

C

G

C#

F#

G#

B

D#

E

R10

P1

C#

C

G#

F

D#

A#

E

A

B

D

F#

G

R1

P3

D#

D

A#

G

F

C

F#

B

C#

E

G#

A

R3

P8

G#

G

D#

C

A#

F

B

E

F#

A

C#

D

R8

P2

D

C#

A

F#

E

B

F

A#

C

D#

G

G# R2

P9

A

G#

E

C#

B

F#

C

F

G

A#

D

D# R9

P7

G

F#

D

B

A

E

A#

D#

F

G#

C

C# R7

P4

E

D#

B

G#

F#

C#

G

C

D

F

A

A# R4

P0

C

B

G

E

D

A

D#

G#

A#

C#

F

F#

R0

P11

B

A#

F#

D#

C#

G#

D

G

A

C

E

F

R11

RI5

RI4

RI0

RI9

RI7

RI2

RI8

RI1

RI3

RI6

RI10 RI11

3-4 (015)

3-9 (027)

3-9 (027)

3-4 (015)

4-20 (0158)

4-9 (0167)

4-20 (0158) 171

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Chapter 27

3.

Normal form of 1st hexachord: [C,D,E,F,G,A] Normal form of 2nd hexachord: [F#,G#,A#,B,C#,D#] Each hexachord appears to have been derived from the diatonic scale.

4.

11 8 9 10 7 6 5 2 3 4 1 It is an all-interval series, that is, it contains exactly one occurrence of each interval. (Also note that the second hexachord is a retrograde of the first.)

C.

172

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Chapter 27

D. 1.

The opening two measures suggest a dominant 13th chord; mm. 3-6 outline various traditional triad types (M, m, d); the five-note ostinato figure that enters in m. 7 creates a somewhat mysterious mood, further enhanced by the deep bass notes in mm. 13-16, as well as the repeated F#-C# figure in mm. 19-23. The closing section presents the pitches of the ostinato in melodic form, perhaps even suggesting the EPhrygian mode, until the piece finally comes to rest on A.

173

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Chapter 27

174

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Chapter 27

2.

175

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Chapter 27

3.

In the analysis, rectangles outline members of I5, and oblongs outline members of R5.

I5

R5

176

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Chapter 27

177

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Chapter 27

Exercise 27-3 A. 1.

rhythm (durations), dynamics, articulation

2.

Anton Webern, Olivier Messiaen

3.

Pierre Boulez

4.

Milton Babbitt

178

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Chapter 27

_______________________ (section)

_______________________________ (name)

Chapter 27 Quiz Part 1 A. Put both pc sets into normal order (not necessarily best normal order) in the space provided.

B. The pc sets below are in normal order. Renotate them in best normal order, beginning on any pitch.

C. The pc sets below are in best normal order. Provide the prime form for each, as in (013).

D. 1. Provide the interval vector (interval-class vector) for the pc set below.

< __ __ __ __ __ __> 2. If a pc set has an interval vector of <220222>, how many pcs will be retained (held invariant) if the pc set is transposed by the following pitch-class intervals?

2 ____

6 ____

9 ____ 179

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Chapter 27

Key for Chapter 27 Quiz Part 1 A. Put both pc sets into normal order (not necessarily best normal order) in the space provided.

B. The pc sets below are in normal order. Renotate them in best normal order, beginning on any pitch.

Transpositionally equivalent answers are correct.

C. The pc sets below are in best normal order. Provide the prime form for each, as in (013).

D. 1. Provide the interval vector (interval-class vector) for the pc set below.

<1 1 1 1 1 1>

2. If a pc set has an interval vector of <220222>, how many pcs will be retained (held invariant) if the pc set is transposed by the following pitch-class intervals?

(2)

2

(6) 4

(9)

0

180

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Chapter 27

_______________________ (section)

_______________________________ (name)

Chapter 27 Quiz Part 2

181

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Chapter 27

Key for Chapter 27 Quiz Part 2 E. The series forms may be notated in a variety of octave equivalent and enharmonically equivalent ways, including: 1. I10

Bb

Eb

Ab

A

B

D

G

F

C#

C

F#

E

2. I3

Eb

Ab

C#

D

E

G

C

Bb

F#

F

B

A

3. RI3

A

B

F

F#

Bb

C

G

E

D

C#

Ab

Eb

4. P0

C

G

D

C#

B

Ab

D#

F

A

Bb

E

F#

F. 1. P9 = R3

G. 1. rhythm (durations), dynamics, articulation 2. Milton Babbitt, Pierre Boulez, Olivier Messiaen, and Anton Webern

182

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CHAPTER 28 New Directions This final chapter introduces the student to a wide range of topics: explorations of texture, timbre, and tuning; indeterminacy; minimalism; and electronic and computer music. Most of these topics contain sub-topics that acquaint the student with terminology that may very well be unfamiliar. Each topic focuses on the discussion of directions not covered in Chapters 26 or 27, or directions that have emerged since 1945. We cannot overemphasize the importance of supplementing this material with recordings and, if possible, live performances in class or in the concert hall.

This material does not lend itself to exercises of the sort that are found in the other chapters of this book. Instead, the exercises emphasize the recollection of factual material to a greater degree, and to that extent the chapter necessarily has much in common with a music history text. But it also provides a number of practical suggestions for analysis and composition projects that are similar to the ones included in Chapters 26 and 27, and which we hope will provide a positive ending to the semester.

Answers to Selected Exercises Exercise 28-1 A. 1. prepared piano 2. just intonation 3. quarter tone 4. graphic notation 5. Proportional notation 6. sound-mass compositions 7. micropolyphony 8. sprechstimme 9. third-stream 10. Indeterminacy or aleatory 11. chance procedures 12. experimental music 13. minimalism 14. phasing, resultant patterns 15. Telharmonium, Theremin, Ondes Martenot 16. tape music 17. musique concrète 18. audible frequency spectrum 19. amplitude envelope 20. modular analog synthesizers 21. synthesizer (or digital synthesizer), FM synthesis 22. sequencer 23. stochastic music 24. hyperinstrument 25. postminimalism

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Chapter 28

_______________________ (section)

_______________________________ (name)

Chapter 28 Quiz A. Given the title of one of the works discussed in Chapter 28, identify the composer by using the list below: a. b. c.

John Cage George Crumb Mario Davidovsky

d. e. f.

Philip Glass Paul Lansky Krzysztof Penderecki

g. h.

Terry Riley Karlheinz Stockhausen

1. Makrokosmos, Volume I (1972)

_____

2. Threnody for the Victims of Hiroshima (1960)

_____

3. In C (1960)

_____

4. Notjustmoreidlechatter (1988)

_____

5. Einstein on the Beach (1975)

_____

6. Studie II (1954)

_____

7. Synchronisms No. 6 (1970)

_____

8. 4'33" (1952)

_____

B. Given the composer and title of one of the works discussed in Chapter 28, match the work with the most appropriate term in the list below: a. b. c. d.

experimental music hyperinstrument micropolyphony modular analog synthesizer

e. f. g.

process music real-time interaction spatially-conceived composition

h. i. j.

sprechstimme tape loop theatre music

1. Steve Reich, Come Out (1966)

_____

2. John Cage, Imaginary Landscape No. 4 (1951)

_____

3. Arnold Schoenberg, Pierrot lunaire (1912)

_____

4. György Ligeti, Atmosphères (1961)

_____

5. Igor Stravinsky, L'Histoire du soldat (1918)

_____

6. Edgard Varèse, Poème électronique (1948)

_____

7. Morton Subotnick, The Wild Bull (1968)

_____

8. Pierre Boulez, Répons (1981)

_____

9. Tod Machover, Brain Opera (1996)

_____

10. Steve Reich Piano Phase (1967)

_____ 184

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Chapter 28

Key for Chapter 28 Quiz A. 1.

b

2.

f

3.

g

4.

e

5.

d

6.

h

7.

c

8.

a

B. 1.

i

2.

a

3.

h

4.

c

5.

j

6.

g

7.

d

8.

f

9.

b

10. e

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The title documents are available in full on the following links Title: SOLUTIONS MANUAL for Tonal Harmony, 9th Edition by Stefan Kostka - Complete, Elaborated & Latest. ALL Chapters [1-28] Included & Updated Link I: https://drive.google.com/file/d/1yACJQ6V6uv3W8oF4YbQc2M5B6rS9wjoT/view?usp=sharing