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Music Theory for the 21st-Century Classroom

Robert Hutchinson

Appendix A Answers to Practice Exercises

1 Basic Concepts
1.6 Practice Exercises

1.6.1.

Answer.
1. A0, 2. F1, 3. D2, 4. G2, 5. B3, 6. E4, 7. A4, 8. G5, 9. A6, 10. B7
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1.6.2.

Answer.
1. E5, 2. D6, 3. F4, 4. G3, 5. A4, 6. E4, 7. G3, 8. A2, 9. E4, 10. E4, 11. G3, 12. C4
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1.6.3.

Answer.
1. \(\text{G}^𝄫\) and \(\text{E}^♯\); 2. \(\text{D}^♯\) and \(\text{F}^𝄫\); 3. \(\text{G}^𝄪\) and \(\text{B}^𝄫\); 4. \(\text{G}^♭\) and \(\text{E}^𝄪\)
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2 Major Scales and Key Signatures
2.4 Practice Exercises

2.4.1.

Answer.
1. \(\text{D}^♭\) \(\text{E}^♭\) \(\text{F}\) \(\text{G}^♭\) \(\text{A}^♭\) \(\text{B}^♭\) \(\text{C}\)
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2. \(\text{A}\) \(\text{B}\) \(\text{C}^♯\) \(\text{D}\) \(\text{E}\) \(\text{F}^♯\) \(\text{G}^♯\)
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2.4.2.

Answer.
1. \(\text{A}^♭\); 2. \(\text{A}\); 3. \(\text{G}\); 4. \(\text{E}^♭\); 5. \(\text{F}\); 6. \(\text{D}\); 7. \(\text{C}^♯\);
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8. \(\text{E}\); 9. \(\text{B}^♭\); 10. \(\text{D}^♭\); 11. \(\text{F}^♯\); 12. \(\text{B}\); 13. \(\text{C}^♭\); 14. \(\text{G}^♭\)
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3 Minor Scales and Key Signatures
3.4 Practice Exercises

3.4.1.

Answer.
1. \(\text{e}^♭\); 2. \(\text{b}\); 3. \(\text{c}^♯\); 4. \(\text{g}\); 5. \(\text{f}\); 6. \(\text{e}\); 7. \(\text{b}^♭\);
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8. \(\text{f}^♯\); 9. \(\text{a}^♭\); 10. \(\text{a}^♯\); 11. \(\text{d}\); 12. \(\text{g}^♯\); 13. \(\text{c}\); 14. \(\text{d}^♯\)
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4 Basics of Rhythm
4.7 Practice Exercises

4.7.2.

Answer.
a. Time Signature: \(\begin{smallmatrix}12\\16\end{smallmatrix}\); Meter: Compound Quadruple
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b. Time Signature: \(\begin{smallmatrix}3\\2\end{smallmatrix}\); Meter: Simple Triple
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c. Time Signature: \(\begin{smallmatrix}3\\8\end{smallmatrix}\); Meter: Simple Triple
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d. Time Signature: \(\begin{smallmatrix}4\\2\end{smallmatrix}\); Meter: Simple Quadruple
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4.7.3.

Answer.
1. Dotted quarter note
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2. Eighth note
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3. Dotted eighth note
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4. Half note
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4.7.4.

Answer.
  1. The meter of \(\begin{smallmatrix}4\\2\end{smallmatrix}\) is simple quadruple
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  2. The meter of \(\begin{smallmatrix}9\\16\end{smallmatrix}\) is compound triple
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  3. The meter of \(\begin{smallmatrix}3\\4\end{smallmatrix}\) is simple triple
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4.7.5.

Answer.
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5 Intervals
5.6 Practice Exercises

5.6.1.

Answer.
1. 6, 2. 4, 3. 2, 4. 8, 5. 7
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5.6.2.

Answer.
1. M6, 2. M3, 3. M2, 4. P5, 5. P8, 6. +4
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5.6.3.

Answer.
Upper notes: 1. \(\text{D}^♭\), 2. \(\text{G}^♭\), 3. \(\text{A}^♯\), 4. \(\text{B}\), 5. \(\text{A}\), 6. \(\text{F}^♭\)
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5.6.4.

Answer.
Lower notes: 1. \(\text{G}^♯\), 2. \(\text{E}\), 3. \(\text{F}\), 4. \(\text{G}^♭\), 5. \(\text{F}^♯\), 6. \(\text{B}\)
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6 Triads
6.7 Practice Exercises

6.7.1.

Answer.
1. \(\left.\text{A}^♯{}^{\circ}{}\right.\), 2. \(\text{F}\)sus4, 3. \(\left.\text{B}^♭{}{+}\right.\), 4. \(\left.\text{D}^♭{}\right.\), 5. \(\text{E}\)sus2
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6.7.2.

Answer.
1. \(\text{B}\)\(\text{D}\)\(\text{F}^♯\), 2. \(\text{E}\)\(\text{G}^♯\)\(\text{B}^♯\), 3. \(\text{A}^♭\)\(\text{B}^♭\)\(\text{E}^♭\), 4. \(\text{C}^♯\)\(\text{E}^♯\)\(\text{G}^♯\), 5. \(\text{D}\)\(\text{G}\)\(\text{A}\), 6. \(\text{F}\)\(\text{A}^♭\)\(\text{C}^♭\)
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6.7.3.

Answer.
1. \(\left.\text{D}\text{m}\middle/\text{F}\right.\), 2. \(\left.\text{G}\text{m}\middle/\text{D}\right.\), 3. \(\left.\text{A}^♯{}^{\circ}{}\middle/\text{C}^{♯}\right.\), 4. \(\left.\text{F}\middle/\text{A}\right.\), 5. \(\left.\text{B}^♭{}\middle/\text{F}\right.\), 6. \(\left.\text{C}\text{m}\middle/\text{G}\right.\)
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6.7.4.

Answer.
(lowest to highest) 1. \(\text{D}\)\(\text{G}\)\(\text{B}\), 2. \(\text{D}\)\(\text{F}^♯\)\(\text{B}\), 3. \(\text{F}\)\(\text{A}^♭\)\(\text{D}^♭\), 4. \(\text{B}^♭\)\(\text{E}\)\(\text{G}\)
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6.7.5.

Answer.
1. \(\text{F}^♯\)\(\text{A}^♯\)\(\text{C}^♯\), 2. \(\text{G}\)\(\text{B}^♭\)\(\text{D}^♭\), 3. \(\text{A}^♭\)\(\text{C}^♭\)\(\text{E}^♭\)
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7 Roman Numerals and Cadences
7.5 Practice Exercises

7.5.1.

Answer.
1. \(\left.\text{F}^♯{}\text{m}\right.\), \(\left.\text{ii}\right.\); 2. \(\left.\text{D}^♯{}^{\circ}{}\middle/\text{F}^{♯}\right.\), \(\left.\text{vii}^{\circ}{}\middle/\text{3rd}\right.\); 3. \(\left.\text{A}\right.\), \(\left.\text{VII}\right.\); 4. \(\left.\text{G}\right.\), \(\left.\text{V}\right.\); 5. \(\left.\text{B}\text{m}\middle/\text{F}^{♯}\right.\), \(\left.\text{ii}\middle/\text{5th}\right.\)
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7.5.2.

Answer.
1. \(\left.\text{C}\right.\), \(\text{C}\)\(\text{E}^♮\)\(\text{G}\); 2. \(\left.\text{G}\middle/\text{D}\right.\), \(\text{D}\)\(\text{G}\)\(\text{B}\); 3. \(\left.\text{A}^{\circ}{}\right.\), \(\text{A}^♮\)\(\text{C}\)\(\text{E}^♭\)
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7.5.3.

Answer.
a. “Columbia, the Gem of the Ocean”: 1. \(\left.\text{G}\right.\), \(\left.\text{I}\right.\); 2. \(\left.\text{D}\right.\), \(\left.\text{V}\right.\); 3. \(\left.\text{G}\right.\), \(\left.\text{I}\right.\); 4. \(\left.\text{C}\right.\), \(\left.\text{IV}\right.\); 5. \(\left.\text{G}\right.\), \(\left.\text{I}\right.\); 6. \(\left.\text{D}\right.\), \(\left.\text{V}\right.\); Cadence type = Half Cadence (HC)
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b. “Could You Be Loved”: 1. \(\left.\text{D}\right.\), \(\left.\text{I}\right.\); 2. \(\left.\text{B}\text{m}\right.\), \(\left.\text{vi}\right.\); 3. \(\left.\text{G}\right.\), \(\left.\text{IV}\right.\); 4. \(\left.\text{D}\right.\), \(\left.\text{I}\right.\); Cadence type = Plagal Cadence (PC)
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8 Seventh Chords
8.4 Practice Exercises

8.4.1.

Answer.
1. \(\left.\text{D}^{7}\right.\), \(\left.\text{V}^{7}\right.\)
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2. \(\left.\text{G}{\Delta}^{7}\right.\), \(\left.\text{IV}^{M7}\right.\)
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3. \(\left.\text{D}^♯{}^ø{}^{7}\right.\), \(\left.\text{ii}^ø{}^{7}\right.\)
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4. \(\left.\text{B}\text{m}^{7}\middle/\text{D}\right.\), \(\left.\text{iii}^{7}\middle/\text{3rd}\right.\)
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5. \(\left.\text{C}^♯{}^{\circ}{}^{7}\middle/\text{E}\right.\), \(\left.\text{vii}^{\circ}{}^{7}\middle/\text{3rd}\right.\)
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8.4.2.

Answer.
1. Bm7, B-D-F♯-A
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2. \(\left.\text{A}^ø{}^{7}\right.\), A-C-E♭-G
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3. \(\left.\text{C}^♯{}^ø{}^{7}\right.\), C♯-E-G-B
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4. \(\left.\text{G}^{7}\right.\), G-B♮-D-F
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5. Emaj\(\left.\text{}^{7}\right.\)/G♯, G♯-B-D♯-E
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8.4.3.

Answer.
a. “No Scrubs”: 1. \(\left.\text{D}^♭{}\text{m}^{7}\right.\), \(\left.\text{iv}^{7}\right.\); 2. \(\left.\text{A}^♭{}\text{m}\right.\), \(\left.\text{i}\right.\); 3. \(\left.\text{E}^♭{}^{7}\right.\), \(\left.\text{V}^{7}\right.\); 4. \(\left.\text{A}^♭{}\text{m}\right.\), \(\left.\text{i}\right.\)
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b. Mozart: 1. \(\left.\text{C}\right.\), \(\left.\text{I}\right.\); 2. \(\left.\text{G}^{7}\middle/\text{D}\right.\), \(\left.\text{V}^{7}\middle/\text{5th}\right.\); 3. \(\left.\text{C}\right.\), \(\left.\text{I}\right.\); 4. \(\left.\text{F}\middle/\text{C}\right.\), \(\left.\text{IV}\middle/\text{5th}\right.\); 5. \(\left.\text{C}\right.\), \(\left.\text{I}\right.\); 6. \(\left.\text{G}^{7}\middle/\text{B}\right.\), \(\left.\text{V}^{7}\middle/\text{3rd}\right.\); 7. \(\left.\text{C}\right.\), \(\left.\text{I}\right.\); Cadence type: Authentic Cadence (AC)
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9 Harmonic Progression and Harmonic Function
9.9 Practice Exercises

9.9.2.

Answer.
1. A𝄫, 2. A♯, 3. D, 4. C♯, 5. G, 6. G
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9.9.3.

Answer.
1. 4 flats in key signature, iv, B♭-D♭-F
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2. 3 sharps in key signature, IV, D-F♯-A
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3. 3 flats in key signature, iiº/3rd, F-A♭-D
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4. 4 sharps in key signature, vi, C♯-E-G♯
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5. 2 flats in signature, viiº7, F♯-A-C-E♭
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6. 5 sharps in key signature, V7/5th, C♯-E-F♯-A♯
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7. 1 flat in key signature, i/3rd, F-A-D
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8. 1 flat in key signature, iii, A-C-E
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9.9.4.

Answer.
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9.9.6.

Answer.
In F major: In E major:
1. F, I 1. C♯m, vi
2. Dm, vi 2. A, IV
3. Gm/B♭, ii/3rd 3. E, I
4. C, V 4. B, V
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9.9.7.

Answer.
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10 Non-Chord Tones
10.12 Practice Exercises

10.12.1.

Answer.
Non-Chord Tone Type Approached by Left by
RETARDATION same tone step up
ESCAPE TONE STEP leap in opposite direction
PASSING TONE step step in same direction
APPOGGIATURA leap STEP
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10.12.2.

Answer.
a. “Stop! In the Name of Love” example
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Lead-sheet symbols: Am, G/B, F, G
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Roman numerals: vi, V/3rd, IV IVM7, V
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Measure 2: 7-6 suspension in voice part and in right hand of piano, appoggiatura in left hand of piano
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Measure 3: 9-8 suspension (or incomplete neighbor) in voice part and right hand of piano
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Measure 4: 6-5 suspension in voice and right hand of piano
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b. Robert Schumann example
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Pickup measure: appoggiatura in right hand of piano;
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Measure 1: appoggiatura in left hand of piano; 7-6 suspension, appoggiatura in right hand of piano; Roman numeral: iv/3rd
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Measure 2: appoggiatura in right hand; Roman numeral: V7
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Measure 3: 7-6 suspension, appoggiatura in voice part; 7-6 suspension, appoggiatura in right hand of piano; Roman numeral: ii/3rd, V7, Lead-sheet symbol: E7
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Measure 4: 4-3 suspension; appoggiatura in right hand; Roman numeral: I, Lead-sheet symbol: A
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11 Melodic Analysis
11.6 Practice Exercises

11.6.1.

Answer.
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11.6.2.

Answer.
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11.6.3.

Answer.
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11.6.4.

Answer.
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12 Form in Popular Music
12.6 Practice Exercises

12.6.1.

Answer.
She’s Out of My Life:
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Penny Lane:
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  • 0:00–0:20, Verse 1, 8 bars
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  • 0:20–0:38, Verse 2, 8 bars
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  • 0:38–0:54, Chorus, 8 bars
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  • 0:54–1:11, Verse 3, 8 bars
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  • 1:11–1:28, Trumpet Solo on Verse progression, 8 bars
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  • 1:28–1:45, Chorus, 8 bars
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  • 1:45–2:02, Verse 4, 8 bars
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  • 2:02–2:19, Verse 5, 8 bars
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  • 2:19–2:36, Chorus, 8 bars
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  • 2:36–3:02, Chorus a whole step higher, 9 bars
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13 Phrases in Combination
13.9 Practice Exercises

13.9.1. Mozart, “Ein Mädchen oder Weibchen,”The Magic Flute.
Answer.
Mozart, The Magic Flute, “Ein Mädchen oder Weibchen”:
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  • Chords: \(\left.\text{I}\right.\)–\(\left.\text{V}\right.\), \(\left.\text{V}\right.\)–\(\left.\text{I}\right.\)
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  • Cadences: HC, PAC
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  • No Sentences
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  • Melodic labels: a, b
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  • Form: contrasting period
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13.9.2. Mozart, Piano Sonata K. 333, I.
Answer.
Mozart, Piano Sonata K. 333, I:
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  • Chords: \(\left.\text{vii}^{\circ}{}\right.\)–\(\left.\text{I}\right.\), \(\left.\text{vi}\right.\)–\(\left.\text{V}\right.\), \(\left.\text{vii}^{\circ}{}\right.\)–\(\left.\text{I}\right.\), \(\left.\text{V}\right.\)–\(\left.\text{I}\right.\)
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  • Cadences: IAC, HC, IAC, PAC
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  • The 2nd phrase is a sentence
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  • Melodic labels: a, b, a, b’
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  • Form: parallel double period
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13.9.3. Edmond Dédé, Chicago, Grande Valse à l’Américaine.
Answer.
Dédé, Chicago:
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  • Chords: \(\left.\text{V}\right.\), \(\left.\text{V}\right.\), \(\left.\text{V}\right.\), \(\left.\text{V}\right.\)–\(\left.\text{I}\right.\)
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  • Cadences: HC, HC, HC, PAC
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  • All four phrases are sentences
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  • Melodic labels: a, a, a, a’
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  • Form: parallel double period
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16 Figured Bass
16.6 Practice Exercises

16.6.1.

Answer.
  • Lead-sheet: 1. \(\left.\text{C}\middle/\text{G}\right.\); 2. \(\left.\text{B}^{\circ}{}\middle/\text{D}\right.\); 3. \(\left.\text{Dm}\middle/\text{A}\right.\); 4. \(\left.\text{G}\right.\)
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  • Figured bass: 1. \(\left.\text{I}^{6}_{4}\right.\); 2. \(\left.\text{vii}^{\circ}{}^{6}\right.\); 3. \(\left.\text{ii}^{6}_{4}\right.\); 4. \(\left.\text{V}\right.\)
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16.6.2.

Answer.
  • Lead-sheet: 1. \(\left.\text{Em7}\middle/\text{G}\right.\); 2. \(\left.\text{G7}\middle/\text{F}\right.\); 3. \(\left.\text{Cmaj7}\middle/\text{G}\right.\); 4. \(\left.\text{Fmaj7}\right.\)
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  • Figured bass: 1. \(\left.\text{iii}^{6}_{5}\right.\); 2. \(\left.\text{V}^{4}_{2}\right.\); 3. \(\left.\text{IM}^{4}_{3}\right.\); 4. \(\left.\text{IVM}^{7}\right.\)
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16.6.3.

Answer.
  • Lead-sheet: 1. \(\left.\text{D}^{\circ}{}\middle/\text{F}\right.\); 2. \(\left.\text{A}^♯{}^{\circ}{}^{7}\middle/\text{G}\right.\); 3. \(\left.\text{E}^ø{}^{7}\right.\); 4. \(\left.\text{Dmaj7}\middle/\text{F}^{♯}\right.\)
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  • Figured bass: 1. \(\left.\text{ii}^{\circ}{}^{6}\right.\); 2. \(\left.\text{vii}^{\circ}{}^{4}_{2}\right.\); 3. \(\left.\text{vii}^ø{}^{7}\right.\); 4. \(\left.\text{IM}^{6}_{5}\right.\)
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16.6.4.

Answer.
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16.6.5.

Answer.
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17 Secondary Dominant Chords
17.7 Practice Exercises

17.7.1.

Answer.
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17.7.2.

Answer.
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17.7.3.

Answer.
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17.7.4.

Answer.
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17.7.5.

Answer.
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18 Secondary Diminished Chords
18.5 Practice Exercises

18.5.1.

Answer.
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18.5.2.

Answer.
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18.5.3.

Answer.
  • Lead–sheet: 1. \(\left.\text{F}\right.\); 2. \(\left.\text{Am}\right.\); 3. \(\left.\text{B}^♭{}\right.\); 4. \(\left.\text{F}^♯{}^{\circ}{}^{7}\right.\); 5. \(\left.\text{D}\middle/\text{F}^{♯}\right.\); 6. \(\left.\text{Gm}\right.\)
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  • Figured bass: 1. \(\left.\text{I}\right.\); 2. \(\left.\text{iii}\right.\); 3. \(\left.\text{IV}\right.\); 4. \(\left.\text{vii}^{\circ}{}^{7}\middle/\text{ii}\right.\); 5. \(\left.\text{V}^{6}\middle/\text{ii}\right.\); 6. \(\left.\text{ii}\right.\)
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19 Mode Mixture
19.6 Practice Exercises

19.6.1.

Answer.
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19.6.2.

Answer.
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19.6.3.

Answer.
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20 The Neapolitan Chord
20.3 Practice Exercises

20.3.1.

Answer.
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20.3.2.

Answer.
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21 Augmented Sixth Chords
21.9 Practice Exercises

21.9.1.

Answer.
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21.9.2.

Answer.
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22 Modulation
22.8 Practice Exercises

22.8.2.

Answer.
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22.8.3.

Answer.
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22.8.4.

Answer.
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22.8.5.

Answer.
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22.8.6.

Answer.
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22.8.7.

Answer.
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22.8.8.

Answer.
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22.8.9.

Answer.
  1. Fm: Am, A♭m, Dm, D♭m
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  2. D♭: F♭, F, B♭, B𝄫 (or A, enharmonically)
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  3. G: B♭, B, E, E♭
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  4. G♯m: Bm, B♯m, Em, E♯m
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23 Enharmonic Modulation
23.4 Practice Exercises

23.4.1.

Answer.
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23.4.2.

Answer.
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23.4.3.

Answer.
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23.4.4.

Answer.
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23.4.5.

Answer.
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24 Binary and Ternary Forms
24.9 Practice Exercises

24.9.1.

Answer.
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24.9.2.

Answer.
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24.9.3.

Answer.
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24.9.4.

Answer.
Two-Reprise Continuous Ternary, if looking at the proportion, or Two-Reprise Continuous Rounded Binary, if you interpret the first two notes in bar 13 as being built from the first two notes in bar 1—and if you are considering that Mozart, as a Classical-era composer, is likely to compose a rounded binary. Two-Reprise Continuous Balanced Binary is a label that describes that the endings of the halves are the same, but doesn’t take into account the return of the opening material in bar 21.
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24.9.5.

Answer.
Sectional Ternary
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24.9.6.

Answer.
Two-Reprise Sectional Rounded Binary (because the motives from the first section are used in the construction of the melody of the second section)
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25 Sonata and Rondo Forms
25.6 Practice Exercises

25.6.2.

Answer.
Figure 25.6.3. Mozart, Piano Sonata K. 545, I.
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Figure 25.6.4. Mozart, Eine kleine nachtmusik, K. 525, I.
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26 Voice Leading Triads
26.13 Practice Exercises

26.13.1.

Answer.
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26.13.2.

Answer.
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26.13.3.

Answer.
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26.13.4.

Answer.
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26.13.5.

Answer.
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26.13.6.

Answer.
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26.13.7.

Answer.
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26.13.8.

Answer.
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26.13.9.

Answer.
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27 Voice Leading Seventh Chords
27.6 Practice Exercises

27.6.1.

Answer.
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27.6.2.

Answer.
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27.6.3.

Answer.
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28 Voice Leading With Non-Chord Tones
28.4 Practice Exercises

28.4.1.

Answer.
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28.4.2.

Answer.
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28.4.3.

Answer.
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29 Voice Leading Chromatic Harmonies
29.5 Practice Exercises

29.5.1.

Answer.
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29.5.2.

Answer.
Notice that the chords on beats 5 and 6 are consecutive first inversion chords (even though one is a 7th chord), therefore the third is doubled on \(\left.\text{I}^{6}\right.\) to avoid parallel fifths.
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29.5.3.

Answer.
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29.5.4.

Answer.
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29.5.5.

Answer.
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30 Introduction to Counterpoint
30.9 Practice Exercises

First and Second Species Exercises
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30.9.1.
Answer.
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30.9.2.
Answer.
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Species Counterpoint: Day Two
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30.9.3.
Answer.
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30.9.4.
Answer.
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Invention Expositions
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30.9.5.
Answer.
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Fugue Analysis
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30.9.6.
Answer.
Table 30.9.3. Mass in B Minor: Fugue Analysis Table
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FORM Exposition 1
SOPRANO
ALTO
TENOR Subject
BASS Subject Subject Sub. Countersubject
KEY F♯m C♯m
Meas. 1 2 3 4
l
FORM (Bridge)
SOPRANO
ALTO
TENOR Subject Bridge Mot. A Bridge Mot. A Bridge Mot. A
BASS Countersubject Bridge Mot. B Bridge Mot. B Bridge Mot. B
KEY
Meas. 5 6 7 8
l
FORM Exposition 1 (continues until 4th voice has subject)
SOPRANO Subject
ALTO Subject Subject Sub. Countersubject
TENOR Countersubject Countersubject C.S. Ctrpt
BASS Ctrpt Ctrpt Ctrpt Ctrpt
KEY F♯m C♯m
Meas. 9 10 11 12
l
FORM Episode 1
SOPRANO Subject Bridge Mot. A Bridge Mot. A
ALTO Countersubject Bridge Mot. B Mot. B Ctrpt Ctrpt
TENOR Ctrpt Ctrpt Ctrpt Ctrpt
BASS Ctrpt
KEY
Meas. 13 14 15 16
l
FORM Exposition 2
SOPRANO Cadential Ctrpt Ctrpt Ctrpt
ALTO Cadential Subject Subject Subject
TENOR Cadential Ctrpt Ctrpt Ctrpt
BASS
KEY F♯m
Meas. 17 18 19 20
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31 Introduction to Jazz Theory
31.12 Practice Exercises

31.12.1.

Answer.
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31.12.2.

Answer.
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31.12.3.

Answer.
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31.12.4.

Answer.
1. G♯ Diminished-Whole Tone
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2. F♯ Octatonic (Half-Whole)
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3. F Locrian ♯2
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4. C Whole-Tone
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5. A♭ Lydian-Dominant
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6. C Locrian
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31.12.5.

Answer.
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31.12.6.

Answer.
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32 Impressionism and Extended Tonality
32.5 Practice Exercises

32.5.1.

Answer.
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32.5.2.

Answer.
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32.5.3.

Answer.
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32.5.4.

Answer.
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33 Set Theory
33.9 Practice Exercises

33.9.1.

Answer.
  1. Normal form is [0, 2, 7]. Prime form is (027).
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  2. Normal form is [1, 3, 6, 8]. Prime form is (0257).
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  3. Normal form is [6, 10, 11, 1]. Prime form is (0237).
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  4. Normal form is [7, 8, 0, 3]. Prime form is (0158).
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  5. Normal form is [11, 0, 1, 4, 6]. Prime form is (01257).
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  6. Normal form is [6, 7, 10, 11, 2]. Prime form is (01458).
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  7. Normal form is [9, 10, 0, 1, 4, 6]. Prime form is (013479).
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33.9.2.

Answer.
Table 33.9.1.
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Set Normal Form Prime Form Forte Number Interval Vector
1 [11, 1, 3, 5, 6] (01357) 5–24 131221
2 [5, 8, 10, 0] (0247) 4–22 021120
3 [9, 0, 1, 4, 5] (01458) 5–21 202420
4 [3, 5, 6, 10] (0237) 4–14 111120
5 [2, 3, 6, 7, 9, 10] (013478) 6–Z19 313431
6 [2, 3, 5, 6, 9, 10] (013478) 6–Z19 313431
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34 Serialism
34.7 Practice Exercises

34.7.3.

Answer.
Table 34.7.2. Twelve-Tone Matrix
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I\(\text{}_{3}\)↓ I\(\text{}_{7}\)↓ I\(\text{}_{11}\)↓ I\(\text{}_{1}\)↓ I\(\text{}_{5}\)↓ I\(\text{}_{0}\)↓ I\(\text{}_{2}\)↓ I\(\text{}_{10}\)↓ I\(\text{}_{6}\)↓ I\(\text{}_{4}\)↓ I\(\text{}_{8}\)↓ I\(\text{}_{9}\)↓
P\(\text{}_{3}\)→ E♭ G B C♯ F C D B♭ G♭ E G♯ A ←R\(\text{}_{3}\)
P\(\text{}_{11}\)→ B D♯ G A C♯ G♯ A♯ F♯ D C E F ←R\(\text{}_{11}\)
P\(\text{}_{7}\)→ G B D♯ F A E F♯ D B♭ A♭ C D♭ ←R\(\text{}_{7}\)
P\(\text{}_{5}\)→ F A C♯ E♭ G D E C A♭ G♭ B♭ B ←R\(\text{}_{5}\)
P\(\text{}_{1}\)→ D♭ F A B E♭ B♭ C A♭ E D G♭ G ←R\(\text{}_{1}\)
P\(\text{}_{6}\)→ G♭ B♭ D E A♭ E♭ F D♭ A G B C ←R\(\text{}_{6}\)
P\(\text{}_{4}\)→ E G♯ C D G♭ D♭ E♭ B G F A B♭ ←R\(\text{}_{4}\)
P\(\text{}_{8}\)→ A♭ C E G♭ B♭ F G E♭ B A D♭ D ←R\(\text{}_{8}\)
P\(\text{}_{0}\)→ C E A♭ B♭ D A B G E♭ D♭ F G♭ ←R\(\text{}_{0}\)
P\(\text{}_{2}\)→ D F♯ A♯ C E B D♭ A F E♭ G A♭ ←R\(\text{}_{2}\)
P\(\text{}_{10}\)→ B♭ D G♭ A♭ C G A F D♭ B D♯ E ←R\(\text{}_{10}\)
P\(\text{}_{9}\)→ A C♯ F G B F♯ A♭ E C B♭ D E♭ ←R\(\text{}_{9}\)
↑RI\(\text{}_{3}\) ↑RI\(\text{}_{7}\) ↑RI\(\text{}_{11}\) ↑RI\(\text{}_{1}\) ↑RI\(\text{}_{5}\) ↑RI\(\text{}_{0}\) ↑RI\(\text{}_{2}\) ↑RI\(\text{}_{10}\) ↑RI\(\text{}_{6}\) ↑RI\(\text{}_{4}\) ↑RI\(\text{}_{8}\) ↑RI\(\text{}_{9}\)
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34.7.4.

Answer.
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34.7.5.

Answer.
  1. Set 1: 3, 7, 11. Normal form: [3, 7, 11] Prime form: (048) Interval vector: 000300
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  2. Set 2: 1, 5, 0. Normal form: [0, 1, 5] Prime form: (015) Interval vector: 100110
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  3. Set 3: 2, 10, 6. Normal form: [2, 6, 10] Prime form: (048) Interval vector: 000300
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  4. Set 4: 4, 8, 9. Normal form: [4, 8, 9] Prime form: (015) Interval vector: 100110
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