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Music Theory for the 21st-Century Classroom

Robert Hutchinson

Exercises 34.7 Practice Exercises

Exercise Group.

Serialism: Day One

1.

Given the prime form of the twelve-tone row in pitch integers, write the specified row forms in the staves below.
  1. P\(\text{}_{1}\)
  2. R\(\text{}_{4}\)
  3. I\(\text{}_{8}\)
  4. RI\(\text{}_{10}\)
Answer.

2.

Given the prime form of a twelve-tone row, label the row forms and transpositions of the permutations given on the staves below.
  1. Row form:
  2. Row form:
  3. Row form:
Answer.
  1. RI\(\text{}_{10}\)
  2. I\(\text{}_{1}\)
  3. R\(\text{}_{5}\)

Exercise Group.

Serialism: Day Two

3.

Construct a 12 by 12 matrix for the prime form of the following twelve-tone row, given in pitch integers: 3, 7, 11, 1, 5, 0, 2, 10, 6, 4, 8, 9. Include labels for all row forms including all transposition levels (P\(\text{}_{0}\), R\(\text{}_{3}\), I\(\text{}_{8}\), RI\(\text{}_{6}\), etc.). Use note names in the matrix, not integers.
Table 34.7.1.
I↓ I↓ I↓ I↓ I↓ I↓ I↓ I↓ I↓ I↓ I↓ I↓
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
P→ ←R
↑RI ↑RI ↑RI ↑RI ↑RI ↑RI ↑RI ↑RI ↑RI ↑RI ↑RI ↑RI
Answer.
Table 34.7.2. Twelve-Tone Matrix
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\(\text{}_{9}\)

4.

For the following excerpt, determine P\(\text{}_{5}\) and identify each row form and statement. This example contains overlap.
Answer.

5.

Referring to the twelve-tone row used to construct the matrix in the practice exercise above (3, 7, 11, 1, 5, 0, 2, 10, 6, 4, 8, 9), find the normal form and prime form for each discrete three-note set from the row, and provide an interval vector for each.
  1. Set 1: 3, 7, 11. Normal form: Prime form: Interval vector:
  2. Set 2: 1, 5, 0. Normal form: Prime form: Interval vector:
  3. Set 3: 2, 10, 6. Normal form: Prime form: Interval vector:
  4. Set 4: 4, 8, 9. Normal form: Prime form: Interval vector:
Answer.
  1. Set 1: 3, 7, 11. Normal form: [3, 7, 11] Prime form: (048) Interval vector: 000300
  2. Set 2: 1, 5, 0. Normal form: [0, 1, 5] Prime form: (015) Interval vector: 100110
  3. Set 3: 2, 10, 6. Normal form: [2, 6, 10] Prime form: (048) Interval vector: 000300
  4. Set 4: 4, 8, 9. Normal form: [4, 8, 9] Prime form: (015) Interval vector: 100110
musictheory.pugetsound.edu/hw/MT21C_HW_64.pdf
musictheory.pugetsound.edu/hw/MT21C_HW_65.pdf
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