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Music Theory for the 21st-Century Classroom

Robert Hutchinson

Exercises 33.9 Practice Exercises

Exercise Group.

Day One

1.

Put each set into normal form and prime form.
Answer.
  1. Normal form is [0, 2, 7]. Prime form is (027).
  2. Normal form is [1, 3, 6, 8]. Prime form is (0257).
  3. Normal form is [6, 10, 11, 1]. Prime form is (0237).
  4. Normal form is [7, 8, 0, 3]. Prime form is (0158).
  5. Normal form is [11, 0, 1, 4, 6]. Prime form is (01257).
  6. Normal form is [6, 7, 10, 11, 2]. Prime form is (01458).
  7. Normal form is [9, 10, 0, 1, 4, 6]. Prime form is (013479).

Exercise Group.

Day Two

2.

For each of the six sets in the example below, determine the normal form, prime form, Forte number, and interval vector.
Answer.
Table 33.9.1.
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

Exercise Group.

Day Three

3.

Transposition (T\(\text{}_{n}\)) of Sets. Transpose the following sets as specified.
  1. Transpose [3, 6, 7] at T\(\text{}_{2}\): [ , , ]
  2. Transpose [2, 4, 8, 9] at T\(\text{}_{7}\): [ , , , ]
  3. Transpose [1, 2, 4, 7, 8] at T\(\text{}_{9}\): [ , , , , ]
Answer.
  1. [5, 8, 9]
  2. [9, 11, 3, 4]
  3. [10, 11, 1, 4, 5]

4.

Inversion (T\(\text{}_{n}\)I) of Sets. Invert the following sets. Write your answers in normal form.
  1. Invert [7, 10, 11] at T\(\text{}_{0}\)I: [ , , ]
  2. Invert [0, 2, 4] at T\(\text{}_{4}\)I: [ , , ]
  3. Invert [4, 6, 10, 11] at T\(\text{}_{9}\)I: [ , , , ]
Answer.
  1. [1, 2, 5]
  2. [0, 2, 4]
  3. [10, 11, 3, 5]

5.

Specify the interval of inversion from the first set to the second set.
  1. [2, 4, 7] inverts to [3, 6, 8] at what T\(\text{}_{n}\)I?
  2. [1, 2, 4, 7] inverts to [4, 7, 9, 10] at what T\(\text{}_{n}\)I?
  3. [6, 7, 10, 1, 2] inverts to [3, 4, 7, 10, 11] at what T\(\text{}_{n}\)I?
Answer.
  1. T\(\text{}_{10}\)I
  2. T\(\text{}_{11}\)I
  3. T\(\text{}_{5}\)I
PDF versions of the textbook, homework exercises, and practice exercises can be found at musictheory.pugetsound.edu 4 
musictheory.pugetsound.edu/hw/MT21C_HW_61.pdf
musictheory.pugetsound.edu/hw/MT21C_HW_62.pdf
musictheory.pugetsound.edu/hw/MT21C_HW_63.pdf
musictheory.pugetsound.edu
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