Questions: Pitch-Class Set Operations

Question 1

Applying T3 (transposition by 3 semitones) to the pitch-class set {0, 4, 7} produces which set?

• A. {3, 6, 9}
• B. {3, 7, 10}
• C. {0, 4, 10}
• D. {1, 5, 8}

Answer: (B)

T3 adds 3 to every pitch class mod 12: 0+3=3, 4+3=7, 7+3=10, giving {3, 7, 10}. {3, 6, 9} would be T3 applied to {0, 3, 6} (a diminished triad). The key is applying the same fixed integer to every element and reducing mod 12.

Question 2

Inversion in pitch-class set theory (the operation I) is the same operation as melodic inversion in tonal counterpoint.

• T. True
• F. False

Answer: False

PC set inversion negates each pitch class mod 12: pitch class n becomes 12 - n (or equivalently, -n mod 12). Melodic inversion in tonal music flips intervals upside down around an axis pitch. The operations are related in spirit but differ in implementation: tonal inversion preserves interval size and direction while PC set inversion is modular arithmetic. Confusing them is a common error when first encountering set theory.

Question 3

What does it mean for two pitch-class sets to belong to the same set class, and what does that imply about their sound?

Model answer: Two sets belong to the same set class if one can be transformed into the other by transposition (Tn) or inversion followed by transposition (TnI). They share the same prime form and interval-class vector, meaning they contain identical interval content. In practice, this implies they have a similar harmonic color or tension quality, even if they are built on different pitch levels or orientations.

Set class equivalence is the atonal analogue of tonal function: just as G7 and D7 are both dominant seventh chords (same structure, different transposition), {0,1,4} and {3,4,7} are both members of set class 3-3 (same prime form). The interval-class vector encodes how many of each interval type the set contains, which is what drives the perceptual similarity.