Suggested Learning Resources


2) Video Lesson:

3) Online Reading: Composing with Pitch-Class Sets , pages 4-6

4) Interactive Lesson: 

Music Theory QuickThink:

- Sets are complementary when one set completes the missing pitch-class tones from the other.

- Example Set [8,10,11] is a complement set to [0,1,2,3,4,5,6,7,9]  (the numbers in the first set are missing from the second set)

- Allen Forte lists complementary sets across from each other on his table. However, he lists all sets in their PRIME FORM.

-The second set listed above, [0,1,2,3,4,5,6,7,9] is already in prime form.  The set [8,10,11] must be reversed and inverted… [1,2,4]  then transposed to arrive at its Prime Form [0,1,3]

-Thus Allen Forte lists the following sets as complements in his table [0,1,3]  and [0,1,2,3,4,5,6,7,9]

-In Allen Forte’s table, each label as two numbers.  The first number is how many pitches there are in a set, and the second number was assigned by Forte.  The second numbers of two complementary sets are the same.

- Allen Forte’s number for [0,1,3] is 3-2 and Forte’s number for [0,1,2,3,4,5,6,7,9] is 9-2.   Thus 3-2 and 9-2 are complements


- Complementary sets Interval-class-vectors, when subtracted from each other, always produce the same number for each labeled spot (except spot 6)

- Z-Related Sets (marked with a Z on Allen Forte's list) – are two sets that share the same Interval-class-vector, but are actually not transpositions or inversions of each other.

Objective 54.4: Examples in Music: YouTube

Objective 54.4: Use Allen-Forte's set-class list to find complement sets