Suggested Learning Resources
- 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.
https://youtu.be/3LvUqWIxquw?t=11m16s
Objective 54.4: Use Allen-Forte's set-class list to find complement sets