Inmusic, acyclic set is aset, "whose alternate elements unfoldcomplementarycycles of a singleinterval."[1] Those cycles are ascending and descending, being related by inversion since complementary:
In the above example, as explained, one interval (7) and its complement (-7 = +5), creates two series of pitches starting from the same note (8):
P7:8 +7=3 +7=10 +7=5...1 +7=8I5:8 +5=1 +5=6 +5=11...3 +5=8
According toGeorge Perle, "aKlumpenhouwer network is achordanalyzed in terms of itsdyadicsums anddifferences," and, "this kind of analysis oftriadic combinations was implicit in," his, "concept of the cyclic set from the beginning".[2]
Acognate set is a set created from joining two sets related throughinversion such that they share a single series of dyads.[3]
0 7 2 9 4 11 6 1 8 3 10 5 (0+ 0 5 10 3 8 1 6 11 4 9 2 7 (0________________________________________= 0 0 0 0 0 0 0 0 0 0 0 0 (0
The two cycles may also be aligned as pairs of sum 7 or sum 5 dyads.[3] All together these pairs of cycles form aset complex, "any cyclic set of the set complex may be uniquely identified by its two adjacency sums," and as such the example above shows p0p7 and i5i0.[4]