A | B | C | D | E | F | G | H | CH | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
In music, a cyclic set is a set, "whose alternate elements unfold complementary cycles of a single interval."[1] Those cycles are ascending and descending, being related by inversion since complementary:
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Berg%27s_Lyric_Suite_cyclic_set.png/400px-Berg%27s_Lyric_Suite_cyclic_set.png)
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= 8 I5: 8 +5= 1 +5= 6 +5= 11...3 +5= 8
According to George Perle, "a Klumpenhouwer network is a chord analyzed in terms of its dyadic sums and differences," and, "this kind of analysis of triadic combinations was implicit in," his, "concept of the cyclic set from the beginning".[2]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Berg%27s_Lyric_Suite_cyclic_set_overlapping_three-note_segments.png/400px-Berg%27s_Lyric_Suite_cyclic_set_overlapping_three-note_segments.png)
A cognate set is a set created from joining two sets related through inversion such that they share a single series of dyads.[3]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Cognate_set_on_C.png/400px-Cognate_set_on_C.png)
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 a set 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]
References
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