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In music, a cyclic set is a set, "whose alternate elements unfold complementary cycles of a single interval."〔Perle, George (1996). ''Twelve-Tone Tonality'', p.21. ISBN 0-520-20142-6.〕 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= 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".〔Perle, George (1993). "Letter from George Perle", ''Music Theory Spectrum'', Vol. 15, No. 2 (Autumn), pp. 300-303.〕 A cognate set is a set created from joining two sets related through inversion such that they share a single series of dyads.〔Perle (1996), p.22.〕 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.〔 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.〔Perle (1996), p.23.〕 ==Sources== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cyclic set」の詳細全文を読む スポンサード リンク
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