| 词条 | Cyclic set |
| 释义 |
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: 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] A cognate set is a set created from joining two sets related through inversion 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 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] Sources1. ^1 2 Perle, George (1996). Twelve-Tone Tonality, p.21. {{ISBN|0-520-20142-6}}. {{Atonality}}2. ^Perle, George (1993). "Letter from George Perle", Music Theory Spectrum, Vol. 15, No. 2 (Autumn), pp. 300-303. 3. ^1 2 Perle (1996), p.22. 4. ^Perle (1996), p.23. 2 : Intervals (music)|Post-tonal music theory |
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