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Determining Ideal Tempos:
A Unified Theory of Tempo Relativity


Table 2

Preliminary matrix of theoretically correct tempos. The left column consists only of integers listed in Table 1. Each row comprises a “tempo class” where a constant fast-note speed (the “fastest common denominator”) defines the class. For example, the tempo quadruplet = 72 belongs to “class 288” because its fast-note speed (the sixteenth note in 4/4) is 288 beats per minute. The progression in this matrix can continue infinitely.


one note duplet triplet quadruplet quintuplet sextuplet septuplet octuplet nonuplet
42 21 14 10.5 8.4 7 6 5.25 4.6
48 24 16 12 9.6 8 6.857 6 5.3
54 27 18 13.5 10.8 9 7.714 6.75 6
56 28 18.6 14 11.2 9.3 8 7 6.2
63 31.5 21 15.75 12.6 10.5 9 7.875 7
64 32 21.3 16 12.8 10.6 9.143 8 7.1
72 36 24 18 14.4 12 10.286 9 8
84 42 28 21 16.8 14 12 10.5 9.3
96 48 32 24 19.2 16 13.714 12 10.6
108 54 36 27 21.6 18 15.429 13.5 12
112 56 37.3 28 22.4 18.6 16 14 12.4
126 63 42 31.5 25.2 21 18 15.75 14
128 64 42.6 32 25.6 21.3 18.286 16 14.2
144 72 48 36 28.8 24 20.571 18 16
168 84 56 42 33.6 28 24 21 18.6
192 96 64 48 38.4 32 27.429 24 21.3
216 108 72 54 43.2 36 30.857 27 24
224 112 74.6 56 44.8 37.3 32 28 24.8
252 126 84 63 50.4 42 36 31.5 28
256 128 85.3 64 51.2 42.6 36.571 32 28.4
288 144 96 72 57.6 48 41.143 36 32
336 168 112 84 67.2 56 48 42 37.3
384 192 128 96 76.8 64 54.857 48 42.6
432 216 144 108 86.4 72 61.714 54 48
448 224 149.3 112 89.6 74.6 64 56 49.7
504 252 168 126 100.8 84 72 63 56
512 256 170.6 128 102.4 85.3 73.143 64 56.8
576 288 192 144 115.2 96 82.286 72 64
672 336 224 168 134.4 112 96 84 74.6
768 384 256 192 153.6 128 109.714 96 85.3

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