Bach Scholar™
Determining Ideal Tempos:
A Unified Theory of Tempo Relativity


Table 3a

Final matrix of theoretically correct tempos. The tempos in this table result are derived when x = 40 is assumed for all the tempos in Table 3b. The progression in this matrix can continue infinitely.


one note duplet triplet quadruplet quintuplet sextuplet septuplet octuplet nonuplet
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
252 126 84 63 50.4 42 36 31.5 28
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
504 252 168 126 100.8 84 72 63 56
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

Copyright © 2008 Bach Scholar™