99693edo: Difference between revisions
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Revision as of 01:46, 4 July 2022
| ← 99692edo | 99693edo | 99694edo → |
99693 equal divisions of the octave (99693edo) is the tuning that divides the octave into 99693 equal steps of about 0.012 cents. It is notable for being the edo below 100000 with the lowest maximum error, using direct approximation for each harmonic, for the first 547 harmonics (547 being the 100th prime number).
Theory
| Odd harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.004 | +0.000 | +0.004 | -0.004 | -0.001 | +0.001 | +0.004 | -0.005 | +0.004 | -0.004 | -0.006 | +0.001 | +0.000 | +0.004 | +0.004 |
| relative (%) | +33 | +2 | +37 | -33 | -12 | +6 | +36 | -43 | +36 | -30 | -46 | +4 | +0 | +30 | +31 | |
| Steps (reduced) | 158010 (58317) | 231480 (32094) | 279874 (80488) | 316019 (16940) | 344881 (45802) | 368908 (69829) | 389490 (90411) | 407491 (8719) | 423489 (24717) | 437883 (39111) | 450967 (52195) | 462960 (64188) | 474029 (75257) | 484307 (85535) | 493899 (95127) | |