99693edo
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Prime factorization
32 × 11 × 19 × 53
Step size
0.012037¢
Fifth
58317\99693 (701.959¢) (→19439\33231)
Semitones (A1:m2)
9447:7494 (113.7¢ : 90.2¢)
Dual sharp fifth
58317\99693 (701.959¢) (→19439\33231)
Dual flat fifth
58316\99693 (701.947¢)
Dual major 2nd
16940\99693 (203.906¢) (→1540\9063)
Consistency limit
7
Distinct consistency limit
7
| ← 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
| 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 (%) | +33.3 | +2.2 | +36.6 | -33.3 | -11.6 | +6.3 | +35.6 | -43.3 | +36.2 | -30.1 | -46.2 | +4.5 | +0.0 | +30.1 | +30.7 | |
| 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) | |