99693edo: Difference between revisions
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'''99693 equal divisions of the octave''' ('''99693edo''') is the tuning that divides the [[octave]] into 99693 equal steps of about 0.012 [[cent|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). | '''99693 equal divisions of the octave''' ('''99693edo''') is the tuning that divides the [[octave]] into 99693 equal steps of about 0.012 [[cent|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 == | == Theory == | ||
{{todo|complete section}} | |||
{{Harmonics in equal|99693|columns=15|prec=3}} | {{Harmonics in equal|99693|columns=15|prec=3}} | ||
[[Category:99693edo| ]] <!-- main article --> | [[Category:99693edo| ]] <!-- main article --> | ||
[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number --> | [[Category:Equal divisions of the octave|#####]] <!-- 5-digit number --> | ||
Revision as of 04:10, 16 December 2024
| ← 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) | |