99693edo: Difference between revisions
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Created page with "{{Infobox ET | Prime factorization = 3<sup>2</sup> × 11 × 19 × 53 | Step size = 0.012037¢ | Fifth = 58317\99693 = 701.959¢ | Major 2nd = 16941\99693 = 203.918¢ | Minor 2..." |
Added a precision on the claim of lowest maximum error |
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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 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 inconsistent approximation for each harmonic, for the first 547 harmonics (547 being the 100th prime number). | ||
== Theory == | == Theory == | ||
Revision as of 19:06, 7 August 2021
| ← 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 inconsistent 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) | |