99693edo: Difference between revisions
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== Theory == | == Theory == | ||
{{todo|complete section}} | {{todo|complete section}} | ||
{{Harmonics in equal|99693|columns= | {{Harmonics in equal|99693|columns=547|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 13:17, 10 January 2025
| ← 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 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | 57 | 59 | 61 | 63 | 65 | 67 | 69 | 71 | 73 | 75 | 77 | 79 | 81 | 83 | 85 | 87 | 89 | 91 | 93 | 95 | 97 | 99 | 101 | 103 | 105 | 107 | 109 | 111 | 113 | 115 | 117 | 119 | 123 | 125 | 127 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 | +0.003 | +0.005 | -0.000 | +0.005 | -0.005 | +0.005 | -0.004 | +0.004 | -0.003 | -0.001 | +0.005 | -0.001 | -0.004 | -0.004 | +0.000 | +0.000 | +0.001 | +0.004 | -0.002 | +0.003 | -0.002 | +0.005 | +0.003 | +0.002 | +0.004 | +0.002 | -0.005 | -0.004 | -0.004 | +0.005 | -0.004 | +0.005 | -0.001 | -0.005 | -0.001 | -0.004 | -0.003 | -0.001 | +0.005 | +0.004 | -0.001 | -0.005 | -0.003 | -0.001 | -0.001 | +0.001 | +0.001 |
| 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 | +21.7 | +38.8 | -3.4 | +39.7 | -43.2 | +38.8 | -31.1 | +37.4 | -26.8 | -10.0 | +42.6 | -9.4 | -30.4 | -33.4 | +0.3 | +3.3 | +8.6 | +37.0 | -12.9 | +26.0 | -18.0 | +37.8 | +24.9 | +18.6 | +33.4 | +19.4 | -41.1 | -36.6 | -29.3 | +42.9 | -35.9 | +38.5 | -11.1 | -45.0 | -7.7 | -29.7 | -27.8 | -6.8 | +40.0 | +29.9 | -10.1 | -44.0 | -27.0 | -6.7 | -9.9 | +6.7 | +5.8 | |
| 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) |
502891 (4426) |
511354 (12889) |
519346 (20881) |
526918 (28453) |
534110 (35645) |
540961 (42496) |
547499 (49034) |
553754 (55289) |
559747 (61282) |
565501 (67036) |
571034 (72569) |
576361 (77896) |
581498 (83033) |
586458 (87993) |
591253 (92788) |
595893 (97428) |
600388 (2230) |
604747 (6589) |
608977 (10819) |
613087 (14929) |
617082 (18924) |
620970 (22812) |
624755 (26597) |
628443 (30285) |
632039 (33881) |
635547 (37389) |
638971 (40813) |
642316 (44158) |
645585 (47427) |
648782 (50624) |
651908 (53750) |
654969 (56811) |
657965 (59807) |
660900 (62742) |
663777 (65619) |
666597 (68439) |
669363 (71205) |
672077 (73919) |
674741 (76583) |
677356 (79198) |
679924 (81766) |
682447 (84289) |
684927 (86769) |
687365 (89207) |
692120 (93962) |
694440 (96282) |
696723 (98565) | |