99edo: Difference between revisions
From Xenharmonic Reference
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'''99edo''' is an equal tuning with steps of size 12.12... cents. It is | '''99edo''' is an equal tuning with steps of size 12.12... cents. It is arguably the edo below 100 that models 7-limit just intonation the most faithfully. | ||
== Theory == | == Theory == | ||
Revision as of 14:39, 8 April 2026
99edo is an equal tuning with steps of size 12.12... cents. It is arguably the edo below 100 that models 7-limit just intonation the most faithfully.
Theory
Prime approximations
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +1.1 | +1.6 | +0.9 | -5.9 | -4.2 | +4.1 | +5.5 | +2.0 | +0.7 | -5.6 |
| Relative (%) | 0.0 | +8.9 | +12.9 | +7.2 | -48.4 | -34.4 | +34.1 | +45.5 | +16.7 | +6.0 | -46.5 | |
| Steps
(reduced) |
99
(0) |
157
(58) |
230
(32) |
278
(80) |
342
(45) |
366
(69) |
405
(9) |
421
(25) |
448
(52) |
481
(85) |
490
(94) | |
Edostep interpretations
1\99 represents the following 7-limit ratios:
- 126/125
- 225/224
- 245/243
- 1029/1024
- 1728/1715
- 2048/2025
- 4000/3969
2\99 represents the following 7-limit ratios:
- 64/63
- 81/80
3\99 represents the following 7-limit ratios:
- 49/48
- 50/49
- 128/125
Temperaments
99edo notably supports
Derivation
Todo: Derive 99edo from
- Didacus
- Aberschismic
- Don't temper out 81/80, 64/63, or 128/125
- Ennealimmal
| View • Talk • EditEqual temperaments | |
|---|---|
| EDOs | |
| Macrotonal | 5 • 7 • 8 • 9 • 10 • 11 |
| 12-23 | 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 |
| 24-35 | 24 • 25 • 26 • 27 • 29 • 31 • 32 • 34 • 35 |
| 36-47 | 36 • 37 • 39 • 40 • 41 • 43 • 44 • 45 • 46 • 47 |
| 48-59 | 48 • 50 • 51 • 53 • 54 • 56 • 57 • 58 |
| 60-71 | 60 • 63 • 64 • 65 • 67 • 68 • 70 |
| 72-83 | 72 • 77 • 80 • 81 |
| 84-95 | 84 • 87 • 89 • 90 • 93 • 94 |
| Large EDOs | 99 • 104 • 106 • 111 • 118 • 130 • 140 • 152 • 159 • 171 • 217 • 224 • 239 • 270 • 306 • 311 • 612 • 665 |
| Nonoctave equal temperaments | |
| Tritave | 4 • 9 • 13 • 17 • 26 • 39 |
| Fifth | 8 • 9 • 11 • 20 |
| Other | |
