66edo: Difference between revisions
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The 66b val tempers out 16875/16384 in the 5-limit, 126/125, 1728/1715 and 2401/2400 in the 7-limit, 99/98 and 385/384 in the 11-limit, and 105/104, 144/143 and 847/845 in the 13-limit. | The 66b val tempers out 16875/16384 in the 5-limit, 126/125, 1728/1715 and 2401/2400 in the 7-limit, 99/98 and 385/384 in the 11-limit, and 105/104, 144/143 and 847/845 in the 13-limit. | ||
109 steps of 66edo is extremely close to [[Pitave|Pi]] with only +0.023 cents of error. | |||
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | ||
[[Category:Ammonite]] | [[Category:Ammonite]] | ||
Revision as of 12:36, 6 March 2023
| ← 65edo | 66edo | 67edo → |
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.14 | -4.50 | -5.19 | -3.91 | -5.86 | -4.16 | +2.64 | +4.14 | -6.60 | +1.95 | +8.09 |
| Relative (%) | +39.2 | -24.7 | -28.5 | -21.5 | -32.2 | -22.9 | +14.5 | +22.7 | -36.3 | +10.7 | +44.5 | |
| Steps (reduced) |
105 (39) |
153 (21) |
185 (53) |
209 (11) |
228 (30) |
244 (46) |
258 (60) |
270 (6) |
280 (16) |
290 (26) |
299 (35) | |
The patent val is contorted in the 5-limit, tempering out the same commas 250/243, 2048/2025 and 3125/3072 as 22edo. In the 7-limit it tempers out 686/675 and 1029/1024, in the 11-limit 55/54, 100/99 and 121/120, in the 13-limit 91/90, 169/168, 196/195 and in the 17-limit 136/135 and 256/255. It provides the optimal patent val for 11- and 13-limit ammonite temperament.
The 66b val tempers out 16875/16384 in the 5-limit, 126/125, 1728/1715 and 2401/2400 in the 7-limit, 99/98 and 385/384 in the 11-limit, and 105/104, 144/143 and 847/845 in the 13-limit.
109 steps of 66edo is extremely close to Pi with only +0.023 cents of error.