764edo: Difference between revisions
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{{EDO intro|764}} | |||
764edo is a very strong 17-limit system distinctly [[consistent]] to the 17-odd-limit, and is the fourteenth [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]]. In the 5-limit it tempers out the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit [[4375/4374]]; in the 11-limit [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; and in the 17-limit 2431/2430, 2500/2499, 4914/4913 and [[5832/5831]]. It provides the [[optimal patent val]] for the [[abigail]] temperament in the 11-limit. | |||
{{ | === Prime harmonics === | ||
{{Harmonics in equal|764|columns=11}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Zeta]] | |||
[[Category: | [[Category:Abigail]] | ||
Revision as of 06:56, 6 October 2022
| ← 763edo | 764edo | 765edo → |
Template:EDO intro 764edo is a very strong 17-limit system distinctly consistent to the 17-odd-limit, and is the fourteenth zeta integral edo. In the 5-limit it tempers out the hemithirds comma, [38 -2 -15⟩; in the 7-limit 4375/4374; in the 11-limit 3025/3024 and 9801/9800; in the 13-limit 1716/1715, 2080/2079, 4096/4095, 4225/4224, 6656/6655 and 10648/10647; and in the 17-limit 2431/2430, 2500/2499, 4914/4913 and 5832/5831. It provides the optimal patent val for the abigail temperament in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.139 | +0.074 | +0.284 | -0.009 | -0.214 | +0.280 | -0.654 | -0.002 | -0.781 | -0.009 |
| Relative (%) | +0.0 | +8.9 | +4.7 | +18.1 | -0.6 | -13.6 | +17.8 | -41.7 | -0.1 | -49.7 | -0.6 | |
| Steps (reduced) |
764 (0) |
1211 (447) |
1774 (246) |
2145 (617) |
2643 (351) |
2827 (535) |
3123 (67) |
3245 (189) |
3456 (400) |
3711 (655) |
3785 (729) | |