954edo: Difference between revisions
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{{EDO intro|954}} | {{EDO intro|954}} | ||
954edo is a very strong 17-limit system, | 954edo is a very strong 17-limit system, [[consistency|distinctly consistent]] in the 17-limit, and is a [[zeta edo|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out|tempers out]] the [[ennealimma]], {{monzo| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|954|columns=11}} | {{Harmonics in equal|954|columns=11}} | ||
=== | === Subsets and supersets === | ||
Since 954 = | Since 954 = {{factorization|954}}, 954edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}. | ||
[[Category:Ennealimmal]] | [[Category:Ennealimmal]] | ||
[[Category:Hemiennealimmal]] | [[Category:Hemiennealimmal]] | ||
[[Category:Semihemiennealimmal]] | [[Category:Semihemiennealimmal]] | ||
Revision as of 11:22, 2 November 2023
| ← 953edo | 954edo | 955edo → |
954edo is a very strong 17-limit system, distinctly consistent in the 17-limit, and is a zeta peak, integral and gap edo. The tuning of the primes to 17 are all flat, and the equal temperament tempers out the ennealimma, [1 -27 18⟩, in the 5-limit and 2401/2400 and 4375/4374 in the 7-limit, so that it supports the ennealimmal temperament. In the 11-limit it tempers out 3025/3024, 9801/9800, 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out 4225/4224 and 10648/10647 and in the 17-limit 2431/2430 and 2601/2600. It supports and gives the optimal patent val for the semihemiennealimmal temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.068 | -0.150 | -0.272 | -0.375 | -0.276 | -0.553 | +0.600 | -0.601 | +0.611 | -0.381 |
| Relative (%) | +0.0 | -5.4 | -11.9 | -21.7 | -29.8 | -21.9 | -44.0 | +47.7 | -47.8 | +48.6 | -30.3 | |
| Steps (reduced) |
954 (0) |
1512 (558) |
2215 (307) |
2678 (770) |
3300 (438) |
3530 (668) |
3899 (83) |
4053 (237) |
4315 (499) |
4635 (819) |
4726 (910) | |
Subsets and supersets
Since 954 = 2 × 32 × 53, 954edo has subset edos 2, 3, 6, 9, 18, 53, 106, 159, 318, 477.