954edo: Difference between revisions
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The '''954 equal division''' divides the octave into 954 equal parts of 1.258 cents each. It is a very strong 17-limit system, uniquely [[consistent|consistent]] in the 17-limit, and is the fifteenth [[ | The '''954 equal division''' divides the octave into 954 equal parts of 1.258 cents each. It is a very strong 17-limit system, uniquely [[consistent|consistent]] in the 17-limit, and is the fifteenth [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]] and is also a zeta gap edo. The tuning of the primes to 17 are all flat, and it 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 === | |||
{{Harmonics in equal|954|columns=11}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 10:21, 26 September 2022
The 954 equal division divides the octave into 954 equal parts of 1.258 cents each. It is a very strong 17-limit system, uniquely consistent in the 17-limit, and is the fifteenth zeta integral edo and is also a zeta gap edo. The tuning of the primes to 17 are all flat, and it 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) | |