940edo: Difference between revisions
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{{EDO intro|940}} | {{EDO intro|940}} | ||
940edo is | 940edo is distinctly [[consistent]] through the [[11-odd-limit]], tempering out [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675. | ||
The non-patent val {{val|940 1491 2184 2638 3254 3481}} gives a tuning almost identical to the POTE tuning for the 13-limit [[ | The non-patent val {{val| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363. | ||
In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location. | |||
=== Odd harmonics === | === Odd harmonics === | ||
{{ | {{Harmonics in equal|940}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
940edo has subset edos {{EDOs| | 940edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which [[94edo]] is notable. | ||
[[1880edo]], which doubles 940edo, provides good correction for harmonics 13 | [[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit. | ||
Revision as of 08:47, 10 May 2023
| ← 939edo | 940edo | 941edo → |
940edo is distinctly consistent through the 11-odd-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it supports decoid and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the optimal patent val for 13-limit decoid. It also gives the optimal patent val for the greenland and baffin temperaments, and for the rank-5 temperament tempering out 676/675.
The non-patent val ⟨940 1491 2184 2638 3254 3481] gives a tuning almost identical to the POTE tuning for the 13-limit pele temperament, tempering out 196/195, 352/351 and 364/363.
In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.173 | +0.495 | +0.110 | +0.345 | +0.171 | -0.528 | -0.609 | -0.275 | -0.066 | +0.283 | -0.189 |
| Relative (%) | +13.5 | +38.8 | +8.6 | +27.0 | +13.4 | -41.3 | -47.7 | -21.5 | -5.2 | +22.2 | -14.8 | |
| Steps (reduced) |
1490 (550) |
2183 (303) |
2639 (759) |
2980 (160) |
3252 (432) |
3478 (658) |
3672 (852) |
3842 (82) |
3993 (233) |
4129 (369) |
4252 (492) | |
Subsets and supersets
940edo has subset edos 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, of which 94edo is notable.
1880edo, which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.