127edo: Difference between revisions
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{{EDO intro|127}} | {{EDO intro|127}} | ||
127edo is interesting because of its approximations, defined by the [[comma]]s it [[ | == Theory == | ||
127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]: | |||
* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]]. | * In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]]. | ||
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* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val. | * In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|127}} | |||
=== | === Subsets and supersets === | ||
127edo is the 31st [[prime edo]]. | |||
=== MOS | == Scales == | ||
[[ | === MOS scales === | ||
See [[List of MOS scales in 127edo]]. | |||
[[Category: | [[Category:Würschmidt]] | ||
[[Category:Hemiwürschmidt]] | [[Category:Hemiwürschmidt]] | ||
[[Category:Minerva]] | [[Category:Minerva]] | ||
Revision as of 05:31, 29 May 2024
| ← 126edo | 127edo | 128edo → |
Theory
127edo is interesting because of its approximations, defined by the commas it tempers out:
- In the 5-limit, it tempers out the würschmidt comma, 393216/390625 and hence supports würschmidt temperament.
- In the 7-limit, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
- In the 11-limit, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.74 | +1.09 | +4.40 | +3.96 | -3.29 | +0.42 | -1.65 | -1.02 | -4.60 | +1.66 | -4.65 |
| Relative (%) | -29.0 | +11.5 | +46.6 | +42.0 | -34.8 | +4.4 | -17.5 | -10.8 | -48.7 | +17.6 | -49.2 | |
| Steps (reduced) |
201 (74) |
295 (41) |
357 (103) |
403 (22) |
439 (58) |
470 (89) |
496 (115) |
519 (11) |
539 (31) |
558 (50) |
574 (66) | |
Subsets and supersets
127edo is the 31st prime edo.