127edo: Difference between revisions
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127edo is the | == 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 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[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-3 temperament]] tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|127}} | |||
[[Category: | === Subsets and supersets === | ||
[[Category: | 127edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]]. | ||
== Scales == | |||
=== MOS scales === | |||
See [[List of MOS scales in 127edo]]. | |||
== Instruments == | |||
* [[Lumatone mapping for 127edo]] | |||
[[Category:Würschmidt]] | |||
[[Category:Hemiwürschmidt]] | |||
[[Category:Minerva]] | [[Category:Minerva]] | ||
Latest revision as of 06:51, 30 July 2025
| ← 126edo | 127edo | 128edo → |
127 equal divisions of the octave (abbreviated 127edo or 127ed2), also called 127-tone equal temperament (127tet) or 127 equal temperament (127et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 127 equal parts of about 9.45 ¢ each. Each step represents a frequency ratio of 21/127, or the 127th root of 2.
Theory
127edo is interesting because of its approximations, defined by the commas it tempers out:
- In the 5-limit, it tempers out 393216/390625 (würschmidt comma) and hence supports the 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-3 temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank-4 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, following 113edo and before 131edo.
Scales
MOS scales
See List of MOS scales in 127edo.