271edo: Difference between revisions
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== Theory == | |||
271edo is the highest edo where the [[3/2|perfect fifth]] has greater absolute error than [[12edo]]. It is in[[consistent]] in the [[5-odd-limit]]. Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[4000/3969]] and [[65625/65536]] in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is the [[optimal patent val]] for the [[pepperoni]] temperament, tempering out 352/351 and 364/363 on the 2.3.11/7.13/7 [[subgroup]] of the 13-limit. | |||
=== | === Odd harmonics === | ||
{{Harmonics in equal|271}} | {{Harmonics in equal|271}} | ||
=== Subsets and supersets === | |||
271edo is the 58th [[prime edo]]. | |||
== Scales == | == Scales == | ||
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* [[Cantonpenta]] | * [[Cantonpenta]] | ||
[[Category: | [[Category:Pepperoni]] | ||
Latest revision as of 07:00, 20 February 2025
| ← 270edo | 271edo | 272edo → |
271 equal divisions of the octave (abbreviated 271edo or 271ed2), also called 271-tone equal temperament (271tet) or 271 equal temperament (271et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 271 equal parts of about 4.43 ¢ each. Each step represents a frequency ratio of 21/271, or the 271st root of 2.
Theory
271edo is the highest edo where the perfect fifth has greater absolute error than 12edo. It is inconsistent in the 5-odd-limit. Using the patent val nonetheless, the equal temperament tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is the optimal patent val for the pepperoni temperament, tempering out 352/351 and 364/363 on the 2.3.11/7.13/7 subgroup of the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.10 | -1.07 | +0.92 | -0.22 | +2.19 | +0.80 | +1.03 | +1.32 | -0.83 | -1.41 | +0.51 |
| Relative (%) | +47.5 | -24.3 | +20.7 | -5.0 | +49.4 | +18.1 | +23.3 | +29.8 | -18.8 | -31.8 | +11.5 | |
| Steps (reduced) |
430 (159) |
629 (87) |
761 (219) |
859 (46) |
938 (125) |
1003 (190) |
1059 (246) |
1108 (24) |
1151 (67) |
1190 (106) |
1226 (142) | |
Subsets and supersets
271edo is the 58th prime edo.