271edo: Difference between revisions

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The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the highest edo where the perfect fifth has greater absolute error than [[12edo]]. It is inconsistent in the 5-limit. Using the [[patent val]], it 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 an [[optimal patent val]] by some measures{{clarify}} for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.
The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the highest edo where the perfect fifth has greater absolute error than [[12edo]]. It is inconsistent in the 5-limit. Using the [[patent val]], it 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 an [[optimal patent val]] by some measures{{clarify}} for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.


Revision as of 21:45, 4 October 2022

← 270edo 271edo 272edo →
Prime factorization 271 (prime)
Step size 4.42804 ¢ 
Fifth 159\271 (704.059 ¢)
Semitones (A1:m2) 29:18 (128.4 ¢ : 79.7 ¢)
Dual sharp fifth 159\271 (704.059 ¢)
Dual flat fifth 158\271 (699.631 ¢)
Dual major 2nd 46\271 (203.69 ¢)
Consistency limit 3
Distinct consistency limit 3

The 271 equal divisions of the octave divides the octave into 271 equal intervals, each 4.428044 cents in size. 271edo is the highest edo where the perfect fifth has greater absolute error than 12edo. It is inconsistent in the 5-limit. Using the patent val, it 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 an optimal patent val by some measures[clarification needed] for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.

271EDO is the 58th prime EDO.

Prime harmonics

Script error: No such module "primes_in_edo".

Scales

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