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 ~~last~~ edo ~~whose~~ perfect fifth ~~is tuned worse~~ 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.

271EDO is the 58th [[prime EDO]].

=== Prime harmonics ===

== Scales ==

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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 last edo whose perfect fifth is tuned worse 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.
 EDO is the 58th [[prime EDO]].
+=== Prime harmonics ===
+{{Primes in edo|edo=271|columns=11|prec=3}}
 == Scales ==