271edo: Difference between revisions

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'''271 EDO''' divides the [[Octave|octave]] into 271 [[Equal|equal]] intervals, each 4.428 [[cent|cent]]s in size. 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 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.

=~~Scales~~=

== Theory ==

[[~~pepperoni7~~|~~pepperoni7~~]]

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.

~~[[pepperoni12~~|~~pepperoni12]]~~

=== Odd harmonics ===

[[~~cantonpenta|cantonpenta~~]] [[~~Category:271edo~~]]

=== Subsets and supersets ===

[[Category:~~edo~~]]

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

== Scales ==

* [[Pepperoni7]]

* [[Pepperoni12]]

* [[Cantonpenta]]

[[Category:Pepperoni]]

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-'''271 EDO''' divides the [[Octave|octave]] into 271 [[Equal|equal]] intervals, each 4.428 [[cent|cent]]s in size. 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 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.
+{{Infobox ET}}
+{{ED intro}}
-=Scales=
+== Theory ==
-[[pepperoni7|pepperoni7]]
+edo 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.
-[[pepperoni12|pepperoni12]]
+=== Odd harmonics ===
+{{Harmonics in equal|271}}
-[[cantonpenta|cantonpenta]]      [[Category:271edo]]
+=== Subsets and supersets ===
-[[Category:edo]]
+edo is the 58th [[prime edo]].
+== Scales ==
+* [[Pepperoni7]]
+* [[Pepperoni12]]
+* [[Cantonpenta]]
+[[Category:Pepperoni]]