271edo: Difference between revisions

(3 intermediate revisions by 2 users not shown)

Line 1:

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~~]].

== 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.

=== ~~Prime~~ harmonics ===

=== Odd harmonics ===

{{~~Primes~~ in ~~edo~~|~~edo~~=~~271|columns~~=~~11|prec~~=~~3}}~~

=== Subsets and supersets ===

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

== Scales ==

Line 12:

Line 16:

* [[Cantonpenta]]

[[Category:~~Equal divisions of the octave|###]] ~~

[[Category:Pepperoni]]

~~[[Category:Prime EDO~~]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-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.
+{{ED intro}}
-EDO is the 58th [[prime EDO]].
+== Theory ==
+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.
-=== Prime harmonics ===
+=== Odd harmonics ===
-{{Primes in edo|edo=271|columns=11|prec=3}}
+{{Harmonics in equal|271}}
+=== Subsets and supersets ===
+edo is the 58th [[prime edo]].
 == Scales ==
@@ Line 12: / Line 16: @@
 * [[Cantonpenta]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Pepperoni]]
-[[Category:Prime EDO]]