271edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled
18,215 edits
mNo edit summary
Rework
Line 1: Line 1:
{{Infobox ET}}
{{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.
{{EDO intro}}


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.


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|271}}
{{Harmonics in equal|271}}
=== Subsets and supersets ===
271edo is the 58th [[prime edo]].


== Scales ==
== Scales ==
Line 12: Line 16:
* [[Cantonpenta]]
* [[Cantonpenta]]


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Pepperoni]]
[[Category:Prime EDO]]

Revision as of 06:48, 8 March 2024

← 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

Template:EDO intro

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

Approximation of odd harmonics in 271edo
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.

Scales

Retrieved from "https://en.xen.wiki/index.php?title=271edo&oldid=138574"