137edo: Difference between revisions

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~~The '''~~137 equal division''' divides the octave into 137 equal parts of 8.759 cents each. It is the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament tempering out 2430/2401. It tempers out 2109375/2097152 (the semicomma) in the 5-limit; 225/224 and 1728/1715 in the 7-limit; 243/242 in the 11-limit; 351/350 in the 13-limit; 375/374 and 442/441 in the 17-limit; and 324/323 and 495/494 in the 19-limit. Since it is the 33rd [[prime number]], 137edo has no proper divisors aside from 1.

A diagram of 7-limit ~~Orwell~~ based on the 31\137edo generator:

== Theory ==

137edo provides the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament tempering out [[2430/2401]]. It tempers out 2109375/2097152 ([[semicomma]]) in the 5-limit; [[225/224]] and [[1728/1715]] in the 7-limit; [[243/242]] in the 11-limit; [[351/350]] in the 13-limit; [[375/374]] and [[442/441]] in the 17-limit; and [[324/323]] and [[495/494]] in the 19-limit.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 137 is the 33rd [[prime number]], 137edo has no proper divisors aside from 1.

== Diagrams ==

A diagram of 7-limit orwell based on the 31\137edo generator:

[[File:137edo_MOS_031_demo_correction.png|alt=137edo_MOS_031_demo_correction.png|137edo_MOS_031_demo_correction.png]]

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[[:File:137edo_MOS_031.svg|137edo_MOS_031.svg]]

~~{{Harmonics in equal|137}}~~

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

[[Category:Nuwell]]

[[Category:Orwell]]

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

[[Category:Orson]]

~~[[Category:Semicomma~~]]

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 {{Infobox ET}}
-The '''137 equal division''' divides the octave into 137 equal parts of 8.759 cents each. It is the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament tempering out 2430/2401. It tempers out 2109375/2097152 (the semicomma) in the 5-limit; 225/224 and 1728/1715 in the 7-limit; 243/242 in the 11-limit; 351/350 in the 13-limit; 375/374 and 442/441 in the 17-limit; and 324/323 and 495/494 in the 19-limit. Since it is the 33rd [[prime number]], 137edo has no proper divisors aside from 1.
+{{EDO intro|137}}
-A diagram of 7-limit Orwell based on the 31\137edo generator:
+== Theory ==
+edo provides the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament tempering out [[2430/2401]]. It tempers out 2109375/2097152 ([[semicomma]]) in the 5-limit; [[225/224]] and [[1728/1715]] in the 7-limit; [[243/242]] in the 11-limit; [[351/350]] in the 13-limit; [[375/374]] and [[442/441]] in the 17-limit; and [[324/323]] and [[495/494]] in the 19-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|137}}
+=== Subsets and supersets ===
+Since 137 is the 33rd [[prime number]], 137edo has no proper divisors aside from 1.
+== Diagrams ==
+A diagram of 7-limit orwell based on the 31\137edo generator:
 [[File:137edo_MOS_031_demo_correction.png|alt=137edo_MOS_031_demo_correction.png|137edo_MOS_031_demo_correction.png]]
@@ Line 8: / Line 18: @@
 [[:File:137edo_MOS_031.svg|137edo_MOS_031.svg]]
-{{Harmonics in equal|137}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Nuwell]]
 [[Category:Orwell]]
-[[Category:Prime EDO]]
+[[Category:Orson]]
-[[Category:Semicomma]]