127edo: Difference between revisions

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127edo is interesting because of its approximations, defined by the [[comma]]s it [[~~tempering_out~~|tempers out]]:

== Theory ==

127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]:

* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]].

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* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

~~127edo is the 31st [[prime_numbers~~|~~prime]] edo.~~

=== Odd harmonics ===

=== ~~Harmonics~~ ===

=== Subsets and supersets ===

~~{{Harmonics in equal|127}}~~

127edo is the 31st [[prime edo]].

=== MOS ~~Scales~~ ===

== Scales ==

[[~~MOS_Scales_of_127edo|~~MOS ~~Scales of~~ 127edo]]

=== MOS scales ===

See [[List of MOS scales in 127edo]].

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

[[Category:Würschmidt]]

[[Category:Hemiwürschmidt]]

[[Category:Minerva]]

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

~~[[Category:Würschmidt]]~~

@@ Line 2: / Line 2: @@
 {{EDO intro|127}}
-edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering_out|tempers out]]:
+== Theory ==
+edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]:
 * In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]].
@@ Line 8: / Line 9: @@
 * In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
-edo is the 31st [[prime_numbers|prime]] edo.
+=== Odd harmonics ===
+{{Harmonics in equal|127}}
-=== Harmonics ===
+=== Subsets and supersets ===
-{{Harmonics in equal|127}}
+edo is the 31st [[prime edo]].
-=== MOS Scales ===
+== Scales ==
-[[MOS_Scales_of_127edo|MOS Scales of 127edo]]
+=== MOS scales ===
+See [[List of MOS scales in 127edo]].
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Würschmidt]]
 [[Category:Hemiwürschmidt]]
 [[Category:Minerva]]
-[[Category:Prime EDO]]
-[[Category:Würschmidt]]