127edo: Difference between revisions

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== 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 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[würschmidt]] temperament.

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

* In the [[7-limit]], it also tempers out [[225/224]], and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.

* In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.

* 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-3 temperament]] tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val.

* 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.

=== Odd harmonics ===

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=== Subsets and supersets ===

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

127edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]].

== Scales ==

=== MOS scales ===

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

== Instruments ==

* [[Lumatone mapping for 127edo]]

[[Category:Würschmidt]]

[[Category:Hemiwürschmidt]]

[[Category:Minerva]]

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 {{Infobox ET}}
-{{EDO intro|127}}
+{{ED intro}}
 == 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 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[würschmidt]] temperament.
-* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]].
+* In the [[7-limit]], it also tempers out [[225/224]], and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
-* In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
+* 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-3 temperament]] tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val.
-* 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.
 === Odd harmonics ===
@@ Line 13: / Line 12: @@
 === Subsets and supersets ===
-edo is the 31st [[prime edo]].
+edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]].
 == Scales ==
 === MOS scales ===
 See [[List of MOS scales in 127edo]].
+== Instruments ==
+* [[Lumatone mapping for 127edo]]
 [[Category:Würschmidt]]
 [[Category:Hemiwürschmidt]]
 [[Category:Minerva]]