127edo: Difference between revisions

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'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is an equal division 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~~]].

== Theory ==

* 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.

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

* 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.

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

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

=== Odd harmonics ===

=== ~~Harmonics~~ ===

=== Subsets and supersets ===

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

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

== Scales ==

=== MOS scales ===

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

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

== Instruments ==

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

* [[Lumatone mapping for 127edo]]

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

[[Category:Würschmidt]]

[[Category:Hemiwürschmidt]]

[[Category:Minerva]]

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

~~[[Category:Würschmidt]]~~

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 {{Infobox ET}}
-'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is an equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering_out|tempers out]]:
+{{ED intro}}
-* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]].
+== Theory ==
-* 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.
+edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]:
-* 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.
+* In the [[5-limit]], it tempers out 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[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 [[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.
-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]], following [[113edo]] and before [[131edo]].
+== Scales ==
+=== MOS scales ===
+See [[List of MOS scales in 127edo]].
-=== MOS Scales ===
+== Instruments ==
-[[MOS_Scales_of_127edo|MOS Scales of 127edo]]
+* [[Lumatone mapping for 127edo]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Würschmidt]]
 [[Category:Hemiwürschmidt]]
 [[Category:Minerva]]
-[[Category:Prime EDO]]
-[[Category:Würschmidt]]