127edo: Difference between revisions

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'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma|comma]]s it [[tempering_out|tempers out]]. In the [[5-limit|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence supports [[Würschmidt_family|würschmidt temperament]]. In the [[7-limit|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|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|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~~.

== 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 [[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.

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

=== Odd harmonics ===

[[~~Category:hemiwuerschmidt~~]]

[[~~Category:minerva~~]]

[[~~Category:prime_edo~~]]

=== Subsets and supersets ===

[[Category:~~theory~~]]

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

[[Category:~~wuerschmidt~~]]

[[Category:~~wurschmidt~~]]

== Scales ==

=== MOS scales ===

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

== Instruments ==

* [[Lumatone mapping for 127edo]]

[[Category:Würschmidt]]

[[Category:Hemiwürschmidt]]

[[Category:Minerva]]

@@ Line 1: / Line 1: @@
-'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma|comma]]s it [[tempering_out|tempers out]]. In the [[5-limit|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence supports [[Würschmidt_family|würschmidt temperament]]. In the [[7-limit|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|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|optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
+{{Infobox ET}}
+{{ED intro}}
-edo is the 31st [[prime_numbers|prime]] edo.
+== 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 [[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.
-[[MOS_Scales_of_127edo|MOS Scales of 127edo]]      [[Category:edo]]
+=== Odd harmonics ===
-[[Category:hemiwuerschmidt]]
+{{Harmonics in equal|127}}
-[[Category:minerva]]
-[[Category:prime_edo]]
+=== Subsets and supersets ===
-[[Category:theory]]
+edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]].
-[[Category:wuerschmidt]]
-[[Category:wurschmidt]]
+== Scales ==
+=== MOS scales ===
+See [[List of MOS scales in 127edo]].
+== Instruments ==
+* [[Lumatone mapping for 127edo]]
+[[Category:Würschmidt]]
+[[Category:Hemiwürschmidt]]
+[[Category:Minerva]]