Würschmidt family: Difference between revisions

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== Septimal würschmidt ==

Würschmidt, aside from the commas listed above, also tempers out [[225/224]]. [[31edo]] or [[127edo]] can be used as tunings. It extends naturally to an 11-limit version ~~{{Multival| 8 1 18 20 … }}~~ which also tempers out [[99/98]], [[176/175]] and 243/242. 127edo is again an excellent tuning for 11-limit würschmidt, as well as for [[minerva]], the 11-limit rank-3 temperament tempering out 99/98 and 176/175.

Würschmidt, aside from the commas listed above, also tempers out [[225/224]]. [[31edo]] or [[127edo]] can be used as tunings. It extends naturally to an 11-limit version which also tempers out [[99/98]], [[176/175]] and 243/242. 127edo is again an excellent tuning for 11-limit würschmidt, as well as for [[minerva]], the 11-limit rank-3 temperament tempering out 99/98 and 176/175.

2-würschmidt, the temperament with all the same commas as würschmidt but a generator of twice the size, is equivalent to [[skwares]] as a 2.3.7.11 subgroup temperament.

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~~{{Multival|legend=1| 8 1 18 -17 6 39 }}~~

[[Optimal tuning]]s:

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~~{{Multival|legend=1| 8 1 -13 -17 -43 -33 }}~~

[[Optimal tuning]]s:

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~~{{Multival|legend=1| 8 1 52 -17 60 118 }}~~

[[Optimal tuning]]s:

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[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Würschmidt family| ]]

[[Category:Würschmidt| ]]

[[Category:Rank 2]]

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 == Septimal würschmidt ==
-Würschmidt, aside from the commas listed above, also tempers out [[225/224]]. [[31edo]] or [[127edo]] can be used as tunings. It extends naturally to an 11-limit version {{Multival| 8 1 18 20 … }} which also tempers out [[99/98]], [[176/175]] and 243/242. 127edo is again an excellent tuning for 11-limit würschmidt, as well as for [[minerva]], the 11-limit rank-3 temperament tempering out 99/98 and 176/175.
+Würschmidt, aside from the commas listed above, also tempers out [[225/224]]. [[31edo]] or [[127edo]] can be used as tunings. It extends naturally to an 11-limit version which also tempers out [[99/98]], [[176/175]] and 243/242. 127edo is again an excellent tuning for 11-limit würschmidt, as well as for [[minerva]], the 11-limit rank-3 temperament tempering out 99/98 and 176/175.
 -würschmidt, the temperament with all the same commas as würschmidt but a generator of twice the size, is equivalent to [[skwares]] as a 2.3.7.11 subgroup temperament.
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 {{Mapping|legend=1| 1 -1 2 -3 | 0 8 1 18 }}
-{{Multival|legend=1| 8 1 18 -17 6 39 }}
 [[Optimal tuning]]s:
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 {{Mapping|legend=1| 1 -1 2 7 | 0 8 1 -13 }}
-{{Multival|legend=1| 8 1 -13 -17 -43 -33 }}
 [[Optimal tuning]]s:
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 {{Mapping|legend=1| 1 -1 2 -14 | 0 8 1 52 }}
-{{Multival|legend=1| 8 1 52 -17 60 118 }}
 [[Optimal tuning]]s:
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 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Würschmidt family| ]] <!-- main article -->
 [[Category:Würschmidt| ]] <!-- key article -->
 [[Category:Rank 2]]