Würschmidt family: Difference between revisions

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[[Mos scale]]s may not be the best approach for würschmidt since they are even more extreme than those of [[magic]]. [[Proper]] scales does not appear until 28, 31 or even 34 notes, depending on the specific tuning.

The 7-limit ~~extension~~ are ~~can be defined by adding another comma~~. Septimal würschmidt adds ~~[[225/224]]~~, worschmidt adds ~~[[126~~/~~125]]~~, whirrschmidt adds 4375/4374 = {{| -1 -7 4 1 }}. These all use the same generator as 5-limit würschmidt.

The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Septimal würschmidt adds {{monzo| 12 3 -6 -1 }}, worschmidt adds 65625/65536 = {{monzo| -16 1 5 1 }}, whirrschmidt adds 4375/4374 = {{monzo| -1 -7 4 1 }}. These all use the same generator as 5-limit würschmidt.

Hemiwürschmidt adds 6144/6125 = {{monzo| 11 1 -3 -2 }} and splits the generator in two. This temperament is the best extension available for würschmidt despite its complexity. The details can be found in [[Hemimean clan #Hemiwürschmidt|Hemimean clan]].

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 [[Mos scale]]s may not be the best approach for würschmidt since they are even more extreme than those of [[magic]]. [[Proper]] scales does not appear until 28, 31 or even 34 notes, depending on the specific tuning.
-The 7-limit extension are can be defined by adding another comma. Septimal würschmidt adds [[225/224]], worschmidt adds [[126/125]], whirrschmidt adds 4375/4374 = {{| -1 -7 4 1 }}. These all use the same generator as 5-limit würschmidt.
+The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Septimal würschmidt adds {{monzo| 12 3 -6 -1 }}, worschmidt adds 65625/65536 = {{monzo| -16 1 5 1 }}, whirrschmidt adds 4375/4374 = {{monzo| -1 -7 4 1 }}. These all use the same generator as 5-limit würschmidt.
 Hemiwürschmidt adds 6144/6125 = {{monzo| 11 1 -3 -2 }} and splits the generator in two. This temperament is the best extension available for würschmidt despite its complexity. The details can be found in [[Hemimean clan #Hemiwürschmidt|Hemimean clan]].