Würschmidt family: Difference between revisions
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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. | 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. | ||
The S-expression-based comma list of the 11-limit würschmidt discussed here is {[[176/175|S8/S10]], [[243/242|S9/S11]], [[225/224|S15]]}. Tempering out [[81/80|S9]] or [[121/120|S11]] results in [[31edo]], and in complementary fashion, tempering out [[64/63|S8]] or [[100/99|S10]] results in [[34edo]], but specifically, the 34d [[val]] where we accept 17edo's mapping of ~7. Their val sum, 31 + 34d = 65d, thus observes all of these [[square superparticular]]s by equating them as S8 = S9 = S10 = S11, hence its S-expression-based comma list is {[[5120/5103|S8/S9]], [[8019/8000|S9/S10]], [[4000/3993|S10/S11]]}, which may be expressed in shortened form as {S8/9/10/11}. The advantage of this form is we can easily see that all of the [[semiparticular]] commas expected are implied by reading them off as ratios, like 8/10 and 9/11, in the shortened form. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||