Würschmidt: Difference between revisions

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{{Infobox Regtemp

| Title = Würschmidt

| Subgroups = 2.3.5, 2.3.5.23

| Comma basis = [[393216/390625]] (2.3.5); <br> [[576/575]], [[12167/12150]] (2.3.5.23)

| Edo join 1 = 31 | Edo join 2 = 34

| Generator = 5/4 | Generator tuning = 387.734 | Optimization method = CTE

| MOS scales = [[3L 1s]], [[3L 4s]] ... [[3L 28s]], [[31L 3s]]

| Mapping = 1; 8 1 14

| Ploidacot = haploid beta-octacot

| Odd limit 1 = 5 | Mistuning 1 = 1.43 | Complexity 1 = 19

| Odd limit 2 = (2.3.5.23) 25 | Mistuning 2 = 2.86 | Complexity 2 = 34

}}

'''Würschmidt''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[würschmidt family]], characterized by tempering out the würschmidt comma, [[393216/390625]]. It can be treated as analogous to [[schismatic]] with the roles of the primes 3 and 5 reversed, since würschmidt is [[generator|generated]] by a [[5/4|classical major third (5/4)]], very slightly sharpened so that eight of them make the sixth harmonic ([[6/1]]), giving [[3/2]] the same complexity [[5/4]] does in schismatic, but with comparable accuracy on the part of the generator. Four generators, therefore, reach the interval [[625/512]], which is equated to [[768/625]] and functions as a neutral third.

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+{{Infobox Regtemp
+| Title = Würschmidt
+| Subgroups = 2.3.5, 2.3.5.23
+| Comma basis = [[393216/390625]] (2.3.5); <br> [[576/575]], [[12167/12150]] (2.3.5.23)
+| Edo join 1 = 31 | Edo join 2 = 34
+| Generator = 5/4 | Generator tuning = 387.734 | Optimization method = CTE
+| MOS scales = [[3L 1s]], [[3L 4s]] ... [[3L 28s]], [[31L 3s]]
+| Mapping = 1; 8 1 14
+| Ploidacot = haploid beta-octacot
+| Odd limit 1 = 5 | Mistuning 1 = 1.43 | Complexity 1 = 19
+| Odd limit 2 = (2.3.5.23) 25 | Mistuning 2 = 2.86 | Complexity 2 = 34
+}}
 '''Würschmidt''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[würschmidt family]], characterized by tempering out the würschmidt comma, [[393216/390625]]. It can be treated as analogous to [[schismatic]] with the roles of the primes 3 and 5 reversed, since würschmidt is [[generator|generated]] by a [[5/4|classical major third (5/4)]], very slightly sharpened so that eight of them make the sixth harmonic ([[6/1]]), giving [[3/2]] the same complexity [[5/4]] does in schismatic, but with comparable accuracy on the part of the generator. Four generators, therefore, reach the interval [[625/512]], which is equated to [[768/625]] and functions as a neutral third.