Würschmidt: Difference between revisions

Line 5:

| 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]]

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

| Mapping = 1; 8 1 14

| Pergen = (P8, ccP5/8)

Line 12:

| 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]] = [17 1 -8⟩. 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.

'''Würschmidt''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[würschmidt family]], characterized by tempering out the [[würschmidt comma]] ([[ratio]]: 393216/390625, {{monzo|legend=1| 17 1 -8 }}). 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.

@@ Line 5: / Line 5: @@
 | 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]]
+| MOS scales = [[3L 1s]], [[3L 4s]], …, [[3L 28s]], [[31L 3s]]
 | Mapping = 1; 8 1 14
 | Pergen = (P8, ccP5/8)
@@ Line 12: / Line 12: @@
 | 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]] = [17 1 -8⟩. 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.
+'''Würschmidt''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] and parent of the [[würschmidt family]], characterized by tempering out the [[würschmidt comma]] ([[ratio]]: 393216/390625, {{monzo|legend=1| 17 1 -8 }}). 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.
 {{Tdlink|Würschmidt family #Würschmidt}}