Würschmidt: Difference between revisions
m Adopt template for monzo. Style in the infobox |
m if prime 11 was included (which i think it should be but idk how to calculate minimax), then a 31 note (not 34) MOS would make sense to reach 3 * 11 = 33 otonally. as is, 23 is at 14 gens, so 25 notes is very generous (barely allows 27 = 3^3 to be reached) |
||
| Line 10: | Line 10: | ||
| Color name = Saquadbiguti | | Color name = Saquadbiguti | ||
| Odd limit 1 = 5 | Mistuning 1 = 1.43 | Complexity 1 = 19 | | 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 = | | Odd limit 2 = (2.3.5.23) 25 | Mistuning 2 = 2.86 | Complexity 2 = 25 | ||
}} | }} | ||
'''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. | '''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. | ||