Würschmidt: Difference between revisions
m got rid of stupidly high-odd-limit intervals |
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{{Infobox | {{interwiki | ||
| de = Würschmidt | |||
| en = Würschmidt | |||
}} | |||
{{Infobox regtemp | |||
| Title = Würschmidt | | Title = Würschmidt | ||
| Subgroups = 2.3.5, 2.3.5.23 | | Subgroups = 2.3.5, 2.3.5.23 | ||
| Comma basis = [[393216/390625]] (2.3.5); <br> [[576/575]], [[12167/12150]] (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 | | Edo join 1 = 31 | Edo join 2 = 34 | ||
| | | Mapping = 1; 8 1 14 | ||
| Generators = 5/4 | Generators tuning = 387.8 | Optimization method = CWE | |||
| MOS scales = [[3L 1s]], [[3L 4s]], …, [[3L 28s]], [[31L 3s]] | | MOS scales = [[3L 1s]], [[3L 4s]], …, [[3L 28s]], [[31L 3s]] | ||
| Pergen = (P8, ccP5/8) | | Pergen = (P8, ccP5/8) | ||
| 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 = | | 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 [[schismic]] 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 schismic, 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 [[schismic]] 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 schismic, 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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=== Optimized tunings === | === Optimized tunings === | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | | |+ style="font-size: 105%; white-space: nowrap;" | Norm-based tunings | ||
|- | |- | ||
! rowspan="2" | Weight-skew\Order !! colspan="2" | Euclidean | ! rowspan="2" | Weight-skew\Order !! colspan="2" | Euclidean | ||
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| | | | ||
| 385.7143 | | 385.7143 | ||
| 28ei val | | 28ei val, major thirds slightly flatter than this fall under 25&28 or [[magic]] | ||
|- | |- | ||
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| | | | ||
| '''400.0000''' | | '''400.0000''' | ||
| '''Upper bound of 2.3.5.23-subgroup 25-odd-limit diamond monotone''' | | '''Upper bound of 2.3.5.23-subgroup 25-odd-limit diamond monotone''', major thirds slightly sharper than this fall under [[smate_family|smate]] | ||
|} | |} | ||
<nowiki />* Besides the octave | <nowiki />* Besides the octave | ||