Hemififths: Difference between revisions
m Text replacement - "[[Logarithmic approximants #" to "[[" |
Added temperament infobox, plus some minor changes |
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: ''This page is about the regular temperament. For the irrational interval of a hemififth, see [[sqrt(3/2)]].'' | : ''This page is about the regular temperament. For the irrational interval of a hemififth, see [[sqrt(3/2)]].'' | ||
{{Infobox regtemp | |||
| Title = Hemififths | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11.13 | |||
| Comma basis = [[2401/2400]], [[5120/5103]] (2.3.5.7); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (2.3.5.7.11.13) | |||
| Generator = 11/9 | |||
| Mapping = 1; 2 25 13 5 -1 | |||
| Pergen = (P8, P5/2) | |||
| Edo join 1 = 41 | Edo join 2 = 58 | |||
| Optimization method = CTE | |||
| Generator tuning = 351.4 | |||
| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]] | |||
| Odd limit 1 = 9 | Mistuning 1 = 1.90 | Complexity 1 = 58 | |||
| Odd limit 2 = (13-limit) 21 | Mistuning 2 = 7.77 | Complexity 2 = 58 | |||
}} | |||
'''Hemififths''' is a [[regular temperament|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the hemifamity comma, [[5120/5103]]. | '''Hemififths''' is a [[regular temperament|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the hemifamity comma, [[5120/5103]]. | ||
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| 351.220 | | 351.220 | ||
| Lower bound of 11- to 15-odd-limit<br>and 13-limit 21-odd-limit diamond monotone | | Lower bound of 11- to 15-odd-limit<br>and (13-limit) 21-odd-limit diamond monotone | ||
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| 15/13 | | 15/13 | ||
| 351.705 | | 351.705 | ||
| 15-odd-limit minimax | | 15-odd-limit and (13-limit) 21-odd-limit minimax | ||
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| [[58edo|17\58]] | | [[58edo|17\58]] | ||
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| 352.941 | | 352.941 | ||
| Upper bound of 7- to 15-odd-limit<br>and 13-limit 21-odd-limit diamond monotone | | Upper bound of 7- to 15-odd-limit<br>and (13-limit) 21-odd-limit diamond monotone | ||
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