Hemimean clan: Difference between revisions
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: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Emka]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Emka]].'' | ||
Emka | Emka may be described as the 37 & 50 temperament, which tempers out the hemimean comma and 84035/82944 (quinzo-ayo). It was named by [[Petr Pařízek]] in 2011. | ||
A related temperament of emka is [[horwell temperaments #Emkay|emkay]] (87 & 224), which is more accurate but more complex, and only differs from emka in the mapping of 7. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Decipentic == | == Decipentic == | ||
Decipentic may be described as the 43 & 56 temperament. The minimal generator for this temperament is the 10th root of the [[5/1|5th harmonic]], 5<sup>1/10</sup>, tuned between [[75/64]] and [[20/17]] (close to [[27/23]]). Aside from the hemimean comma, this temperament tempers out the [[bronzisma]], 2097152/2083725. [[99edo]] is a good tuning for decipentic, with generator 23\99, and [[mos scale]]s of 9, 13, 17, 30, 43 or 56 notes are available. | Decipentic may be described as the 43 & 56 temperament. The minimal generator for this temperament is the 10th root of the [[5/1|5th harmonic]], 5<sup>1/10</sup>, tuned between [[75/64]] and [[20/17]] (close to [[27/23]]). Aside from the hemimean comma, this temperament tempers out the [[bronzisma]], 2097152/2083725. [[99edo]] is a good tuning for decipentic, with generator 23\99, and [[mos scale]]s of 9, 13, 17, 30, 43 or 56 notes are available. | ||
Decipentic was named by [[Xenllium]] in 2021 for the fact that it splits the 5th harmonic into ten equal parts. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Mowgli]].'' | : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Mowgli]].'' | ||
Mowglic may be described as the 19 & 161 temperament. | Mowglic may be described as the 19 & 161 temperament, named by [[Xenllium]] in 2021 as a variant of ''mowgli''. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Tremka == | == Tremka == | ||
The name ''tremka'' was initially used for the [[no-sevens subgroup temperaments #Tremka|no-7's version]] | Tremka may be described as the 50 & 111 temperament. The name ''tremka'' was devised by [[Petr Pařízek]] in 2011, initially used for the [[no-sevens subgroup temperaments #Tremka|no-7's version]], especially in the 2.3.5.11.13 subgroup<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group (archive) | ''Suggested names for the unclasified temperaments'']</ref>, but extending to the full 13-limit or higher does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Undetrita (5-limit)]].'' | : ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Undetrita (5-limit)]].'' | ||
Undetrita tempers out the | Undetrita tempers out 14348907/14336000, the [[scheme comma]], in addition to the hemimean comma, and may be described as the 111 & 118 temperament. It splits 3rd harmonic into eleven parts; its [[ploidacot]] is thus alpha-hendecacot. It tempers out [[3025/3024]], [[3388/3375]], and [[8019/8000]] in the [[11-limit]], which relates itself to [[no-sevens subgroup temperaments #Twentcufo|twentcufo]], the no-7's version of 111 & 118. | ||
It was named by [[Xenllium]] in 2021 as a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||