Jubilismic clan: Difference between revisions
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== Jubilic == | == Jubilic == | ||
The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave give ~[[7/4]]. | The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave give ~[[7/4]]. As such, a reasonable tuning would tune the 5/4 flat and 7/4 sharp. | ||
[[Subgroup]]: 2.5.7 | [[Subgroup]]: 2.5.7 | ||
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Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]] | * [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]] | ||
* [[Diminished (temperament)|Diminished]] (+36/35) → [[ | * [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]] | ||
* [[Pajara]] (+64/63) → [[Diaschismic family #Pajara|Diaschismic family]] | * [[Pajara]] (+64/63) → [[Diaschismic family #Pajara|Diaschismic family]] | ||
* ''[[Dubbla]]'' (+78125/73728) → [[Wesley family #Dubbla|Wesley family]] | * ''[[Dubbla]]'' (+78125/73728) → [[Wesley family #Dubbla|Wesley family]] | ||
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: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Lemba]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Lemba]].'' | ||
Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth. | Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth. It may be described as the {{nowrap| 10 & 16 }} temperament; its [[ploidacot]] is diploid tricot. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Astrology == | == Astrology == | ||
Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3. | Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3. It may be described as the {{nowrap| 16 & 22 }} temperament; its ploidacot is diploid pentacot. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Walid == | == Walid == | ||
This low-accuracy extension tempers out 16/15, so the perfect fifth stands in for ~8/5 as in [[father]]. Its ploidacot is diploid monocot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }} | {{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }} | ||
[[Badness]] (Sintel): 0.253 | [[Badness]] (Sintel): 0.253 | ||
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== Doublewide == | == Doublewide == | ||
: ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Doublewide (5-limit)]].'' | : ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Doublewide (5-limit)]].'' | ||
Doublewide is generated by a sharply tuned ~6/5 minor third, four of which and a semi-octave period give the 3rd harmonic. It may be described as the {{nowrap| 22 & 26 }} temperament; its ploidacot is diploid alpha-tetracot. An 11-limit extension is immediately available by identifying two generator steps as ~16/11. [[48edo]] makes for an excellent tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 50/49, 99/98, | Comma list: 50/49, 99/98, 385/384 | ||
Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }} | Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }} | ||
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== Elvis == | == Elvis == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Elvis]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Elvis]].'' | ||
Elvis is generated by a ptolemaic diminished fifth, tuned sharp such that two generators and a semi-octave period give the 3rd harmonic. Its ploidacot is diploid alpha-dicot. [[26edo]] makes for an obvious tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Comic == | == Comic == | ||
: ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Comic (5-limit)]].'' | : ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Comic (5-limit)]].'' | ||
Comic is generated by a grave fifth, tuned flat such that two generators and a semi-octave period give the 3rd harmonic. Its ploidacot is diploid alpha-dicot. [[22edo]] makes for an obvious tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Bipyth == | == Bipyth == | ||
Bipyth tempers out the 5-limit [[superpyth comma]], 20480/19683, making it an alternative extension of 5-limit [[superpyth]]. Its ploidacot is diploid monocot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Sedecic == | == Sedecic == | ||
Sedecic has 1/16-octave period and may be thought of as 16edo with an independent generator for prime 3. Its ploidacot is 16-ploid monocot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||