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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{{Mapping|legend=2| 2 0 1 | 0 1 1 }} | {{Mapping|legend=2| 2 0 1 | 0 1 1 }} | ||
{{Mapping|legend=3| 2 0 0 1 | 0 0 1 1 }} | |||
: mapping generators: ~7/5, ~5 | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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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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* ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]] | * ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]] | ||
* ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]] | * ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]] | ||
* ''[[ | * ''[[Weasel]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]] | ||
Considered below are lemba, astrology, walid | Considered below are lemba, astrology, walid, doublewide, elvis, comic, and bipyth. | ||
== Lemba == | == Lemba == | ||
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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. | [[:de:Magische_Temperaturen#Astrology|Deutsch]] | ||
{{see also| Magic family }} | |||
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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Badness (Sintel): 0.965 | Badness (Sintel): 0.965 | ||
== | == Doublewide == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide]].'' | |||
Doublewide tempers out not only the keema, [[875/864]], but the orwellisma, [[1728/1715]], and may be described as the {{nowrap| 22 & 26 }} temperament. It is the unique temperament that equates the classical chroma ([[25/24]]), the large septimal diesis ([[49/48]]), and the interval between the classical and septimal thirds ([[36/35]]). It is generated by a sharply tuned [[~]][[6/5]] minor third, four of which and a [[semi-octave]] period give the [[3/1|3rd]] [[harmonic]], so 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 [[ | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Comic]].'' | ||
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 | ||
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Badness (Sintel): 3.07 | Badness (Sintel): 3.07 | ||
== | == Subgroup extensions == | ||
=== Antikythera (2.9.5.7) === | |||
Antikythera is every other step of [[pajara]]. It was allegedly named by [[Keenan Pepper]] in 2011 after the {{w|Antikythera mechanism}} for its association with [[astrology]] and [[machine]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>. | |||
[[Subgroup]]: 2.9.5.7 | |||
[[Comma list]]: 50/49, 64/63 | |||
{{Mapping|legend=2| 2 0 11 12 | 0 1 -1 -1 }} | |||
{{Mapping|legend=3| 2 0 11 12 | 0 1/2 -1 -1 }} | |||
: mapping generators: ~7/5, ~9 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~7/5 = 598.8483{{c}}, ~9/8 = 213.6844{{c}} | |||
: [[error map]]: {{val| -2.303 +2.864 -5.756 +10.580 }} | |||
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/8 = 214.6875{{c}} | |||
: error map: {{val| 0.000 +10.778 -1.001 +16.487 }} | |||
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }} | |||
[[Badness]] (Sintel): 0.253 | |||
== References == | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Jubilismic clan| ]] <!-- main article --> | [[Category:Jubilismic clan| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||