Jubilismic clan: Difference between revisions

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* ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]]

* ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]]

* ''[[~~Byhearted~~]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]

* ''[[Weasel]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]

Considered below are lemba, astrology, walid~~, antikythera~~, doublewide, elvis, comic, and bipyth.

Considered below are lemba, astrology, walid, doublewide, elvis, comic, and bipyth.

== Lemba ==

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== Astrology ==

[[:de:Magische_Temperaturen#Astrology|Deutsch]]

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.

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Badness (Sintel): 0.965

~~== Antikythera ==~~

Named by [[Gene Ward Smith]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>, antikythera is every other step of [[pajara]].

~~[[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~~

== Doublewide ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide ~~(5-limit)~~]].''

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide]].''

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.

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

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Badness (Sintel): 3.07

== ~~Notes~~ ==

== 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 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 }}

[[Badness]] (Sintel): 0.253

== References ==

[[Category:Temperament clans]]

[[Category:Jubilismic clan| ]]

~~[[Category:Jubilismic| ]] ~~

[[Category:Rank 2]]

@@ Line 41: / Line 41: @@
 * ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]]
 * ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]]
-* ''[[Byhearted]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]
+* ''[[Weasel]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]
-Considered below are lemba, astrology, walid, antikythera, doublewide, elvis, comic, and bipyth.
+Considered below are lemba, astrology, walid, doublewide, elvis, comic, and bipyth.
 == Lemba ==
@@ Line 100: / Line 100: @@
 == Astrology ==
+[[: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.
@@ Line 203: / Line 207: @@
 Badness (Sintel): 0.965
-== Antikythera ==
-Named by [[Gene Ward Smith]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>, antikythera is every other step of [[pajara]].
-[[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
 == Doublewide ==
-: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide (5-limit)]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide]].''
-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.
+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
@@ Line 501: / Line 482: @@
 Badness (Sintel): 3.07
-== Notes ==
+== 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:Jubilismic clan| ]] <!-- main article -->
-[[Category:Jubilismic| ]] <!-- key article -->
 [[Category:Rank 2]]