Jubilismic clan: Difference between revisions

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The '''jubilismic clan''' tempers out the jubilisma, [[50/49]], which means [[7/5]] and [[10/7]] are both equated to the 600-cent tritone and the [[octave]] is divided in two.

== Jubilic ==

The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave ~~gives~~ ~[[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

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: sval mapping generators: ~7/5, ~5

~~[[Gencom]] [[mapping]]: [~~{{~~val~~| 2 0 0 1 ~~}}, {{val~~| 0 0 1 1 }}]

[[Optimal tuning]] ([[~~POTE~~]]): ~7/5 = ~~1\2~~, ~5/4 = 380.~~840~~

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 599.6673{{c}}, ~5/4 = 380.6287{{c}} (~8/7 = 219.0386{{c}})

: [[error map]]: {{val| -0.665 -7.016 +10.139 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.0086{{c}} (~8/7 = 219.9914{{c}})

: error map: {{val| 0.000 -6.305 +11.183 }}

{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d~~, 82d, 104dd~~ }}

[[Badness]] (Sintel): 0.140

=== Overview to extensions ===

Lemba finds the perfect fifth three steps away by tempering out [[1029/1024]]. Astrology, five steps away by tempering out [[3125/3072]]. Decimal, two steps away by tempering out [[25/24]] and [[49/48]]. Walid merges ~5/4 and ~4/3 by tempering out [[16/15]].

Diminished splits the ~7/5 period ~~into~~ a further two. Pajara slices the ~7/4 ~~into~~ two, with antikythera being every other step thereof. Injera slices the ~5/1 into ~~four~~. ~~Hedgehog~~ slices the ~7/~~1 into~~ five.

Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.

~~Lemba, astrology, and doublewide are~~ discussed ~~below; others in the clan~~ are

Temperaments discussed elsewhere are:

* [[Diminished]] → [[~~Dimipent~~ family #Diminished~~|Dimipent~~ family]]

* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]

* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]]

* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]

* [[~~Decimal~~]] → [[~~Dicot~~ family #~~Decimal~~|~~Dicot~~ family]]

* [[Pajara]] (+64/63) → [[Diaschismic family #Pajara|Diaschismic family]]

* [[Injera]] → [[Meantone family #Injera|Meantone family]]

* ''[[Dubbla]]'' (+78125/73728) → [[Wesley family #Dubbla|Wesley family]]

* [[Octokaidecal]] → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]

* ''[[Injera]]'' (+81/80) → [[Meantone family #Injera|Meantone family]]

* [[~~Hedgehog~~]] → [[~~Porcupine family~~ #~~Hedgehog~~|~~Porcupine~~ family]]

* ''[[Octokaidecal]]'' (+28/27) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]

* [[~~Bipelog~~]] → [[~~Pelogic~~ family #~~Bipelog~~|~~Pelogic~~ family]]

* ''[[Bipelog]]'' (+135/128) → [[Mavila #Bipelog|Mavila family]]

* [[~~Dubbla~~]] → [[~~Wesley~~ family #~~Dubbla~~|~~Wesley~~ family]]

* ''[[Hexe]]'' (+128/125) → [[Augmented family #Hexe|Augmented family]]

* [[~~Hexe~~]] → [[~~Augmented~~ family #~~Hexe~~|~~Augmented~~ family]]

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

* [[Byhearted]] → [[Tetracot family #Byhearted|Tetracot family]]

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

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

~~which~~ are ~~discussed elsewhere~~.

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

== 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

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: mapping generators: ~7/5, ~8/7

[[Optimal tuning]] ([[~~POTE~~]]): ~7/5 = 1\2, ~8/7 = 232.~~089~~

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 601.4623{{c}}, ~8/7 = 232.6544{{c}}

: [[error map]]: {{val| +2.925 -1.067 -11.656 +7.294 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~8/7 = 232.2655{{c}}

: error map: {{val| 0.000 -5.158 -18.579 -1.091 }}

[[Badness]]: 0.~~062208~~

[[Badness]] (Sintel): 1.57

=== 11-limit ===

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Mapping: {{mapping| 2 2 5 6 5 | 0 3 -1 -1 5 }}

Optimal ~~tuning (POTE)~~: ~7/5 = ~~1\2~~, ~8/7 = ~~230~~.~~974~~

Optimal tunings:

* WE: ~7/5 = 601.1769{{c}}, ~8/7 = 231.4273{{c}}

* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1781{{c}}

Badness: 0.~~041563~~

Badness (Sintel): 1.37

=== 13-limit ===

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Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}

Optimal ~~tuning (POTE)~~: ~7/5 = ~~1\2~~, ~8/7 = ~~230~~.~~966~~

Optimal tunings:

* WE: ~7/5 = 601.1939{{c}}, ~8/7 = 231.4261{{c}}

* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1617{{c}}

Badness: 0.~~025477~~

Badness (Sintel): 1.05

== 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

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: mapping geenerators: ~7/5, ~5/4

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 599.6999{{c}}, ~5/4 = 380.3881{{c}} (~8/7 = 219.3119{{c}})

: [[error map]]: {{val| -0.600 -0.015 -7.126 +10.062 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5123{{c}} (~8/7 = 219.4877{{c}})

: error map: {{val| 0.000 +0.606 -5.801 +11.686 }}

[[Optimal ~~tuning]] ([[POTE]]): ~7/5~~ = 1\2, ~~~5/4 = 380.578~~

~~{{Optimal ET sequence|legend=1| 6, 16, 22, 60d, 82d }}~~

[[Badness]] (Sintel): 2.09

[[Badness]]: 0.~~082673~~

=== 11-limit ===

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Mapping: {{mapping| 2 0 4 5 5 | 0 5 1 1 3 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~5/4 = 380.~~530~~

Optimal tunings:

* WE: ~7/5 = 600.0538{{c}}, ~5/4 = 380.5640{{c}} (~8/7 = 219.4897{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5419{{c}} (~8/7 = 219.4581{{c}})

Badness: 0.~~039151~~

Badness (Sintel): 1.29

==== 13-limit ====

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Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~5/4 = 379.~~787~~

Optimal tunings:

* WE: ~7/5 = 600.7886{{c}}, ~5/4 = 380.2857{{c}} (~8/7 = 220.5028{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.9119{{c}} (~8/7 = 220.0881{{c}})

Badness: 0.~~034376~~

Badness (Sintel): 1.42

; Music

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Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~5/4 = 379.~~837~~

Optimal tunings:

* WE: ~7/5 = 599.8927{{c}}, ~5/4 = 379.7688{{c}} (~8/7 = 220.1239{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.8117{{c}} (~8/7 = 220.1883{{c}})

Badness: 0.~~035284~~

Badness (Sintel): 1.46

== 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

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: mapping generators: ~7/5, ~3

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 589.0384{{c}}, ~3/2 = 735.7242{{c}} (~15/14 = 146.6857{{c}})

[[~~Optimal tuning~~]] ([[~~POTE~~]]): ~7/5 = ~~1\2~~, ~3/2 = ~~749~~.~~415~~

: [[error map]]: {{val| -21.923 +11.846 +12.193 +18.719 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 750.4026{{c}} (~15/14 = 150.4026{{c}})

: error map: {{val| 0.000 +48.448 +63.284 +80.771 }}

[[Badness]]: 0.~~048978~~

[[Badness]] (Sintel): 1.24

=== 11-limit ===

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Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~3/2 = ~~749~~.~~756~~

Optimal tunings:

* WE: ~7/5 = 589.7684{{c}}, ~3/2 = 736.9708{{c}} (~12/11 = 147.2023{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 750.5221{{c}} (~12/11 = 150.5221{{c}})

Badness: 0.~~029193~~

Badness (Sintel): 0.965

== Antikythera ==

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: [[gencom]]: [7/5 8/7; 50/49 64/63]

[[Optimal tuning]] ([[~~POTE~~]]): ~7/5 = 1\2, ~8/7 = 214.~~095~~

[[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]]: 0.~~00501~~

[[Badness]] (Sintel): 0.253

== Doublewide ==

: ''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

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~~[[Optimal tuning]] ([[POTE]])~~: ~7/5 ~~= 1\2~~, ~6/5 ~~= 325.719~~

: mapping generators: ~7/5, ~6/5

{{~~Optimal ET sequence~~|~~legend~~=1~~| 4, 14bd, 18, 22, 48, 70c~~ }}

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 600.0365{{c}}, ~6/5 = 325.7389{{c}} (~7/6 = 274.2975{{c}})

: [[error map]]: {{val| -2.303 +2.864 -5.756 +10.580 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~6/5 = 325.7353{{c}} (~7/6 = 274.2647{{c}})

: error map: {{val| 0.000 +10.778 -1.001 +16.487 }}

[[Badness]]: 0.~~043462~~

[[Badness]] (Sintel): 1.10

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, ~~875~~/~~864~~

Comma list: 50/49, 99/98, 385/384

Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~6/5 = 325.~~545~~

Optimal tunings:

* WE: ~7/5 = 600.1818{{c}}, ~6/5 = 325.6434{{c}} (~7/6 = 274.5384{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 325.5854{{c}} (~7/6 = 274.4146{{c}})

{{Optimal ET sequence|legend=1| 4~~, 14bd~~, 18, 22, 48~~, 70c, 118cd~~ }}

Badness: 0.~~032058~~

Badness (Sintel): 1.06

=== Fleetwood ===

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Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~6/5 = ~~327~~.~~038~~

Optimal tunings:

* WE: ~7/5 = 599.6049{{c}}, ~6/5 = 326.8229{{c}} (~7/6 = 272.7819{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 326.8890{{c}} (~7/6 = 273.1110{{c}})

Badness: 0.~~035202~~

Badness (Sintel): 1.16

==== 13-limit ====

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Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~6/5 = 327.~~841~~

Optimal tunings:

* WE: ~7/5 = 599.5482{{c}}, ~6/5 = 327.5939{{c}} (~7/6 = 271.9543{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 327.6706{{c}} (~7/6 = 272.3294{{c}})

Badness: 0.~~031835~~

Badness (Sintel): 1.32

=== Cavalier ===

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Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~6/5 = 323.~~427~~

Optimal tunings:

* WE: ~7/5 = 600.9467{{c}}, ~6/5 = 323.9369{{c}} (~7/6 = 277.0098{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.7272{{c}} (~7/6 = 276.2728{{c}})

Badness: 0.~~052899~~

Badness (Sintel): 1.75

==== 13-limit ====

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Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~6/5 = 323.~~396~~

Optimal tunings:

* WE: ~7/5 = 600.9537{{c}}, ~6/5 = 323.9097{{c}} (~7/6 = 277.0440{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.6876{{c}} (~7/6 = 276.3124{{c}})

Badness: 0.~~035040~~

Badness (Sintel): 1.45

== Elvis ==

: ''For the 5-limit version ~~of this temperament~~, see [[~~High badness~~ 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

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~~{{Multival|legend=1| 4 -10 -10 -25 -27~~ 5 }}

: mapping generators: ~7/5, ~64/45

[[Optimal tuning]] ([[~~POTE~~]]): ~7/5 = ~~1\2~~, ~45/32 = ~~553~~.~~721~~

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 601.6846{{c}}, ~64/45 = 648.0937{{c}} (~64/63 = 46.4091{{c}})

: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~64/45 = 646.0539{{c}} (~64/63 = 46.0539{{c}})

: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}

[[Badness]]: 0.~~141473~~

[[Badness]] (Sintel): 3.58

=== 11-limit ===

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Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~11/8 = ~~553~~.~~882~~

Optimal tunings:

* WE: ~7/5 = 601.2186{{c}}, ~16/11 = 647.4300{{c}} (~56/55 = 46.2114{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9681{{c}} (~56/55 = 45.9681{{c}})

Badness: 0.~~063212~~

Badness (Sintel): 2.09

=== 13-limit ===

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Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~11/8 = ~~553~~.~~892~~

Optimal tunings:

* WE: ~7/5 = 601.2206{{c}}, ~16/11 = 647.4219{{c}} (~56/55 = 46.2013{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9362{{c}} (~56/55 = 45.9362{{c}})

Badness: 0.~~043997~~

Badness (Sintel): 1.82

== Comic ==

: ''For the 5-limit version ~~of this temperament~~, see [[~~High badness temperaments~~ #Comic]].''

: ''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

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~~{{Multival|legend=1| 4 14 14 13 11 -~~7 }}

: mapping generators: ~7/5, ~40/27

[[Optimal tuning]] ([[~~POTE~~]]): ~7/5 = ~~1\2~~, ~81/80 = 54.~~699~~

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 598.9554{{c}}, ~40/27 = 653.5596{{c}} (~28/27 = 54.6042{{c}})

: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~40/27 = 654.3329{{c}} (~28/27 = 54.3329{{c}})

: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}

[[Badness]]: 0.~~084395~~

[[Badness]] (Sintel): 2.14

=== 11-limit ===

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Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~81/80 = 55.~~184~~

Optimal tunings:

* WE: ~7/5 = 598.8161{{c}}, ~22/15 = 653.8909{{c}} (~28/27 = 55.0747{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.7898{{c}} (~28/27 = 54.7898{{c}})

Badness: 0.~~045052~~

Badness (Sintel): 1.49

=== 13-limit ===

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Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~81/80 = 54.~~435~~

Optimal tunings:

* WE: ~7/5 = 600.1030{{c}}, ~22/15 = 654.5470{{c}} (~28/27 = 54.4440{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.4665{{c}} (~28/27 = 54.4665{{c}})

Badness: 0.~~041470~~

Badness (Sintel): 1.71

== Bipyth ==

~~{{See also| Archytas clan #Superpyth }}~~

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

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~~{{Multival|legend=1| 2 18 18 24 23 -9 }}~~

: mapping generators: ~7/5, ~3

[[Optimal tuning]] ([[~~POTE~~]]): ~7/5 = ~~1\2~~, ~3/2 = 709.~~437~~

[[Optimal tuning]]s:

* [[WE]]: ~7/5 = 598.7533{{c}}, ~3/2 = 707.9630{{c}} (~15/14 = 109.2098{{c}})

: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1579{{c}} (~15/14 = 109.1579{{c}})

: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}

[[Badness]]: 0.~~165033~~

[[Badness]] (Sintel): 4.18

=== 11-limit ===

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Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}

Optimal ~~tuning~~ (~~POTE~~): ~7/5 = ~~1\2~~, ~3/2 = 709.~~310~~

Optimal tunings:

* WE: ~7/5 = 599.2296{{c}}, ~3/2 = 708.3992{{c}} (~15/14 = 109.1697{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1395{{c}} (~15/14 = 109.1395{{c}})

Badness: 0.~~070910~~

Badness (Sintel): 2.34

== 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

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[[Optimal tuning]]s:

* [[WE]]: ~128/125 = 75.0539{{c}}, ~3/2 = 701.0578{{c}} (~525/512 = 25.5726{{c}})

~~[[Optimal tuning]] (~~[[~~POTE~~]]): ~128/125 = ~~1\16~~, ~3/2 = 700.~~554~~

: [[error map]]: {{val| 0.000 0.000 -11.314 +6.174 }}

* [[CWE]]: ~128/125 = 75.0000{{c}}, ~3/2 = 700.8957{{c}} (~525/512 = 25.8957{{c}})

: error map: {{val| 0.000 -1.401 -11.314 +6.174 }}

[[Badness]]: 0.~~265972~~

[[Badness]] (Sintel): 6.73

=== 11-limit ===

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Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}

Optimal ~~tuning (POTE)~~: ~22/21 = ~~1\16~~, ~3/2 = 700.~~331~~

Optimal tunings:

* WE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.7810{{c}} (~45/44 = 25.3476{{c}})

* CWE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.6780{{c}} (~45/44 = 25.6780{{c}})

~~Badness~~: 0.~~092774~~

~~== Duodecim ==~~

~~[[Subgroup]]:~~ 2.~~3.5.7~~.11

~~[[Comma list]]: 36/35, 50/49, 64/63~~

[[Optimal ~~tuning]] ([[POTE]]): ~~~16~~/15 = 1\12~~, ~~~11/8 = 565.023~~

~~{{Optimal ET sequence|legend=1| 12, 24d, 36d }}~~

Badness (Sintel): 3.07

~~[[Badness]]: 0.030536~~

== Notes ==

[[Category:Temperament clans]]

[[Category:Pages with mostly numerical content]]

[[Category:Jubilismic clan| ]]

[[Category:Jubilismic| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
+{{Technical data page}}
 The '''jubilismic clan''' tempers out the jubilisma, [[50/49]], which means [[7/5]] and [[10/7]] are both equated to the 600-cent tritone and the [[octave]] is divided in two.
 == Jubilic ==
-The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave gives ~[[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
@@ Line 12: / Line 13: @@
 : sval mapping generators: ~7/5, ~5
-[[Gencom]] [[mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 0 1 1 }}]
+{{Mapping|legend=3| 2 0 0 1 | 0 0 1 1 }}
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~5/4 = 380.840
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 599.6673{{c}}, ~5/4 = 380.6287{{c}} (~8/7 = 219.0386{{c}})
+: [[error map]]: {{val| -0.665 -7.016 +10.139 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.0086{{c}} (~8/7 = 219.9914{{c}})
+: error map: {{val| 0.000 -6.305 +11.183 }}
-{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
+{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d }}
+[[Badness]] (Sintel): 0.140
 === Overview to extensions ===
 Lemba finds the perfect fifth three steps away by tempering out [[1029/1024]]. Astrology, five steps away by tempering out [[3125/3072]]. Decimal, two steps away by tempering out [[25/24]] and [[49/48]]. Walid merges ~5/4 and ~4/3 by tempering out [[16/15]].
-Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two, with antikythera being every other step thereof. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five.
+Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.
-Lemba, astrology, and doublewide are discussed below; others in the clan are
+Temperaments discussed elsewhere are:
-* [[Diminished]] → [[Dimipent family #Diminished|Dimipent family]]
+* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
-* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]]
+* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
-* [[Decimal]] → [[Dicot family #Decimal|Dicot family]]
+* [[Pajara]] (+64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
-* [[Injera]] → [[Meantone family #Injera|Meantone family]]
+* ''[[Dubbla]]'' (+78125/73728) → [[Wesley family #Dubbla|Wesley family]]
-* [[Octokaidecal]] → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
+* ''[[Injera]]'' (+81/80) → [[Meantone family #Injera|Meantone family]]
-* [[Hedgehog]] → [[Porcupine family #Hedgehog|Porcupine family]]
+* ''[[Octokaidecal]]'' (+28/27) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
-* [[Bipelog]] → [[Pelogic family #Bipelog|Pelogic family]]
+* ''[[Bipelog]]'' (+135/128) → [[Mavila #Bipelog|Mavila family]]
-* [[Dubbla]] → [[Wesley family #Dubbla|Wesley family]]
+* ''[[Hexe]]'' (+128/125) → [[Augmented family #Hexe|Augmented family]]
-* [[Hexe]] → [[Augmented family #Hexe|Augmented family]]
+* ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]]
-* [[Byhearted]] → [[Tetracot family #Byhearted|Tetracot family]]
+* ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]]
+* ''[[Byhearted]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]
-which are discussed elsewhere.
+Considered below are lemba, astrology, walid, antikythera, doublewide, elvis, comic, and bipyth.
 == Lemba ==
 {{Main| 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
@@ Line 50: / Line 59: @@
 : mapping generators: ~7/5, ~8/7
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 232.089
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 601.4623{{c}}, ~8/7 = 232.6544{{c}}
+: [[error map]]: {{val| +2.925 -1.067 -11.656 +7.294 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~8/7 = 232.2655{{c}}
+: error map: {{val| 0.000 -5.158 -18.579 -1.091 }}
-{{Optimal ET sequence|legend=1| 10, 16, 26, 62c }}
+{{Optimal ET sequence|legend=1| 10, 16, 26, 36c, 62c }}
-[[Badness]]: 0.062208
+[[Badness]] (Sintel): 1.57
 === 11-limit ===
@@ Line 63: / Line 76: @@
 Mapping: {{mapping| 2 2 5 6 5 | 0 3 -1 -1 5 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974
+Optimal tunings:
+* WE: ~7/5 = 601.1769{{c}}, ~8/7 = 231.4273{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1781{{c}}
-{{Optimal ET sequence|legend=1| 10, 16, 26 }}
+{{Optimal ET sequence|legend=0| 10, 16, 26 }}
-Badness: 0.041563
+Badness (Sintel): 1.37
 === 13-limit ===
@@ Line 76: / Line 91: @@
 Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966
+Optimal tunings:
+* WE: ~7/5 = 601.1939{{c}}, ~8/7 = 231.4261{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1617{{c}}
-{{Optimal ET sequence|legend=1| 10, 16, 26 }}
+{{Optimal ET sequence|legend=0| 10, 16, 26 }}
-Badness: 0.025477
+Badness (Sintel): 1.05
 == 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
@@ Line 93: / Line 110: @@
 : mapping geenerators: ~7/5, ~5/4
-{{Multival|legend=1| 10 2 2 -20 -25 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 599.6999{{c}}, ~5/4 = 380.3881{{c}} (~8/7 = 219.3119{{c}})
+: [[error map]]: {{val| -0.600 -0.015 -7.126 +10.062 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5123{{c}} (~8/7 = 219.4877{{c}})
+: error map: {{val| 0.000 +0.606 -5.801 +11.686 }}
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~5/4 = 380.578
+{{Optimal ET sequence|legend=1| 6, 16, 22, 60d }}
-{{Optimal ET sequence|legend=1| 6, 16, 22, 60d, 82d }}
+[[Badness]] (Sintel): 2.09
-[[Badness]]: 0.082673
 === 11-limit ===
@@ Line 108: / Line 127: @@
 Mapping: {{mapping| 2 0 4 5 5 | 0 5 1 1 3 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.530
+Optimal tunings:
+* WE: ~7/5 = 600.0538{{c}}, ~5/4 = 380.5640{{c}} (~8/7 = 219.4897{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5419{{c}} (~8/7 = 219.4581{{c}})
-{{Optimal ET sequence|legend=1| 6, 16, 22, 60de, 82de }}
+{{Optimal ET sequence|legend=0| 6, 16, 22 }}
-Badness: 0.039151
+Badness (Sintel): 1.29
 ==== 13-limit ====
@@ Line 121: / Line 142: @@
 Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.787
+Optimal tunings:
+* WE: ~7/5 = 600.7886{{c}}, ~5/4 = 380.2857{{c}} (~8/7 = 220.5028{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.9119{{c}} (~8/7 = 220.0881{{c}})
-{{Optimal ET sequence|legend=1| 6, 16, 22, 38f }}
+{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}
-Badness: 0.034376
+Badness (Sintel): 1.42
 ; Music
@@ Line 137: / Line 160: @@
 Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.837
+Optimal tunings:
+* WE: ~7/5 = 599.8927{{c}}, ~5/4 = 379.7688{{c}} (~8/7 = 220.1239{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.8117{{c}} (~8/7 = 220.1883{{c}})
-{{Optimal ET sequence|legend=1| 16, 22f, 38 }}
+{{Optimal ET sequence|legend=0| 6f, 16, 22f, 38 }}
-Badness: 0.035284
+Badness (Sintel): 1.46
 == 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
@@ Line 152: / Line 179: @@
 : mapping generators: ~7/5, ~3
-{{Multival|legend=1| 2 -2 -2 -8 -9 1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 589.0384{{c}}, ~3/2 = 735.7242{{c}} (~15/14 = 146.6857{{c}})
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 749.415
+: [[error map]]: {{val| -21.923 +11.846 +12.193 +18.719 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 750.4026{{c}} (~15/14 = 150.4026{{c}})
+: error map: {{val| 0.000 +48.448 +63.284 +80.771 }}
 {{Optimal ET sequence|legend=1| 2, 6, 8d }}
-[[Badness]]: 0.048978
+[[Badness]] (Sintel): 1.24
 === 11-limit ===
@@ Line 167: / Line 196: @@
 Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.756
+Optimal tunings:
+* WE: ~7/5 = 589.7684{{c}}, ~3/2 = 736.9708{{c}} (~12/11 = 147.2023{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 750.5221{{c}} (~12/11 = 150.5221{{c}})
-{{Optimal ET sequence|legend=1| 2, 6, 8d }}
+{{Optimal ET sequence|legend=0| 2, 6, 8d }}
-Badness: 0.029193
+Badness (Sintel): 0.965
 == Antikythera ==
@@ Line 188: / Line 219: @@
 : [[gencom]]: [7/5 8/7; 50/49 64/63]
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 214.095
+[[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| 4, 6, 16, 22, 28 }}
+{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }}
-[[Badness]]: 0.00501
+[[Badness]] (Sintel): 0.253
 == Doublewide ==
+: ''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
@@ Line 201: / Line 240: @@
 {{Mapping|legend=1| 2 1 3 4 | 0 4 3 3 }}
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~6/5 = 325.719
+: mapping generators: ~7/5, ~6/5
-{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48, 70c }}
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 600.0365{{c}}, ~6/5 = 325.7389{{c}} (~7/6 = 274.2975{{c}})
+: [[error map]]: {{val| -2.303 +2.864 -5.756 +10.580 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~6/5 = 325.7353{{c}} (~7/6 = 274.2647{{c}})
+: error map: {{val| 0.000 +10.778 -1.001 +16.487 }}
-[[Badness]]: 0.043462
+{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48 }}
+[[Badness]] (Sintel): 1.10
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 50/49, 99/98, 875/864
+Comma list: 50/49, 99/98, 385/384
 Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545
+Optimal tunings:
+* WE: ~7/5 = 600.1818{{c}}, ~6/5 = 325.6434{{c}} (~7/6 = 274.5384{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 325.5854{{c}} (~7/6 = 274.4146{{c}})
-{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48, 70c, 118cd }}
+{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}
-Badness: 0.032058
+Badness (Sintel): 1.06
 === Fleetwood ===
@@ Line 227: / Line 274: @@
 Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038
+Optimal tunings:
+* WE: ~7/5 = 599.6049{{c}}, ~6/5 = 326.8229{{c}} (~7/6 = 272.7819{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 326.8890{{c}} (~7/6 = 273.1110{{c}})
-{{Optimal ET sequence|legend=1| 4e, 18e, 22 }}
+{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}
-Badness: 0.035202
+Badness (Sintel): 1.16
 ==== 13-limit ====
@@ Line 240: / Line 289: @@
 Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841
+Optimal tunings:
+* WE: ~7/5 = 599.5482{{c}}, ~6/5 = 327.5939{{c}} (~7/6 = 271.9543{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 327.6706{{c}} (~7/6 = 272.3294{{c}})
-{{Optimal ET sequence|legend=1| 4ef, 18e, 22, 84bddf }}
+{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}
-Badness: 0.031835
+Badness (Sintel): 1.32
 === Cavalier ===
@@ Line 253: / Line 304: @@
 Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427
+Optimal tunings:
+* WE: ~7/5 = 600.9467{{c}}, ~6/5 = 323.9369{{c}} (~7/6 = 277.0098{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.7272{{c}} (~7/6 = 276.2728{{c}})
-{{Optimal ET sequence|legend=1| 22e, 26 }}
+{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}
-Badness: 0.052899
+Badness (Sintel): 1.75
 ==== 13-limit ====
@@ Line 266: / Line 319: @@
 Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396
+Optimal tunings:
+* WE: ~7/5 = 600.9537{{c}}, ~6/5 = 323.9097{{c}} (~7/6 = 277.0440{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.6876{{c}} (~7/6 = 276.3124{{c}})
-{{Optimal ET sequence|legend=1| 22ef, 26 }}
+{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}
-Badness: 0.035040
+Badness (Sintel): 1.45
 == Elvis ==
-: ''For the 5-limit version of this temperament, see [[High badness 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
@@ Line 281: / Line 338: @@
 {{Mapping|legend=1| 2 1 10 11 | 0 2 -5 -5 }}
-{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
+: mapping generators: ~7/5, ~64/45
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~45/32 = 553.721
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 601.6846{{c}}, ~64/45 = 648.0937{{c}} (~64/63 = 46.4091{{c}})
+: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~64/45 = 646.0539{{c}} (~64/63 = 46.0539{{c}})
+: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}
 {{Optimal ET sequence|legend=1| 2, 24c, 26 }}
-[[Badness]]: 0.141473
+[[Badness]] (Sintel): 3.58
 === 11-limit ===
@@ Line 296: / Line 357: @@
 Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882
+Optimal tunings:
+* WE: ~7/5 = 601.2186{{c}}, ~16/11 = 647.4300{{c}} (~56/55 = 46.2114{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9681{{c}} (~56/55 = 45.9681{{c}})
-{{Optimal ET sequence|legend=1| 2, 24c, 26 }}
+{{Optimal ET sequence|legend=0| 2, 24c, 26 }}
-Badness: 0.063212
+Badness (Sintel): 2.09
 === 13-limit ===
@@ Line 309: / Line 372: @@
 Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892
+Optimal tunings:
+* WE: ~7/5 = 601.2206{{c}}, ~16/11 = 647.4219{{c}} (~56/55 = 46.2013{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9362{{c}} (~56/55 = 45.9362{{c}})
-{{Optimal ET sequence|legend=1| 2f, 24cf, 26 }}
+{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}
-Badness: 0.043997
+Badness (Sintel): 1.82
 == Comic ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Comic]].''
+: ''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
@@ Line 324: / Line 391: @@
 {{Mapping|legend=1| 2 1 -3 -2 | 0 2 7 7 }}
-{{Multival|legend=1| 4 14 14 13 11 -7 }}
+: mapping generators: ~7/5, ~40/27
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~81/80 = 54.699
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 598.9554{{c}}, ~40/27 = 653.5596{{c}} (~28/27 = 54.6042{{c}})
+: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~40/27 = 654.3329{{c}} (~28/27 = 54.3329{{c}})
+: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}
-{{Optimal ET sequence|legend=1| 20cd, 22 }}
+{{Optimal ET sequence|legend=1| 2cd, …, 20cd, 22 }}
-[[Badness]]: 0.084395
+[[Badness]] (Sintel): 2.14
 === 11-limit ===
@@ Line 339: / Line 410: @@
 Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184
+Optimal tunings:
+* WE: ~7/5 = 598.8161{{c}}, ~22/15 = 653.8909{{c}} (~28/27 = 55.0747{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.7898{{c}} (~28/27 = 54.7898{{c}})
-{{Optimal ET sequence|legend=1| 20cde, 22 }}
+{{Optimal ET sequence|legend=0| 2cde, …, 20cde, 22 }}
-Badness: 0.045052
+Badness (Sintel): 1.49
 === 13-limit ===
@@ Line 352: / Line 425: @@
 Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435
+Optimal tunings:
+* WE: ~7/5 = 600.1030{{c}}, ~22/15 = 654.5470{{c}} (~28/27 = 54.4440{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.4665{{c}} (~28/27 = 54.4665{{c}})
-{{Optimal ET sequence|legend=1| 22 }}
+{{Optimal ET sequence|legend=0| 2cde, 20cde, 22 }}
-Badness: 0.041470
+Badness (Sintel): 1.71
 == Bipyth ==
-{{See also| Archytas clan #Superpyth }}
+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
@@ Line 367: / Line 442: @@
 {{Mapping|legend=1| 2 0 -24 -23 | 0 1 9 9 }}
-{{Multival|legend=1| 2 18 18 24 23 -9 }}
+: mapping generators: ~7/5, ~3
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 709.437
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 598.7533{{c}}, ~3/2 = 707.9630{{c}} (~15/14 = 109.2098{{c}})
+: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1579{{c}} (~15/14 = 109.1579{{c}})
+: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}
 {{Optimal ET sequence|legend=1| 10cd, 12cd, 22 }}
-[[Badness]]: 0.165033
+[[Badness]] (Sintel): 4.18
 === 11-limit ===
@@ Line 382: / Line 461: @@
 Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310
+Optimal tunings:
+* WE: ~7/5 = 599.2296{{c}}, ~3/2 = 708.3992{{c}} (~15/14 = 109.1697{{c}})
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1395{{c}} (~15/14 = 109.1395{{c}})
-{{Optimal ET sequence|legend=1| 10cd, 12cde, 22 }}
+{{Optimal ET sequence|legend=0| 10cd, 12cde, 22 }}
-Badness: 0.070910
+Badness (Sintel): 2.34
 == 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
@@ Line 395: / Line 478: @@
 {{Mapping|legend=1| 16 0 37 45 | 0 1 0 0 }}
-{{Multival|legend=1| 16 0 0 -37 -45 0 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~128/125 = 75.0539{{c}}, ~3/2 = 701.0578{{c}} (~525/512 = 25.5726{{c}})
-[[Optimal tuning]] ([[POTE]]): ~128/125 = 1\16, ~3/2 = 700.554
+: [[error map]]: {{val| 0.000 0.000 -11.314 +6.174 }}
+* [[CWE]]: ~128/125 = 75.0000{{c}}, ~3/2 = 700.8957{{c}} (~525/512 = 25.8957{{c}})
+: error map: {{val| 0.000 -1.401 -11.314 +6.174 }}
 {{Optimal ET sequence|legend=1| 16, 32, 48 }}
-[[Badness]]: 0.265972
+[[Badness]] (Sintel): 6.73
 === 11-limit ===
@@ Line 410: / Line 495: @@
 Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}
-Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331
+Optimal tunings:
+* WE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.7810{{c}} (~45/44 = 25.3476{{c}})
-{{Optimal ET sequence|legend=1| 16, 32, 48 }}
+* CWE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.6780{{c}} (~45/44 = 25.6780{{c}})
-Badness: 0.092774
-== Duodecim ==
-{{See also| Compton family #Duodecim }}
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 36/35, 50/49, 64/63
-{{Mapping|legend=1| 12 19 28 34 0 | 0 0 0 0 1 }}
-[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~11/8 = 565.023
+{{Optimal ET sequence|legend=0| 16, 32, 48 }}
-{{Optimal ET sequence|legend=1| 12, 24d, 36d }}
+Badness (Sintel): 3.07
-[[Badness]]: 0.030536
+== Notes ==
 [[Category:Temperament clans]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Jubilismic clan| ]] <!-- main article -->
 [[Category:Jubilismic| ]] <!-- key article -->
 [[Category:Rank 2]]