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The '''jubilismic clan''' tempers out the jubilisma, [[50/49]], which means [[7/5]] and [[10/7]] are identified and the [[octave]] is divided in two.  
{{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 ==
== 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
[[Subgroup]]: 2.5.7
Line 8: Line 9:
[[Comma list]]: 50/49
[[Comma list]]: 50/49


[[Sval]] [[mapping]]: [{{val| 2 0 1 }}, {{val| 0 1 1 }}]
{{Mapping|legend=2| 2 0 1 | 0 1 1 }}


Sval mapping generators: ~7/5, ~5
: 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 ===
=== 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]]. Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five.  
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]].  


Lemba, astrology, and doublewide are discussed below; others in the clan are
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.
* [[Diminished]] → [[Dimipent family #Diminished|Dimipent family]]
* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]]
* [[Decimal]] → [[Dicot family #Decimal|Dicot family]]
* [[Injera]] → [[Meantone family #Injera|Meantone family]]
* [[Octokaidecal]] → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
* [[Hedgehog]] → [[Porcupine family #Hedgehog|Porcupine family]]
* [[Bipelog]] → [[Pelogic family #Bipelog|Pelogic family]]
* [[Dubbla]] → [[Wesley family #Dubbla|Wesley family]]
* [[Hexe]] → [[Augmented family #Hexe|Augmented family]]


which are discussed elsewhere.
Temperaments discussed elsewhere are:
* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
* [[Pajara]] (+64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
* ''[[Dubbla]]'' (+78125/73728) → [[Wesley family #Dubbla|Wesley family]]
* ''[[Injera]]'' (+81/80) → [[Meantone family #Injera|Meantone family]]
* ''[[Octokaidecal]]'' (+28/27) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
* ''[[Bipelog]]'' (+135/128) → [[Mavila #Bipelog|Mavila family]]
* ''[[Hexe]]'' (+128/125) → [[Augmented family #Hexe|Augmented family]]
* ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]]
* ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]]
* ''[[Byhearted]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]
 
Considered below are lemba, astrology, walid, antikythera, doublewide, elvis, comic, and bipyth.


== Lemba ==
== Lemba ==
{{Main| 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. 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
Line 41: Line 55:
[[Comma list]]: 50/49, 525/512
[[Comma list]]: 50/49, 525/512


[[Mapping]]: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]
{{Mapping|legend=1| 2 2 5 6 | 0 3 -1 -1 }}


Mapping generators: ~7/5, ~8/7
: 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 ===
=== 11-limit ===
Line 56: Line 74:
Comma list: 45/44, 50/49, 385/384
Comma list: 45/44, 50/49, 385/384


Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
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 ===
=== 13-limit ===
Line 69: Line 89:
Comma list: 45/44, 50/49, 65/64, 78/77
Comma list: 45/44, 50/49, 65/64, 78/77


Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
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 ==
{{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
Line 84: Line 106:
[[Comma list]]: 50/49, 3125/3072
[[Comma list]]: 50/49, 3125/3072


[[Mapping]]: [{{val| 2 0 4 5 }}, {{val| 0 5 1 1 }}]
{{Mapping|legend=1| 2 0 4 5 | 0 5 1 1 }}


Mapping geenerators: ~7/5, ~5/4
: 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 ===
=== 11-limit ===
Line 101: Line 125:
Comma list: 50/49, 121/120, 176/175
Comma list: 50/49, 121/120, 176/175


Mapping: [{{val| 2 0 4 5 5 }}, {{val| 0 5 1 1 3 }}]
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 ====
==== 13-limit ====
Line 114: Line 140:
Comma list: 50/49, 65/64, 78/77, 121/120
Comma list: 50/49, 65/64, 78/77, 121/120


Mapping: [{{val| 2 0 4 5 5 8 }}, {{val| 0 5 1 1 3 -1 }}]
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
; Music
Line 130: Line 158:
Comma list: 50/49, 66/65, 105/104, 121/120
Comma list: 50/49, 66/65, 105/104, 121/120


Mapping: [{{val| 2 0 4 5 5 3 }}, {{val| 0 5 1 1 3 7 }}]
Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}
 
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}})


POTE generator: ~5/4 = 379.837
{{Optimal ET sequence|legend=0| 6f, 16, 22f, 38 }}


{{Optimal ET sequence|legend=1| 16, 22f, 38 }}
Badness (Sintel): 1.46


Badness: 0.035284
== 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.  


== Doublewide ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 875/864
[[Comma list]]: 16/15, 50/49
 
{{Mapping|legend=1| 2 0 8 9 | 0 1 -1 -1 }}


[[Mapping]]: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]
: mapping generators: ~7/5, ~3


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~6/5 = 325.719
[[Optimal tuning]]s:
* [[WE]]: ~7/5 = 589.0384{{c}}, ~3/2 = 735.7242{{c}} (~15/14 = 146.6857{{c}})
: [[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| 4, 14bd, 18, 22, 48, 70c }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}


[[Badness]]: 0.043462
[[Badness]] (Sintel): 1.24


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 50/49, 99/98, 875/864
Comma list: 16/15, 22/21, 50/49
 
Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}
 
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=0| 2, 6, 8d }}


Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]
Badness (Sintel): 0.965


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545
== 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]].  


{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48, 70c, 118cd }}
[[Subgroup]]: 2.9.5.7


Badness: 0.032058
[[Comma list]]: 50/49, 64/63


=== Fleetwood ===
{{Mapping|legend=2| 2 0 11 12 | 0 1 -1 -1 }}
Subgroup: 2.3.5.7.11
 
: mapping generators: ~7/5, ~9
 
{{Mapping|legend=3| 2 3 5 6 | 0 1/2 -1 -1 }}


Comma list: 50/49, 55/54, 176/175
: [[gencom]]: [7/5 8/7; 50/49 64/63]


Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 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 tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }}


{{Optimal ET sequence|legend=1| 4e, 18e, 22 }}
[[Badness]] (Sintel): 0.253


Badness: 0.035202
== Doublewide ==
: ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Doublewide (5-limit)]].''


==== 13-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: 2.3.5.7.11.13


Comma list: 50/49, 55/54, 65/63, 176/175
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]
[[Comma list]]: 50/49, 875/864


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841
{{Mapping|legend=1| 2 1 3 4 | 0 4 3 3 }}


{{Optimal ET sequence|legend=1| 4ef, 18e, 22, 84bddf }}
: mapping generators: ~7/5, ~6/5


Badness: 0.031835
[[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 }}


=== Cavalier ===
{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48 }}
Subgroup: 2.3.5.7.11


Comma list: 45/44, 50/49, 875/864
[[Badness]] (Sintel): 1.10


Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427
Comma list: 50/49, 99/98, 385/384


{{Optimal ET sequence|legend=1| 22e, 26 }}
Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}


Badness: 0.052899
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}})


==== 13-limit ====
{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}
Subgroup: 2.3.5.7.11.13


Comma list: 45/44, 50/49, 78/77, 325/324
Badness (Sintel): 1.06


Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]
=== Fleetwood ===
Subgroup: 2.3.5.7.11


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396
Comma list: 50/49, 55/54, 176/175


{{Optimal ET sequence|legend=1| 22ef, 26 }}
Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}


Badness: 0.035040
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}})


== Elvis ==
{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Elvis]].''


[[Subgroup]]: 2.3.5.7
Badness (Sintel): 1.16


[[Comma list]]: 50/49, 8505/8192
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


[[Mapping]]: [{{val| 2 1 10 11 }}, {{val| 0 2 -5 -5 }}]
Comma list: 50/49, 55/54, 65/63, 176/175


{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~45/32 = 553.721
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| 2, 24c, 26 }}
{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}


[[Badness]]: 0.141473
Badness (Sintel): 1.32


=== 11-limit ===
=== Cavalier ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 45/44, 50/49, 1344/1331
Comma list: 45/44, 50/49, 875/864


Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]
Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882
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| 2, 24c, 26 }}
{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}


Badness: 0.063212
Badness (Sintel): 1.75


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 45/44, 50/49, 78/77, 1053/1024
Comma list: 45/44, 50/49, 78/77, 325/324
 
Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}


Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]
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 tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892
{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}


{{Optimal ET sequence|legend=1| 2f, 24cf, 26 }}
Badness (Sintel): 1.45


Badness: 0.043997
== Elvis ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Elvis]].''


== Crepuscular ==
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.
{{See also| Fifive family #Crepuscular }}


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 4375/4374
[[Comma list]]: 50/49, 8505/8192


[[Mapping]]: [{{val| 2 2 3 4 }}, {{val| 0 5 7 7 }}]
{{Mapping|legend=1| 2 1 10 11 | 0 2 -5 -5 }}


{{Multival|legend=1|10 14 14 -1 -6 -7}}
: mapping generators: ~7/5, ~64/45


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349
[[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| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=1| 2, 24c, 26 }}


[[Badness]]: 0.086669
[[Badness]] (Sintel): 3.58


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 50/49, 99/98, 864/847
Comma list: 45/44, 50/49, 1344/1331


Mapping: [{{val| 2 2 3 4 6 }}, {{val| 0 5 7 7 4 }}]
Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587
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| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=0| 2, 24c, 26 }}


Badness: 0.040758
Badness (Sintel): 2.09


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 50/49, 78/77, 99/98, 144/143
Comma list: 45/44, 50/49, 78/77, 1053/1024


Mapping: [{{val| 2 2 3 4 6 6 }}, {{val| 0 5 7 7 4 6 }}]
Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554
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| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}


Badness: 0.024368
Badness (Sintel): 1.82


== Comic ==
== 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
[[Subgroup]]: 2.3.5.7
Line 309: Line 389:
[[Comma list]]: 50/49, 2240/2187
[[Comma list]]: 50/49, 2240/2187


[[Mapping]]: [{{val| 2 1 -3 -2 }}, {{val| 0 2 7 7 }}]
{{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 ===
=== 11-limit ===
Line 324: Line 408:
Comma list: 50/49, 99/98, 2662/2625
Comma list: 50/49, 99/98, 2662/2625


Mapping: [{{val| 2 1 -3 -2 -4 }}, {{val| 0 2 7 7 10 }}]
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 ===
=== 13-limit ===
Line 337: Line 423:
Comma list: 50/49, 65/63, 99/98, 968/945
Comma list: 50/49, 65/63, 99/98, 968/945


Mapping: [{{val| 2 1 -3 -2 -4 3 }}, {{val| 0 2 7 7 10 4 }}]
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 ==
== 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
[[Subgroup]]: 2.3.5.7
Line 352: Line 440:
[[Comma list]]: 50/49, 20480/19683
[[Comma list]]: 50/49, 20480/19683


[[Mapping]]: [{{val| 2 0 -24 -23 }}, {{val| 0 1 9 9 }}]
{{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 }}
{{Optimal ET sequence|legend=1| 10cd, 12cd, 22 }}


[[Badness]]: 0.165033
[[Badness]] (Sintel): 4.18


=== 11-limit ===
=== 11-limit ===
Line 367: Line 459:
Comma list: 50/49, 121/120, 896/891
Comma list: 50/49, 121/120, 896/891


Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
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 ==
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


[[Comma list]]: 50/49, 546875/524288
[[Comma list]]: 50/49, 546875/524288


[[Mapping]]: [{{val| 16 0 37 45 }}, {{val| 0 1 0 0 }}]
{{Mapping|legend=1| 16 0 37 45 | 0 1 0 0 }}
 
{{Multival|legend=1| 16 0 0 -37 -45 0 }}


[[Optimal tuning]] ([[POTE]]): ~128/125 = 1\16, ~3/2 = 700.554
[[Optimal tuning]]s:
* [[WE]]: ~128/125 = 75.0539{{c}}, ~3/2 = 701.0578{{c}} (~525/512 = 25.5726{{c}})
: [[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 }}
{{Optimal ET sequence|legend=1| 16, 32, 48 }}


[[Badness]]: 0.265972
[[Badness]] (Sintel): 6.73


=== 11-limit ===
=== 11-limit ===
Line 395: Line 493:
Comma list: 50/49, 385/384, 1331/1323
Comma list: 50/49, 385/384, 1331/1323


Mapping: [{{val| 16 0 37 45 30 }}, {{val| 0 1 0 0 1 }}]
Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}
 
Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331
 
{{Optimal ET sequence|legend=1| 16, 32, 48 }}
 
Badness: 0.092774
 
== Duodecim ==
{{See also| Compton family #Duodecim }}
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 36/35, 50/49, 64/63
 
[[Mapping]]: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
 
[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~11/8 = 565.023
 
{{Optimal ET sequence|legend=1| 12, 24d, 36d }}
 
[[Badness]]: 0.030536
 
== Vigintiduo ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 50/49, 64/63, 245/243
 
[[Mapping]]: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]
 
[[Optimal tuning]] ([[POTE]]): ~36/35 = 1\22, ~11/8 = 557.563
 
{{Optimal ET sequence|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }}
 
[[Badness]]: 0.048372
 
== Vigin ==
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: 50/49, 55/54, 64/63, 99/98


[[Mapping]]: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]
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}})


[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\22, ~13/8 = 844.624
{{Optimal ET sequence|legend=0| 16, 32, 48 }}


{{Optimal ET sequence|legend=1| 22, 44 }}
Badness (Sintel): 3.07


[[Badness]]: 0.029849
== Notes ==


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Jubilismic clan| ]] <!-- main article -->
[[Category:Jubilismic clan| ]] <!-- main article -->
[[Category:Jubilismic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Jubilismic_clan"