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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
Line 16: Line 16:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~5/4 = 379.210 (~8/7 = 220.890)
* [[WE]]: ~7/5 = 599.6673{{c}}, ~5/4 = 380.6287{{c}} (~8/7 = 219.0386{{c}})
: [[error map]]: {{val| 0.000 -7.104 +10.384 }}
: [[error map]]: {{val| -0.665 -7.016 +10.139 }}
* [[POTE]]: ~7/5 = 600.000, ~5/4 = 380.840 (~8/7 = 219.160)
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.0086{{c}} (~8/7 = 219.9914{{c}})
: error map: {{val| 0.000 -5.474 +12.014 }}
: error map: {{val| 0.000 -6.305 +11.183 }}


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


[[Badness]] (Smith): 0.00190
[[Badness]] (Sintel): 0.140


=== Overview to extensions ===
=== Overview to extensions ===
Line 32: Line 32:
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) → [[Dimipent family #Diminished|Dimipent family]]
* [[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]]
Line 49: Line 49:
: ''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
Line 60: Line 60:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~8/7 = 232.927
* [[WE]]: ~7/5 = 601.4623{{c}}, ~8/7 = 232.6544{{c}}
: [[error map]]: {{val| 0.000 -3.175 -19.241 -1.753 }}
: [[error map]]: {{val| +2.925 -1.067 -11.656 +7.294 }}
* [[POTE]]: ~7/5 = 600.000, ~8/7 = 232.089
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~8/7 = 232.2655{{c}}
: error map: {{val| 0.000 -5.689 -18.402 -0.915 }}
: 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]] (Smith): 0.062208
[[Badness]] (Sintel): 1.57


=== 11-limit ===
=== 11-limit ===
Line 77: Line 77:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~8/7 = 231.997
* WE: ~7/5 = 601.1769{{c}}, ~8/7 = 231.4273{{c}}
* POTE: ~7/5 = 600.000, ~8/7 = 230.974
* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1781{{c}}


{{Optimal ET sequence|legend=0| 10, 16, 26 }}
{{Optimal ET sequence|legend=0| 10, 16, 26 }}


Badness (Smith): 0.041563
Badness (Sintel): 1.37


=== 13-limit ===
=== 13-limit ===
Line 92: Line 92:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~8/7 = 232.100
* WE: ~7/5 = 601.1939{{c}}, ~8/7 = 231.4261{{c}}
* POTE: ~7/5 = 600.000, ~8/7 = 230.966
* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1617{{c}}


{{Optimal ET sequence|legend=0| 10, 16, 26 }}
{{Optimal ET sequence|legend=0| 10, 16, 26 }}


Badness (Smith): 0.025477
Badness (Sintel): 1.05


== 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
Line 111: Line 111:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~5/4 = 380.355 (~8/7 = 219.645)
* [[WE]]: ~7/5 = 599.6999{{c}}, ~5/4 = 380.3881{{c}} (~8/7 = 219.3119{{c}})
: [[error map]]: {{val| 0.000 -0.180 -5.959 +11.529 }}
: [[error map]]: {{val| -0.600 -0.015 -7.126 +10.062 }}
* [[POTE]]: ~7/5 = 600.000, ~5/4 = 380.578 (~8/7 = 219.422)
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5123{{c}} (~8/7 = 219.4877{{c}})
: error map: {{val| 0.000 +0.937 -5.735 +11.752 }}
: error map: {{val| 0.000 +0.606 -5.801 +11.686 }}


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


[[Badness]] (Smith): 0.082673
[[Badness]] (Sintel): 2.09


=== 11-limit ===
=== 11-limit ===
Line 128: Line 128:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~5/4 = 380.588 (~8/7 = 219.412)
* WE: ~7/5 = 600.0538{{c}}, ~5/4 = 380.5640{{c}} (~8/7 = 219.4897{{c}})
* POTE: ~7/5 = 600.000, ~5/4 = 380.530 (~8/7 = 219.470)
* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5419{{c}} (~8/7 = 219.4581{{c}})


{{Optimal ET sequence|legend=0| 6, 16, 22 }}
{{Optimal ET sequence|legend=0| 6, 16, 22 }}


Badness (Smith): 0.039151
Badness (Sintel): 1.29


==== 13-limit ====
==== 13-limit ====
Line 143: Line 143:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~5/4 = 380.449 (~8/7 = 219.551)
* WE: ~7/5 = 600.7886{{c}}, ~5/4 = 380.2857{{c}} (~8/7 = 220.5028{{c}})
* POTE: ~7/5 = 600.000, ~5/4 = 379.787 (~8/7 = 220.213)
* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.9119{{c}} (~8/7 = 220.0881{{c}})


{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}
{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}


Badness (Smith): 0.034376
Badness (Sintel): 1.42


; Music
; Music
Line 161: Line 161:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~5/4 = 379.762 (~8/7 = 220.238)
* WE: ~7/5 = 599.8927{{c}}, ~5/4 = 379.7688{{c}} (~8/7 = 220.1239{{c}})
* POTE: ~7/5 = 600.000, ~5/4 = 379.837 (~8/7 = 220.163)
* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.8117{{c}} (~8/7 = 220.1883{{c}})


{{Optimal ET sequence|legend=0| 16, 22f, 38 }}
{{Optimal ET sequence|legend=0| 6f, 16, 22f, 38 }}


Badness (Smith): 0.035284
Badness (Sintel): 1.46


== 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


Line 178: Line 180:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 754.204 (~15/14 = 154.204)
* [[WE]]: ~7/5 = 589.0384{{c}}, ~3/2 = 735.7242{{c}} (~15/14 = 146.6857{{c}})
: [[error map]]: {{val| 0.000 +52.249 +59.482 +76.970 }}
: [[error map]]: {{val| -21.923 +11.846 +12.193 +18.719 }}
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 749.415 (~15/14 = 149.415)
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 750.4026{{c}} (~15/14 = 150.4026{{c}})
: error map: {{val| 0.000 +47.460 +64.271 +81.759 }}
: error map: {{val| 0.000 +48.448 +63.284 +80.771 }}


{{Optimal ET sequence|legend=1| 2, 6, 8d }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}


[[Badness]] (Smith): 0.048978
[[Badness]] (Sintel): 1.24


=== 11-limit ===
=== 11-limit ===
Line 195: Line 197:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~3/2 = 754.205 (~15/14 = 154.205)
* WE: ~7/5 = 589.7684{{c}}, ~3/2 = 736.9708{{c}} (~12/11 = 147.2023{{c}})
* POTE: ~7/5 = 600.000, ~3/2 = 749.756 (~15/14 = 149.756)
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 750.5221{{c}} (~12/11 = 150.5221{{c}})


{{Optimal ET sequence|legend=0| 2, 6, 8d }}
{{Optimal ET sequence|legend=0| 2, 6, 8d }}


Badness (Smith): 0.029193
Badness (Sintel): 0.965


== Antikythera ==
== Antikythera ==
Line 218: Line 220:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~9/8 = 216.711
* [[WE]]: ~7/5 = 598.8483{{c}}, ~9/8 = 213.6844{{c}}
: [[error map]]: {{val| 0.000 +12.801 +3.025 +14.463 }}
: [[error map]]: {{val| -2.303 +2.864 -5.756 +10.580 }}
* [[POTE]]: ~7/5 = 600.000, ~9/8 = 214.095
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/8 = 214.6875{{c}}
: error map: {{val| 0.000 +10.815 -0.409 +17.079 }}
: error map: {{val| 0.000 +10.778 -1.001 +16.487 }}


{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }}
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }}


[[Tp tuning #T2 tuning|RMS error]]: 2.572 cents
[[Badness]] (Sintel): 0.253
 
[[Badness]] (Smith): 0.00501


== 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
Line 241: Line 243:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~6/5 = 325.769 (~7/6 = 274.231)
* [[WE]]: ~7/5 = 600.0365{{c}}, ~6/5 = 325.7389{{c}} (~7/6 = 274.2975{{c}})
: [[error map]]: {{val| 0.000 +1.120 -9.007 +8.481 }}
: [[error map]]: {{val| -2.303 +2.864 -5.756 +10.580 }}
* [[POTE]]: ~7/5 = 600.000, ~6/5 = 325.719 (~7/6 = 274.281)
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~6/5 = 325.7353{{c}} (~7/6 = 274.2647{{c}})
: error map: {{val| 0.000 +0.921 -9.156 +8.331 }}
: error map: {{val| 0.000 +10.778 -1.001 +16.487 }}


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


[[Badness]] (Smith): 0.043462
[[Badness]] (Sintel): 1.10


=== 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: 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 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~6/5 = 325.719 (~7/6 = 274.281)
* WE: ~7/5 = 600.1818{{c}}, ~6/5 = 325.6434{{c}} (~7/6 = 274.5384{{c}})
* POTE: ~7/5 = 600.000, ~6/5 = 325.545 (~7/6 = 274.455)
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 325.5854{{c}} (~7/6 = 274.4146{{c}})


{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}
{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}


Badness (Smith): 0.032058
Badness (Sintel): 1.06


=== Fleetwood ===
=== Fleetwood ===
Line 273: Line 275:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~6/5 = 326.684 (~7/6 = 273.316)
* WE: ~7/5 = 599.6049{{c}}, ~6/5 = 326.8229{{c}} (~7/6 = 272.7819{{c}})
* POTE: ~7/5 = 600.000, ~6/5 = 327.038 (~7/6 = 272.962)
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 326.8890{{c}} (~7/6 = 273.1110{{c}})


{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}
{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}


Badness (Smith): 0.035202
Badness (Sintel): 1.16


==== 13-limit ====
==== 13-limit ====
Line 288: Line 290:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~6/5 = 327.450 (~7/6 = 272.540)
* WE: ~7/5 = 599.5482{{c}}, ~6/5 = 327.5939{{c}} (~7/6 = 271.9543{{c}})
* POTE: ~7/5 = 600.000, ~6/5 = 327.841 (~7/6 = 272.159)
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 327.6706{{c}} (~7/6 = 272.3294{{c}})


{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}
{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}


Badness (Smith): 0.031835
Badness (Sintel): 1.32


=== Cavalier ===
=== Cavalier ===
Line 303: Line 305:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~6/5 = 324.238 (~7/6 = 275.762)
* WE: ~7/5 = 600.9467{{c}}, ~6/5 = 323.9369{{c}} (~7/6 = 277.0098{{c}})
* POTE: ~7/5 = 600.000, ~6/5 = 323.427 (~7/6 = 276.573)
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.7272{{c}} (~7/6 = 276.2728{{c}})


{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}
{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}


Badness (Smith): 0.052899
Badness (Sintel): 1.75


==== 13-limit ====
==== 13-limit ====
Line 318: Line 320:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~6/5 = 324.187 (~7/6 = 275.813)
* WE: ~7/5 = 600.9537{{c}}, ~6/5 = 323.9097{{c}} (~7/6 = 277.0440{{c}})
* POTE: ~7/5 = 600.000, ~6/5 = 323.396 (~7/6 = 276.604)
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.6876{{c}} (~7/6 = 276.3124{{c}})


{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}
{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}


Badness (Smith): 0.035040
Badness (Sintel): 1.45


== 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
Line 337: Line 341:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~64/45 = 645.313 (~64/63 = 45.313)
* [[WE]]: ~7/5 = 601.6846{{c}}, ~64/45 = 648.0937{{c}} (~64/63 = 46.4091{{c}})
: [[error map]]: {{val| 0.000 -11.329 -12.879 +4.609 }}
: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
* [[POTE]]: ~7/5 = 600.000, ~64/45 = 646.279 (~64/63 = 46.279)
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~64/45 = 646.0539{{c}} (~64/63 = 46.0539{{c}})
: error map: {{val| 0.000 -9.397 -17.710 -0.222 }}
: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}


{{Optimal ET sequence|legend=1| 2, 24c, 26 }}
{{Optimal ET sequence|legend=1| 2, 24c, 26 }}


[[Badness]] (Smith): 0.141473
[[Badness]] (Sintel): 3.58


=== 11-limit ===
=== 11-limit ===
Line 354: Line 358:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~16/11 = 645.343 (~56/55 = 45.343)
* WE: ~7/5 = 601.2186{{c}}, ~16/11 = 647.4300{{c}} (~56/55 = 46.2114{{c}})
* POTE: ~7/5 = 600.000, ~16/11 = 646.118 (~56/55 = 46.118)
* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9681{{c}} (~56/55 = 45.9681{{c}})


{{Optimal ET sequence|legend=0| 2, 24c, 26 }}
{{Optimal ET sequence|legend=0| 2, 24c, 26 }}


Badness (Smith): 0.063212
Badness (Sintel): 2.09


=== 13-limit ===
=== 13-limit ===
Line 369: Line 373:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~16/11 = 645.208 (~56/55 = 45.208)
* WE: ~7/5 = 601.2206{{c}}, ~16/11 = 647.4219{{c}} (~56/55 = 46.2013{{c}})
* POTE: ~7/5 = 600.000, ~16/11 = 646.108 (~56/55 = 46.108)
* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9362{{c}} (~56/55 = 45.9362{{c}})


{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}
{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}


Badness (Smith): 0.043997
Badness (Sintel): 1.82


== 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
Line 388: Line 394:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~40/27 = 653.872 (~28/27 = 53.872)
* [[WE]]: ~7/5 = 598.9554{{c}}, ~40/27 = 653.5596{{c}} (~28/27 = 54.6042{{c}})
: [[error map]]: {{val| 0.000 +5.789 -9.211 +8.277 }}
: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
* [[POTE]]: ~7/5 = 600.000, ~40/27 = 654.699 (~28/27 = 54.699)
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~40/27 = 654.3329{{c}} (~28/27 = 54.3329{{c}})
: error map: {{val| 0.000 +7.444 -3.417 +14.070 }}
: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}


{{Optimal ET sequence|legend=1| 2cd, …, 20cd, 22 }}
{{Optimal ET sequence|legend=1| 2cd, …, 20cd, 22 }}


[[Badness]] (Smith): 0.084395
[[Badness]] (Sintel): 2.14


=== 11-limit ===
=== 11-limit ===
Line 405: Line 411:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~22/15 = 654.289 (~28/27 = 54.289)
* WE: ~7/5 = 598.8161{{c}}, ~22/15 = 653.8909{{c}} (~28/27 = 55.0747{{c}})
* POTE: ~7/5 = 600.000, ~22/15 = 655.184 (~28/27 = 55.184)
* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.7898{{c}} (~28/27 = 54.7898{{c}})


{{Optimal ET sequence|legend=0| 2cde, …, 20cde, 22 }}
{{Optimal ET sequence|legend=0| 2cde, …, 20cde, 22 }}


Badness (Smith): 0.045052
Badness (Sintel): 1.49


=== 13-limit ===
=== 13-limit ===
Line 420: Line 426:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~22/15 = 654.547 (~28/27 = 54.547)
* WE: ~7/5 = 600.1030{{c}}, ~22/15 = 654.5470{{c}} (~28/27 = 54.4440{{c}})
* POTE: ~7/5 = 600.000, ~22/15 = 654.435 (~28/27 = 54.435)
* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.4665{{c}} (~28/27 = 54.4665{{c}})


{{Optimal ET sequence|legend=0| 2cde, 20cde, 22 }}
{{Optimal ET sequence|legend=0| 2cde, 20cde, 22 }}


Badness (Smith): 0.041470
Badness (Sintel): 1.71


== Bipyth ==
== Bipyth ==
: ''For the 5-limit version, see [[Superpyth–22 equivalence continuum]].''
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 439: Line 445:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 708.695 (~15/14 = 108.695)
* [[WE]]: ~7/5 = 598.7533{{c}}, ~3/2 = 707.9630{{c}} (~15/14 = 109.2098{{c}})
: [[error map]]: {{val| 0.000 +6.740 -8.058 +9.430 }}
: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 709.437 (~15/14 = 109.437)
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1579{{c}} (~15/14 = 109.1579{{c}})
: error map: {{val| 0.000 +7.482 -1.379 +16.109 }}
: 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]] (Smith): 0.165033
[[Badness]] (Sintel): 4.18


=== 11-limit ===
=== 11-limit ===
Line 456: Line 462:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~3/2 = 708.813 (~15/14 = 108.813)
* WE: ~7/5 = 599.2296{{c}}, ~3/2 = 708.3992{{c}} (~15/14 = 109.1697{{c}})
* POTE: ~7/5 = 600.000, ~3/2 = 709.310 (~15/14 = 109.310)
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1395{{c}} (~15/14 = 109.1395{{c}})


{{Optimal ET sequence|legend=0| 10cd, 12cde, 22 }}
{{Optimal ET sequence|legend=0| 10cd, 12cde, 22 }}


Badness (Smith): 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


Line 471: Line 479:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~128/125 = 75.000, ~3/2 = 701.955 (~525/512 = 26.955)
* [[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 }}
: [[error map]]: {{val| 0.000 0.000 -11.314 +6.174 }}
* [[POTE]]: ~128/125 = 75.000, ~3/2 = 700.554 (~525/512 = 25.554)
* [[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 }}
: 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]] (Smith): 0.265972
[[Badness]] (Sintel): 6.73


=== 11-limit ===
=== 11-limit ===
Line 488: Line 496:


Optimal tunings:  
Optimal tunings:  
* CTE: ~22/21 = 75.000, ~3/2 = 701.844 (~45/44 = 26.844)
* WE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.7810{{c}} (~45/44 = 25.3476{{c}})
* POTE: ~22/21 = 75.000, ~3/2 = 700.331 (~45/44 = 25.331)
* CWE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.6780{{c}} (~45/44 = 25.6780{{c}})


{{Optimal ET sequence|legend=0| 16, 32, 48 }}
{{Optimal ET sequence|legend=0| 16, 32, 48 }}


Badness (Smith): 0.092774
Badness (Sintel): 3.07


== Notes ==
== Notes ==
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