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Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to temper out very large “commas” such as 9/8, 32/27, or 15/14, equating wildly different interval sizes. All temperaments listed temper out an interval of at least size 15/14.
{{Technical data page}}
Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to [[tempering out|temper out]] very large intervals such as [[9/8]], [[10/9]], [[32/27]], or [[15/14]], equating wildly different interval sizes with [[semitone (interval size measure)|semitone]]-level or even greater [[error]]s, and often swapping the sizes of simple ratios compared to just intonation. As a result, all of them are right on or even beyond the edge of what can be sensibly called a temperament at all; that is to say, they are [[exotemperament]]s.


== Antitonic ==
== Antitonic ==
This temperament is characterized by [[9/8]] being tempering out, and has been termed a "troll temperament". It is named on account of 4/3 and 3/2 both being represented by the 600 cent half octave, which, in terms of diatonic function, serves as an antitonic. Surprisingly, it has extensions all the way up to the 11-limit, as confirmed by the data from [http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=2_4p&tuning=po x31eq]. The original 5-limit is basically the 3-limit music of [[2edo]] with the addition of harmonic 5 represented by an independent generator.  
This temperament is characterized by [[9/8]] being tempered out and has been termed a "troll temperament" by its namers. Its [[ploidacot]] is diploid acot. It is named on account of 4/3 and 3/2 both being represented by the 600-cent half octave, which, in terms of diatonic function, serves as an antitonic. The 7-limit extension tempers out 15/14 and 21/20, equating 5/4 with 7/6 and 6/5 with 8/7. The 11-limit extension tempers out 12/11 and 33/32. The original 5-limit is basically the 3-limit music of [[2edo]] with the addition of harmonic 5 represented by an independent generator.  


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: [[9/8]]
[[Comma list]]: [[9/8]]


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


Mapping generators: ~3/2, ~5
: mapping generators: ~3/2, ~5


[[POTE generator]]: ~5/4 = 313.690 or ~6/5 = 286.310
[[Optimal tuning]]s:  
* [[WE]]: ~3/2 = 615.125{{c}}, ~5/4 = 321.597{{c}} (~6/5 = 293.528{{c}})
: [[error map]]: {{val| +30.250 -56.581 -4.217 }}
* [[CWE]]: ~3/2 = 600.000{{c}}, ~5/4 = 336.527{{c}} (~6/5 = 263.473{{c}})
: error map: {{val| 0.000 -101.955 -49.787 }}


{{Optimal ET sequence|legend=1| 2, 4 }}
{{Optimal ET sequence|legend=1| 2, 4 }}


[[Badness]]: 0.021647
[[Badness]] (Sintel): 0.508
 
; Music
* [[:File:Antitonic(8).mp3|''Antitonic(8)'']] (2024) – short composition by [[Wensik]] in POTE-tuned 5-limit antitonic using an 8-note ternary scale.


=== 7-limit ===
=== Septimal antitonic ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 9/8, 15/14
Comma list: 9/8, 15/14


[[Mapping]]: [{{val| 2 3 0 1 }}, {{val| 0 0 1 1 }}]
Mapping: {{mapping| 2 3 0 1 | 0 0 1 1 }}


[[POTE generator]]: ~5/4 = 301.997 or ~6/5 = 298.003
Optimal tunings:  
* WE: ~3/2 = 614.759{{c}}, ~7/6 = 309.426{{c}} (~6/5 = 305.334{{c}})
* CWE: ~3/2 = 600.000{{c}}, ~7/6 = 326.047{{c}} (~6/5 = 273.953{{c}})


{{Optimal ET sequence|legend=1| 2, 4 }}
{{Optimal ET sequence|legend=0| 2, 4 }}


[[Badness]]: 0.019373
Badness (Sintel): 0.490


==== 11-limit ====
==== 11-limit ====
Line 36: Line 46:
Comma list: 9/8, 12/11, 15/14
Comma list: 9/8, 12/11, 15/14


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


POTE generator: ~5/4 = 340.293 or ~6/5 = 259.707
Optimal tunings:  
* WE: ~3/2 = 606.293{{c}}, ~5/4 = 343.862{{c}} (~8/7 = 262.431{{c}})
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 348.102{{c}} (~8/7 = 251.898{{c}})


{{Optimal ET sequence|legend=1| 2, 4 }}
{{Optimal ET sequence|legend=0| 2, 4 }}


Badness: 0.021810
Badness (Sintel): 0.721


==== Antietam ====
==== Antietam ====
Line 49: Line 61:
Comma list: 9/8, 11/10, 15/14
Comma list: 9/8, 11/10, 15/14


Mapping: [{{val| 2 3 0 1 2 }}, {{val | 0 0 1 1 1}}]
Mapping: {{mapping| 2 3 0 1 2 | 0 0 1 1 1 }}


POTE generator: ~5/4 = 322.080 or ~6/5 = 277.920
Optimal tunings:  
* WE: ~3/2 = 616.135{{c}}, ~5/4 = 330.741{{c}} (~6/5 = 285.393{{c}})
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 349.843{{c}} (~8/7 = 250.157{{c}})


{{Optimal ET sequence|legend=1| 2, 4e }}
{{Optimal ET sequence|legend=0| 2, 4e }}


Badness: 0.018993
Badness (Sintel): 0.628


=== Antaeus ===
=== Antaeus ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 9/8, 35/32
Comma list: 9/8, 35/32


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


[[POTE generator]]: ~5/4 = 315.962 or ~6/5 = 284.038
Optimal tunings:  
* WE: ~3/2 = 614.854{{c}}, ~5/4 = 323.784{{c}} (~6/5 = 291.070{{c}})
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 317.349{{c}} (~6/5 = 282.651{{c}})


{{Optimal ET sequence|legend=1| 2d, 4 }}
{{Optimal ET sequence|legend=0| 2d, 4 }}


[[Badness]]: 0.037537
Badness (Sintel): 0.950


==== 11-limit ====
==== 11-limit ====
Line 75: Line 91:
Comma list: 9/8, 12/11, 35/32
Comma list: 9/8, 12/11, 35/32


Mapping: [{{val| 2 3 0 10 7 }}, {{val| 0 0 1 -1 0 }}]
Mapping: {{mapping| 2 3 0 10 7 | 0 0 1 -1 0 }}
 
Optimal tunings:
* WE: ~3/2 = 609.311{{c}}, ~5/4 = 323.110{{c}} (~6/5 = 286.200{{c}})
* CWE: ~3/2 = 600.000{{c}}, ~5/4 = 318.904{{c}} (~6/5 = 281.096{{c}})
 
{{Optimal ET sequence|legend=0| 2d, 4 }}
 
Badness (Sintel): 1.12
 
== Alteraugment ==
Alteraugment tempers out the [[32/27|Pythagorean minor third (32/27)]]. It is like [[augmented (temperament)|augmented]], but the period represents 4/3 instead of 5/4, and the generator in turn provides 5/4 instead of 3/2. Its ploidacot is triploid acot. [[User:VectorGraphics|Vector Graphics]] suggests the name ''kinsborough'' for this temperament.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: [[32/27]]
 
{{Mapping|legend=1| 3 5 0 | 0 0 1 }}
 
: mapping generators: ~4/3, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~4/3 = 389.212{{c}}, ~5/4 = 447.530{{c}} (~10/9 = 58.318{{c}})
: [[error map]]: {{val| -32.364 +44.105 -3.512 }}
* [[CWE]]: ~4/3 = 400.000{{c}}, ~5/4 = 434.191{{c}} (~15/16 = 34.191{{c}})
: error map: {{val| 0.000 +98.045 +47.878 }}
 
{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc }}
 
[[Badness]] (Sintel): 1.83
 
== Antonian ==
{{Main| Antonian }}
This temperament family is characterized by the [[color notation|yo 2nd]] ([[10/9]]) being tempered out. It identifies [[3/2]] with [[5/3]], [[4/3]] with [[6/5]], and [[5/4]] with [[9/8]].
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: [[10/9]]
 
{{Mapping|legend=1| 1 0 -1 | 0 1 2 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1187.236{{c}}, ~3/2 = 767.716{{c}}
: [[error map]]: {{val| -12.764 +52.997 -63.645 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 767.718{{c}}
: error map: {{val| 0.000 +65.763 -50.877 }}
 
{{Optimal ET sequence|legend=1| 2c, 3 }}


POTE generator: ~5/4 = 318.173 or ~6/5 = 281.827
[[Badness]] (Sintel): 0.392


{{Optimal ET sequence|legend=1| 2d, 4 }}
=== Septimal antonian ===
{{See also| Trienstonic clan }}


Badness: 0.033786
Subgroup: 2.3.5.7


=== Music ===
Comma list: 10/9, 15/14
[[File:Antitonic(8).mp3]]


short composition by Wensik in POTE-tuned 5-limit antitonic using an 8-note ternary scale.
Mapping: {{mapping| 1 0 -1 -2 | 0 1 2 3 }}


== Alteraugment ==
Optimal tunings:
Like [[augmented]], but the generator provides 5/4 instead of 3/2.
* WE: ~2 = 1193.691{{c}}, ~3/2 = 742.509{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.086{{c}}


Subgroup: 2.3.5
{{Optimal ET sequence|legend=0| 2cd, 3d, 5c }}


[[Comma]]: [[32/27]]
Badness (Sintel): 0.606


[[Mapping]]: [{{val| 3 5 7 }}, {{val| 0 0 1 }}]
=== Antonym ===
Subgroup: 2.3.5.7


[[POTE generator]]: ~10/9 = 59.935
Comma list: 7/6, 10/9


{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc, 18bbcc }}
Mapping: {{mapping| 1 0 -1 1 | 0 1 2 1 }}


[[Badness]]: 0.078042
Optimal tunings:  
* WE: ~2 = 1209.795{{c}}, ~3/2 = 765.995{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 765.949{{c}}


Vector Graphics suggests the name kinsborough for this temperament.
{{Optimal ET sequence|legend=0| 2cd, 3 }}


== Yo (2c&3) ==
Badness (Sintel): 0.568
This temperament family is characterized by the [[Color notation|yo 2nd]] [[10/9]] being tempering out.


Subgroup: 2.3.5
=== Antony ===
Subgroup: 2.3.5.7


[[Comma list]]: [[10/9]]
Comma list: 8/7, 10/9


[[Mapping]]: [{{val| 1 0 -1 }}, {{val| 0 1 2 }}]
Mapping: {{mapping| 1 0 -1 3 | 0 1 2 0 }}


[[POTE generator]]: ~3/2 = 775.970
Optimal tunings:  
* WE: ~2 = 1151.235{{c}}, ~3/2 = 789.399{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 800.996{{c}}


{{Optimal ET sequence|legend=1| 3, 11bc, 14bc, 17bb }}
{{Optimal ET sequence|legend=0| 1c, 3d }}


[[Badness]]: 0.016712
Badness (Sintel): 0.720


=== Brutus ===
=== Brutus ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 10/9, 28/25
Comma list: 10/9, 28/25


[[Mapping]]: [{{val| 1 0 -1 -4 }}, {{val| 0 1 2 4 }}]
Mapping: {{mapping| 1 0 -1 -4 | 0 1 2 4 }}


[[POTE generator]]: ~3/2 = 848.221
Optimal tunings:  
* WE: ~2 = 1158.982{{c}}, ~3/2 = 819.228{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 831.346{{c}}


{{Optimal ET sequence|legend=1| 3, 7bc, 10bc }}
{{Optimal ET sequence|legend=0| 3, 7bc }}


[[Badness]]: 0.053389
Badness (Sintel): 1.35


=== Phlegyas ===
=== Phlegyas ===
{{See also| Archytas clan }}
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 10/9, 35/32
Comma list: 10/9, 35/32


[[Mapping]]: [{{val| 1 0 -1 6 }}, {{val| 0 1 2 -2 }}]
Mapping: {{mapping| 1 0 -1 6 | 0 1 2 -2 }}


[[POTE generator]]: ~3/2 = 743.135
Optimal tunings:  
* WE: ~2 = 1206.510{{c}}, ~3/2 = 747.166{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.797{{c}}


{{Optimal ET sequence|legend=1| 3, 5c, 8c, 13bcc }}
{{Optimal ET sequence|legend=0| 3, 5c, 8c }}


[[Badness]]: 0.051293
Badness (Sintel): 1.30


=== Charon ===
=== Charon ===
{{See also| Jubilismic clan }}
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 10/9, 49/45
Comma list: 10/9, 49/45


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


[[POTE generator]]: ~3/2 = 782.604 (or ~10/9 = 182.604)
Optimal tunings:  
* WE: ~7/5 = 593.832{{c}}, ~3/2 = 774.559{{c}} (~15/14 = 180.726{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 774.466{{c}} (~15/14 = 174.466{{c}})


{{Optimal ET sequence|legend=1| 6, 14bc, 20bb }}
{{Optimal ET sequence|legend=0| 4bcd, 6 }}


[[Badness]]: 0.056404
Badness (Sintel): 1.43


=== Nessus ===
=== Nessus ===
{{See also| Semaphoresmic clan }}
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 10/9, 49/48
Comma list: 10/9, 49/48
 
Mapping: {{mapping| 1 0 -1 2 | 0 2 4 1 }}
: mapping generators: ~2, ~7/4
 
Optimal tunings:
* WE: ~2 = 1189.201{{c}}, ~7/4 = 978.002{{c}}
* CWE: ~2 = 1200.000{{c}}, ~7/4 = 983.918{{c}}
 
{{Optimal ET sequence|legend=0| 5c, 6 }}


[[Mapping]]: [{{val| 1 0 -1 2 }}, {{val| 0 2 4 1 }}]
Badness (Sintel): 1.49


[[POTE generator]]: ~7/6 = 213.117
== Ternary ==
Ternary is identical to [[3edo|3et]] in the 5-limit, but has an independent generator for prime 7.  


{{Optimal ET sequence|legend=1| 5c, 6, 11bc, 17bb }}
[[Subgroup]]: 2.3.5.7


[[Badness]]: 0.059070
[[Comma list]]: 10/9, 16/15
 
{{Mapping|legend=1| 3 5 7 0 | 0 0 0 1 }}
 
: mapping generators: ~5/4, ~7
 
[[Optimal tuning]]s:
* [[WE]]: ~5/4 = 391.796{{c}}, ~7/4 = 1012.806{{c}} (~15/14 = 162.582{{c}})
: [[error map]]: {{val| -24.612 +57.026 -43.741 -5.243 }}
* [[CWE]]: ~5/4 = 400.000{{c}}, ~7/4 = 1016.378{{c}} (~8/7 = 183.622{{c}})
: error map: {{val| 0.000 +98.045 +13.686 +47.552 }}
 
{{Optimal ET sequence|legend=1| 3d, 6, 9bd }}
 
[[Badness]] (Sintel): 0.726
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 10/9, 16/15, 22/21
 
Mapping: {{mapping| 3 5 7 0 2 | 0 0 0 1 1 }}
 
Optimal tunings:
* WE: ~5/4 = 391.788{{c}}, ~7/4 = 1011.942{{c}} (~12/11 = 163.422{{c}})
* CWE: ~5/4 = 400.000{{c}}, ~7/4 = 1013.973{{c}} (~12/11 = 186.027{{c}})
 
{{Optimal ET sequence|legend=0| 3de, 6 }}
 
Badness (Sintel): 0.846
 
== Quad ==
Quad is identical to [[4edo|4et]] in the 5-limit, but has an independent generator for prime 7.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 9/8, 25/24
 
{{Mapping|legend=1| 4 6 9 0 | 0 0 0 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~6/5 = 308.074{{c}}, ~7/4 = 963.670{{c}}
: [[error map]]: {{val| +32.295 -53.513 -13.650 -5.150 }}
* [[CWE]]: ~6/5 = 300.000{{c}}, ~7/4 = 897.589{{c}}
: error map: {{val| 0.000 -101.955 -86.314 -71.236 }}
 
{{Optimal ET sequence|legend=1| 4 }}
 
[[Badness]] (Sintel): 1.16
 
== Quint ==
Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is already quite accurately approximated by 5edo for its size, this temperament provides little improvement, so it is only provided below for bookkeeping purposes. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 16/15, 27/25
 
{{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}
: Mapping generators: ~6/5, ~7
 
[[Optimal tuning]]s:
* [[WE]]: ~6/5 = 236.416{{c}}, ~7/4 = 1002.701{{c}} (~28/27 = 57.038{{c}})
: [[error map]]: {{val| -17.921 -10.628 +50.676 -1.966 }}
* [[CWE]]: ~6/5 = 240.000{{c}}, ~7/4 = 1005.135{{c}} (~28/27 = 45.135{{c}})
: error map: {{val| 0.000 +18.045 +93.686 +36.309 }}
 
{{Optimal ET sequence|legend=1| 5, 15ccd, 20cccd }}
 
[[Badness]] (Sintel): 1.22


== Geryon ==
== Geryon ==
{{see also| Dicot family }}
{{See also| Dicot family }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 8/7, 25/21
[[Comma list]]: 8/7, 25/21


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


[[POTE generator]]: ~5/4 = 385.440
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1164.885{{c}}, ~5/4 = 374.162{{c}}
: [[error map]]: {{val| -35.115 +11.253 -82.382 +125.830 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 375.277{{c}}
: error map: {{val| 0.000 +48.600 -11.036 +231.174 }}


{{Optimal ET sequence|legend=1| 3d }}, {{val| 16 26 37 48 }}, {{val| 19 31 44 57 }}, {{val| 22 36 51 66 }}
{{Optimal ET sequence|legend=1| 1b, 2b, 3d }}


[[Badness]]: 0.051009
[[Badness]] (Sintel): 1.29


== Malacoda ==
== Malacoda ==
Subgroup: 2.3.5.7
{{See also| Semaphoresmic clan }}
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 15/14, 35/32
[[Comma list]]: 15/14, 35/32


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


[[POTE generator]]: ~7/6 = 276.283
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1223.542{{c}}, ~7/4 = 941.838{{c}}
: [[error map]]: {{val| +23.542 -18.278 -57.528 +20.096 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/4 = 927.096{{c}}
: error map: {{val| 0.000 -47.763 -113.410 -41.730 }}


{{Optimal ET sequence|legend=1| 1, 4, 9c, 13bcc }}
{{Optimal ET sequence|legend=1| 1, 3b, 4, 9c, 13bcc }}


[[Badness]]: 0.037207
[[Badness]] (Sintel): 0.942


== Ugolino ==
== Ugolino ==
{{see also| Bug family }}
{{See also| Bug family }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 15/14, 27/25
[[Comma list]]: 15/14, 27/25


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


[[POTE generator]]: ~6/5 = 278.360
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1206.628{{c}}, ~7/4 = 926.730{{c}}
: [[error map]]: {{val| +6.628 -48.494 -6.122 +58.198 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/4 = 923.776{{c}}
: error map: {{val| 0.000 -54.403 -14.986 +50.054 }}


{{Optimal ET sequence|legend=1| 4, 9d, 13bd }}
{{Optimal ET sequence|legend=1| 1cdd, 3bcdd, 4, 9d }}


[[Badness]]: 0.043758
[[Badness]] (Sintel): 1.11


== Uncle ==
== Medusa ==
{{see also| Trienstonic clan#Uncle }}
{{See also| Archytas clan | Mavila family }}


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4096/3645
[[Comma list]]: 15/14, 64/63


[[Mapping]]: [{{val| 1 1 6 }}, {{val| 0 1 -6 }}]
{{Mapping|legend=1| 1 0 7 6 | 0 1 -3 -2 }}


Optimal tuning ([[CWE]]): ~2 = 1\1, ~3/2 = 731.732
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.960{{c}}, ~3/2 = 686.181{{c}}
: [[error map]]: {{val| +0.960 -14.814 -41.014 +62.655 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 685.511{{c}}
: error map: {{val| 0.000 -16.443 -42.849 +60.150 }}


Supporting ETs: 5, 13, 8c, 18, 23bc, 28bc, 33bcc, 41bbc, 51bbccc
{{Optimal ET sequence|legend=1| 2, 5c, 7 }}


[[Badness]] (Sintel): 6.332
[[Badness]] (Sintel): 1.08


== Medusa ==
=== 11-limit ===
{{see also| Pelogic family }}
Subgroup: 2.3.5.7.11


Subgroup: 2.3.5.7
Comma list: 15/14, 22/21, 33/32


[[Comma list]]: 15/14, 64/63
Mapping: {{mapping| 1 0 7 6 5 | 0 1 -3 -2 -1 }}


[[Mapping]]: [{{val| 1 0 7 6 }}, {{val| 0 1 -3 -2 }}]
Optimal tunings:  
* WE: ~2 = 1202.757{{c}}, ~3/2 = 687.384{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 685.462{{c}}


[[POTE generator]]: ~3/2 = 685.632
{{Optimal ET sequence|legend=0| 2, 5c, 7 }}


{{Optimal ET sequence|legend=1| 2, 5c, 7 }}
Badness (Sintel): 0.887


[[Badness]]: 0.042712
== Wallaby ==
{{See also| Trienstonic clan | Mavila family }}


=== 11-limit ===
[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7.11


Comma list: 15/14, 22/21, 33/32
[[Comma list]]: 28/27, 35/32


Mapping: [{{val| 1 0 7 6 5 }}, {{val| 0 1 -3 -2 -1 }}]
{{Mapping|legend=1| 1 0 7 -2 | 0 1 -3 3 }}


POTE generator: ~3/2 = 685.809
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1216.024{{c}}, ~3/2 = 700.583{{c}}
: [[error map]]: {{val| +16.024 +14.652 -23.967 -51.053 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 691.757{{c}}
: error map: {{val| 0.000 -10.198 -61.585 -93.555 }}


{{Optimal ET sequence|legend=1| 2, 5c, 7 }}
{{Optimal ET sequence|legend=1| 2d, 5c, 7d, 19ccdd }}


Badness: 0.026828
[[Badness]] (Sintel): 1.48


== Plutus ==
== Plutus ==
{{see also| Meantone family }}
{{Distinguish| Pluto }}
{{See also| Meantone family }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 15/14, 81/80
[[Comma list]]: 15/14, 81/80


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


[[POTE generator]]: ~3/2 = 682.895
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.936{{c}}, ~3/2 = 685.135{{c}}
: [[error map]]: {{val| +3.936 -12.884 -45.774 +56.849 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 683.935{{c}}
: error map: {{val| 0.000 -18.020 -50.573 +50.850 }}


{{Optimal ET sequence|legend=1| 2cd, 5d, 7 }}
{{Optimal ET sequence|legend=1| 2cd, 5d, 7 }}


[[Badness]]: 0.045275
[[Badness]] (Sintel): 1.14


=== 11-limit ===
=== 11-limit ===
Line 278: Line 469:
Comma list: 15/14, 22/21, 81/80
Comma list: 15/14, 22/21, 81/80


Mapping: [{{val| 1 0 -4 -5 -6 }}, {{val| 0 1 4 5 6 }}]
Mapping: {{mapping| 1 0 -4 -5 -6 | 0 1 4 5 6 }}
 
POTE generator: ~3/2 = 685.234
 
{{Optimal ET sequence|legend=1| 2cde, 5de, 7 }}
 
Badness: 0.032521
 
== Involution ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: [[45/32]]


[[Mapping]]: [{{val|1 1 3}}, {{val|0 1 -2}}]
Optimal tunings:  
* WE: ~2 = 1203.293{{c}}, ~3/2 = 687.114{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 686.078{{c}}


[[CTE|CTE generator]]: ~[[3/2]] = 509.892
{{Optimal ET sequence|legend=0| 2cde, 5de, 7 }}


[[Optimal ET sequence]]: None aside from extremely absurd alternative ETs
Badness (Sintel): 1.08


[[Badness]]: 0.133021
== Codex ==
{{See also| Bug family }}
Codex was named by [[User:Jerdle|Jerdle]] as an abbreviation of "co-decimal", as it resembles [[decimal]] in many ways, but exchanges the roles of 5's and 7's. While decimal equates [[8/7]] and [[7/6]], as well as [[6/5]] and [[5/4]], this equates [[10/9]] and [[6/5]], as well as [[7/6]] and [[9/7]]. It is an extension of [[bug]] and [[54/49|mujannabic]] in the same way decimal is of [[semaphore]] and [[dicot]]. Its ploidacot is diploid dicot.  


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 45/28, 8/7
[[Comma list]]: [[27/25]], [[50/49]]


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


[[CTE|CTE generator]]: ~[[3/2]] = 509.892
[[Optimal tuning]]s:
* [[WE]]: ~7/5 = 598.589{{c}}, ~5/3 = 934.978{{c}}
: [[error map]]: {{val| -2.821 -31.998 +18.621 +34.699 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~5/3 = 936.030{{c}}
: error map: {{val| 0.000 -29.895 +21.776 +39.264 }}


[[Optimal ET sequence]]: None aside from extremely absurd alternative ETs
{{Optimal ET sequence|legend=1| 4, 10cd, 14d }}


[[Badness]]: 0.118764
[[Badness]] (Sintel): 1.95


== Devolution ==
== Oxygen ==
{{See also| Porcupine family }}
Oxygen extends porcupine into the 7-limit by conflating 6/5 with 8/7, and conflating 10/9 with 7/6. While this means it does not represent 7-limit JI with any real accuracy, it is still of interest because its comma basis suggests potential utility to construct [[fokker block|Fokker blocks]].


[[Subgroup]]: 3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: [[35/27]]
[[Comma list]]: 21/20, 175/162


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


[[CTE|CTE generator]]: ~[[5/3]] = 701.863
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1213.695{{c}}, ~10/9 = 171.042{{c}}
: error map: {{val| +13.695 +12.309 -0.438 -69.825 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~10/9 = 166.042{{c}}
: error map: {{val| 0.000 -0.083 -16.526 -100.911 }}


{{Optimal ET sequence|legend=1| 8cdd }}, otherwise none aside from extremely absurd alternative ETs
{{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}*


[[Badness]] (Sintel): 0.751
<nowiki/>* [[optimal patent val]]: [[8edo|8]]


[[Category:Temperament collections]]
[[Badness]] (Sintel): 1.52
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