Compton family: Difference between revisions

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The '''Compton family''' tempers out the [[Pythagorean comma]], 531441/524288 = {{monzo| -19 12 }}, and hence the fifths form a closed 12-note circle of fifths, identical to [[12edo]]. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.
The '''Compton family''' tempers out the [[Pythagorean comma]], 531441/524288 = {{monzo| -19 12 }}, and hence the fifths form a closed 12-note circle of fifths, identical to [[12edo|12EDO]]. While the tuning of the fifth will be that of 12EDO, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.


== Compton  ==
== Compton  ==
In terms of the normal list, compton adds 413343/409600 = {{monzo| -14 10 -2 1 }} to the Pythagorean comma; however it can also be characterized by saying it adds [[225/224]]. Compton, however, does not need to be used as a 7-limit temperament; in the 5-limit it becomes the rank two 5-limit temperament tempering out the Pythagorean comma. In terms of equal temperaments, it is the 12&72 temperament, and [[72edo|72EDO]], [[84edo|84EDO]] or [[240edo|240EDO]] make for good tunings. Possible generators are 21/20, 10/9, the secor, 6/5, 5/4, 7/5 and most importantly, 81/80.


In terms of the normal list, compton adds 413343/409600 = {{monzo| -14 10 -2 1 }} to the Pythagorean comma; however it can also be characterized by saying it adds [[225/224]]. Compton, however, does not need to be used as a 7-limit temperament; in the 5-limit it becomes the rank two 5-limit temperament tempering out the Pythagorean comma. In terms of equal temperaments, it is the 12&72 temperament, and [[72edo]], [[84edo]] or [[240edo]] make for good tunings. Possible generators are 21/20, 10/9, the secor, 6/5, 5/4, 7/5 and most importantly, 81/80.  
In either the 5 or 7-limit, 240EDO is an excellent tuning, with 81/80 coming in at 15 cents exactly. In the 12EDO, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.


In either the 5 or 7-limit, [[240edo]] is an excellent tuning, with 81/80 coming in at 15 cents exactly. The major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.
In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]. For this 72EDO can be recommended as a tuning.


In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]. For this [[72edo]] can be recommended as a tuning.
Subgroup: 2.3.5


Comma list: 531441/524288
[[Comma]]: 531441/524288
 
[[Mapping]]: [{{val| 12 19 0 }}, {{val| 0 0 1 }}


[[POTE generator]]: ~5/4 = 384.884 or ~81/80 = 15.116
[[POTE generator]]: ~5/4 = 384.884 or ~81/80 = 15.116


Mapping: [{{val| 12 19 0 }}, {{val| 0 0 1 }}
{{Val list|legend=1| 12, 72, 84, 156, 240, 396b }}


{{Val list|legend=1| 12, 72, 84, 156, 240, 396b }}
[[Badness]]: 0.094494
 
=== 7-limit (aka Waage) ===
Subgroup: 2.3.5.7
 
[[Comma list]]: 225/224, 250047/250000


=== 7-limit (aka Waage)  ===
[[Mapping]]: [{{val| 12 19 0 -22 }}, {{val| 0 0 1 2 }}]
Comma list: 225/224, 250047/250000


[[POTE generator]]: ~5/4 = 383.7752
[[POTE generator]]: ~5/4 = 383.7752


Mapping: [{{val| 12 19 0 -22 }}, {{val| 0 0 1 2 }}]
{{Val list|legend=1| 12, 60, 72, 228, 300c, 372bc, 444bc }}


{{Val list|legend=1| 12, 60, 72, 228, 300c, 372bc, 444bc }}
[[Badness]]: 0.035686


Badness: 0.035686
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 225/224, 441/440, 4375/4356
Comma list: 225/224, 441/440, 4375/4356


[[POTE generator]]: ~5/4 = 383.2660
Mapping: [{{val|12 19 0 -22 -42 }}, {{val| 0 0 1 2 3 }}]


Mapping: [{{val|12 19 0 -22 -42 }}, {{val| 0 0 1 2 3 }}]
POTE generator: ~5/4 = 383.2660


{{Val list|legend=1| 12, 60e, 72 }}
Vals: {{Val list| 12, 60e, 72 }}


Badness: 0.022235
Badness: 0.022235


==== 13-limit ====
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 351/350, 364/363, 441/440
Comma list: 225/224, 351/350, 364/363, 441/440
Mapping: [{{val| 12 19 0 -22 -42 -67 }}, {{val| 0 0 1 2 3 4 }}]


POTE generator: ~5/4 = 383.9628
POTE generator: ~5/4 = 383.9628


Mapping: [{{val| 12 19 0 -22 -42 -67 }}, {{val| 0 0 1 2 3 4 }}]
Vals: {{Val list| 12f, 72, 84, 156, 228f, 300cf }}


{{Val list|legend=1| 12f, 72, 84, 156, 228f, 300cf }}
Badness: 0.021852


Badness: 0.021852
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


===== 17-limit  =====
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440
Mapping: [{{val| 12 19 0 -22 -42 -67 49 }}, {{val| 0 0 1 2 3 4 0 }}]


POTE generator: ~5/4 = 383.7500
POTE generator: ~5/4 = 383.7500


Mapping: [{{val| 12 19 0 -22 -42 -67 49 }}, {{val| 0 0 1 2 3 4 0 }}]
Vals: {{Val list| 12f, 72, 84, 156g, 228fg }}


{{Val list|legend=1| 12f, 72, 84, 156g, 228fg }}
Badness: 0.017131


Badness: 0.017131
=== Comptone ===
Subgroup: 2.3.5.7.11.13


==== Comptone  ====
Comma list: 225/224, 325/324, 441/440, 1001/1000
Comma list: 225/224, 325/324, 441/440, 1001/1000
Mapping: [{{val| 12 19 0 -22 -42 100 }}, {{val| 0 0 1 2 3 -2 }}]


POTE generator: ~5/4 = 382.6116
POTE generator: ~5/4 = 382.6116


Mapping: [{{val| 12 19 0 -22 -42 100 }}, {{val| 0 0 1 2 3 -2 }}]
Vals: {{Val list| 12, 60e, 72, 204cdef, 276cdef }}


{{Val list|legend=1| 12, 60e, 72, 204cdef, 276cdef }}
Badness: 0.025144


Badness: 0.025144
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


===== 17-limit  =====
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440
Mapping: [{{val| 12 19 0 -22 -42 100 49 }}, {{val| 0 0 1 2 3 -2 0 }}]


POTE generator: ~5/4 = 382.5968
POTE generator: ~5/4 = 382.5968


Mapping: [{{val| 12 19 0 -22 -42 100 49 }}, {{val| 0 0 1 2 3 -2 0 }}]
Vals: {{Val list| 12, 60e, 72, 132deg, 204cdefg }}
 
Badness: 0.016361


{{Val list|legend=1| 12, 60e, 72, 132deg, 204cdefg }}
== Catler ==
In terms of the normal comma list, catler is characterized by the addition of the [[schisma]], 32805/32768, to the Pythagorean comma, though it can also be characterized as adding [[81/80]], [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of [[12edo|12EDO]]. Catler can also be characterized as the 12&24 temperament. [[36edo|36EDO]] or [[48edo|48EDO]] are possible tunings. Possible generators are 36/35, 21/20, 15/14, 8/7, 7/6, 6/5, 9/7, 7/5, and most importantly, 64/63. 


Badness: 0.016361
Subgroup: 2.3.5.7


== Catler  ==
[[Comma list]]: 81/80, 128/125
In terms of the normal comma list, catler is characterized by the addition of the [[schisma]], 32805/32768, to the Pythagorean comma, though it can also be characterized as adding [[81/80]], [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of [[12edo]]. Catler can also be characterized as the 12&24 temperament. [[36edo]] or [[48edo]] are possible tunings. Possible generators are 36/35, 21/20, 15/14, 8/7, 7/6, 6/5, 9/7, 7/5, and most importantly, 64/63. 


Comma list: 81/80, 128/125
[[Mapping]]: [{{val| 12 19 28 0 }}, {{val| 0 0 0 1 }}]


[[POTE generator]]: ~64/63 = 26.790
[[POTE generator]]: ~64/63 = 26.790


Mapping: [{{val| 12 19 28 0 }}, {{val| 0 0 0 1 }}]
{{Val list|legend=1| 12, 24, 36, 48c }}


{{Val list|legend=1| 12, 36, 48, 132, 180 }}
[[Badness]]: 0.050297
 
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 81/80, 99/98, 128/125
Comma list: 81/80, 99/98, 128/125


Line 101: Line 122:
Mapping: [{{val| 12 19 28 0 -26 }}, {{val| 0 0 0 1 2 }}]
Mapping: [{{val| 12 19 28 0 -26 }}, {{val| 0 0 0 1 2 }}]


{{Val list|legend=1| 12, 48c, 108cd }}
Vals: {{Val list| 12, 36e, 48c, 108ccd }}


Badness: 0.0582
Badness: 0.058213
 
=== Catlat ===
Subgroup: 2.3.5.7.11


=== Catlat  ===
Comma list: 81/80, 128/125, 540/539
Comma list: 81/80, 128/125, 540/539


Line 112: Line 135:
Mapping: [{{val| 12 19 28 0 109 }}, {{val| 0 0 0 1 -2 }}]
Mapping: [{{val| 12 19 28 0 109 }}, {{val| 0 0 0 1 -2 }}]


{{Val list|legend=1| 36, 48c, 84c }}
Vals: {{Val list| 36, 48c, 84c }}


Badness: 0.0819
Badness: 0.081909
 
=== Catcall ===
Subgroup: 2.3.5.7.11


=== Catcall  ===
Comma list: 56/55, 81/80, 128/125
Comma list: 56/55, 81/80, 128/125


Line 123: Line 148:
Mapping: [{{val| 12 19 28 0 8 }}, {{val| 0 0 0 1 1 }}]
Mapping: [{{val| 12 19 28 0 8 }}, {{val| 0 0 0 1 1 }}]


{{Val list|legend=1| 12, 24, 36, 72ce }}
Vals: {{Val list| 12, 24, 36, 72ce }}
 
Badness: 0.034478


Badness: 0.0345
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==== 13-limit  ====
Comma list: 56/55, 66/65, 81/80, 105/104
Comma list: 56/55, 66/65, 81/80, 105/104


Line 134: Line 161:
Mapping: [{{val| 12 19 28 0 8 11 }}, {{val| 0 0 0 1 1 1 }}]
Mapping: [{{val| 12 19 28 0 8 11 }}, {{val| 0 0 0 1 1 1 }}]


{{Val list|legend=1| 12f, 24, 36f, 60cf }}
Vals: {{Val list| 12f, 24, 36f, 60cf }}
 
Badness: 0.028363


Badness: 0.0284
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 51/50, 56/55, 66/65, 81/80, 105/104
 
POTE generator: ~36/35 = 39.777
 
Mapping: [{{val| 12 19 28 0 8 11 49 }}, {{val| 0 0 0 1 1 1 0 }}]
 
Vals: {{Val list| 12f, 24, 36f, 60cf }}
 
Badness: 0.023246
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 51/50, 56/55, 66/65, 76/75, 81/80, 96/95
 
POTE generator: ~36/35 = 40.165
 
Mapping: [{{val| 12 19 28 0 8 11 49 51 }}, {{val| 0 0 0 1 1 1 0 0 }}]
 
Vals: {{Val list| 12f, 24, 36f, 60cf }}
 
Badness: 0.018985
 
==== Duodecic ====
Subgroup: 2.3.5.7.11.13


==== Duodecic  ====
Comma list: 56/55, 81/80, 91/90, 128/125
Comma list: 56/55, 81/80, 91/90, 128/125


Line 145: Line 200:
Mapping: [{{val| 12 19 28 0 8 78 }}, {{val| 0 0 0 1 1 -1 }}]
Mapping: [{{val| 12 19 28 0 8 78 }}, {{val| 0 0 0 1 1 -1 }}]


{{Val list|legend=1| 12, 24, 36, 60c }}
Vals: {{Val list| 12, 24, 36, 60c }}


Badness: 0.0383
Badness: 0.038307


===== 17-limit =====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 51/50, 56/55, 81/80, 91/90, 128/125
Comma list: 51/50, 56/55, 81/80, 91/90, 128/125


Line 156: Line 212:
Mapping: [{{val| 12 19 28 0 8 78 49 }}, {{val| 0 0 0 1 1 -1 0 }}]
Mapping: [{{val| 12 19 28 0 8 78 49 }}, {{val| 0 0 0 1 1 -1 0 }}]


{{Val list|legend=1| 12, 24, 36, 60c }}
Vals: {{Val list| 12, 24, 36, 60c }}


Badness: 0.0275
Badness: 0.027487
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


===== 19-limit  =====
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95


Line 167: Line 225:
Mapping: [{{val| 12 19 28 0 8 78 49 51 }}, {{val| 0 0 0 1 1 -1 0 0 }}]
Mapping: [{{val| 12 19 28 0 8 78 49 51 }}, {{val| 0 0 0 1 1 -1 0 0 }}]


{{Val list|legend=1| 12, 24, 36, 60c }}
Vals: {{Val list| 12, 24, 36, 60c }}
 
Badness: 0.020939


Badness: 0.0209
== Duodecim ==
Subgroup: 2.3.5.7.11


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


POTE generator: ~45/44 = 34.977
[[Mapping]]: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]


Mapping: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
[[POTE generator]]: ~45/44 = 34.977


{{Val list|legend=1| 12, 24d }}
{{Val list|legend=1| 12, 24d }}


== Omicronbeta  ==
[[Badness]]: 0.030536
Comma list: 225/224, 243/242, 441/440, 4375/4356
 
== Hours ==
Subgroup: 2.3.5.7


POTE generator: ~13/8 = 837.814
[[Comma list]]: 19683/19600, 33075/32768


Mapping: [{{val| 72 114 167 202 249 266 }}, {{val| 0 0 0 0 0 1 }}]
[[Mapping]]: [{{val| 24 38 0 123 }}, {{val| 0 0 1 -1 }}]


{{Val list|legend=1| 72, 144, 216c, 288cdf, 504bcdef }}
{{Multival|legend=1| 0 24 -24 38 -38 -123 }}
 
[[POTE generator]]: ~5/4 = 384.033
 
{{Val list|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdd, 528bcdd, 600bccdd }}


Badness: 0.0300
[[Badness]]: 0.116091


== Hours  ==
=== 11-limit ===
Comma list: 19683/19600, 33075/32768
Subgroup: 2.3.5.7.11


POTE generator: ~225/224 = 2.100
Comma list: 243/242, 385/384, 9801/9800


Mapping: [{{val| 24 38 0 123 83 }}, {{val| 0 0 1 -1 0 }}]
Mapping: [{{val| 24 38 0 123 83 }}, {{val| 0 0 1 -1 0 }}]


{{Multival|legend=1| 0 24 -24 38 -38 -123 }}
POTE generator: ~5/4 = 384.054
 
Vals: {{Val list| 24, 48, 72, 312bd, 384bcdd, 456bcdde, 528bcdde }}
 
Badness: 0.036248
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 243/242, 351/350, 364/363, 385/384
 
Mapping: [{{val| 24 38 0 123 83 33 }}, {{val| 0 0 1 -1 0 1 }}]
 
POTE generator: ~5/4 = 384.652
 
Vals: {{Val list| 24, 48f, 72, 168df, 240dff }}
 
Badness: 0.026931
 
== Decades ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 118098/117649
 
[[Mapping]]: [{{val| 36 57 0 101 }}, {{val| 0 0 1 0 }}]
 
{{Multival|legend=1| 0 36 0 57 0 -101 }}
 
[[POTE generator]]: ~5/4 = 384.764
 
{{Val list|legend=1| 36, 72, 252, 324bd, 396bd }}
 
[[Badness]]: 0.108016


{{Val list|legend=1| 24, 48, 72, 312bd, 384bcd, 456bcd, 528bcd, 600bcd }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.1161
Comma list: 540/539, 1029/1024, 4000/3993


=== 11-limit  ===
Mapping: [{{val| 36 57 0 101 41 }}, {{val| 0 0 1 0 1 }}]
Comma list: 243/242, 385/384, 9801/9800


POTE generator: ~225/224 = 2.161
POTE generator: ~5/4 = 384.150


Mapping: [{{val| 24 38 0 123 83 }}, {{val| 0 0 1 -1 0 }}]
Vals: {{Val list| 36, 72, 396bd, 468bcd, 540bcd, 612bccdd, 684bbccdd, 756bbccdd }}


{{Val list|legend=1| 24, 48, 72, 312bd, 384bcd, 456bcde, 528bcde }}
Badness: 0.043088


Badness: 0.0362
== Omicronbeta ==
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
[[Comma list]]: 225/224, 243/242, 441/440, 4375/4356
Comma list: 243/242, 351/350, 364/363, 385/384


POTE generator: ~225/224 = 3.955
[[Mapping]]: [{{val| 72 114 167 202 249 266 }}, {{val| 0 0 0 0 0 1 }}]


Mapping: [{{val| 24 38 0 123 83 33 }}, {{val| 0 0 1 -1 0 1 }}]
[[POTE generator]]: ~13/8 = 837.814


{{Val list|legend=1| 24, 48f, 72, 168df, 240df }}
{{Val list|legend=1| 72, 144, 216c, 288cdf, 504bcdef }}


Badness: 0.0269
[[Badness]]: 0.029956


[[Category:Theory]]
[[Category:Theory]]

Revision as of 12:22, 2 June 2021

The Compton family tempers out the Pythagorean comma, 531441/524288 = [-19 12⟩, and hence the fifths form a closed 12-note circle of fifths, identical to 12EDO. While the tuning of the fifth will be that of 12EDO, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.

Compton

In terms of the normal list, compton adds 413343/409600 = [-14 10 -2 1⟩ to the Pythagorean comma; however it can also be characterized by saying it adds 225/224. Compton, however, does not need to be used as a 7-limit temperament; in the 5-limit it becomes the rank two 5-limit temperament tempering out the Pythagorean comma. In terms of equal temperaments, it is the 12&72 temperament, and 72EDO, 84EDO or 240EDO make for good tunings. Possible generators are 21/20, 10/9, the secor, 6/5, 5/4, 7/5 and most importantly, 81/80.

In either the 5 or 7-limit, 240EDO is an excellent tuning, with 81/80 coming in at 15 cents exactly. In the 12EDO, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.

In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds 441/440. For this 72EDO can be recommended as a tuning.

Subgroup: 2.3.5

Comma: 531441/524288

Mapping: [⟨12 19 0], ⟨0 0 1]

POTE generator: ~5/4 = 384.884 or ~81/80 = 15.116

Template:Val list

Badness: 0.094494

7-limit (aka Waage)

Subgroup: 2.3.5.7

Comma list: 225/224, 250047/250000

Mapping: [⟨12 19 0 -22], ⟨0 0 1 2]]

POTE generator: ~5/4 = 383.7752

Template:Val list

Badness: 0.035686

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 4375/4356

Mapping: [⟨12 19 0 -22 -42], ⟨0 0 1 2 3]]

POTE generator: ~5/4 = 383.2660

Vals: Template:Val list

Badness: 0.022235

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 351/350, 364/363, 441/440

Mapping: [⟨12 19 0 -22 -42 -67], ⟨0 0 1 2 3 4]]

POTE generator: ~5/4 = 383.9628

Vals: Template:Val list

Badness: 0.021852

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 225/224, 289/288, 351/350, 441/440

Mapping: [⟨12 19 0 -22 -42 -67 49], ⟨0 0 1 2 3 4 0]]

POTE generator: ~5/4 = 383.7500

Vals: Template:Val list

Badness: 0.017131

Comptone

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 325/324, 441/440, 1001/1000

Mapping: [⟨12 19 0 -22 -42 100], ⟨0 0 1 2 3 -2]]

POTE generator: ~5/4 = 382.6116

Vals: Template:Val list

Badness: 0.025144

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 273/272, 289/288, 325/324, 441/440

Mapping: [⟨12 19 0 -22 -42 100 49], ⟨0 0 1 2 3 -2 0]]

POTE generator: ~5/4 = 382.5968

Vals: Template:Val list

Badness: 0.016361

Catler

In terms of the normal comma list, catler is characterized by the addition of the schisma, 32805/32768, to the Pythagorean comma, though it can also be characterized as adding 81/80, 128/125 or 648/625. In any event, the 5-limit is exactly the same as the 5-limit of 12EDO. Catler can also be characterized as the 12&24 temperament. 36EDO or 48EDO are possible tunings. Possible generators are 36/35, 21/20, 15/14, 8/7, 7/6, 6/5, 9/7, 7/5, and most importantly, 64/63.

Subgroup: 2.3.5.7

Comma list: 81/80, 128/125

Mapping: [⟨12 19 28 0], ⟨0 0 0 1]]

POTE generator: ~64/63 = 26.790

Template:Val list

Badness: 0.050297

11-limit

Subgroup: 2.3.5.7.11

Comma list: 81/80, 99/98, 128/125

POTE generator: ~64/63 = 22.723

Mapping: [⟨12 19 28 0 -26], ⟨0 0 0 1 2]]

Vals: Template:Val list

Badness: 0.058213

Catlat

Subgroup: 2.3.5.7.11

Comma list: 81/80, 128/125, 540/539

POTE generator: ~64/63 = 27.864

Mapping: [⟨12 19 28 0 109], ⟨0 0 0 1 -2]]

Vals: Template:Val list

Badness: 0.081909

Catcall

Subgroup: 2.3.5.7.11

Comma list: 56/55, 81/80, 128/125

POTE generator: ~36/35 = 32.776

Mapping: [⟨12 19 28 0 8], ⟨0 0 0 1 1]]

Vals: Template:Val list

Badness: 0.034478

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 66/65, 81/80, 105/104

POTE generator: ~36/35 = 37.232

Mapping: [⟨12 19 28 0 8 11], ⟨0 0 0 1 1 1]]

Vals: Template:Val list

Badness: 0.028363

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 51/50, 56/55, 66/65, 81/80, 105/104

POTE generator: ~36/35 = 39.777

Mapping: [⟨12 19 28 0 8 11 49], ⟨0 0 0 1 1 1 0]]

Vals: Template:Val list

Badness: 0.023246

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 51/50, 56/55, 66/65, 76/75, 81/80, 96/95

POTE generator: ~36/35 = 40.165

Mapping: [⟨12 19 28 0 8 11 49 51], ⟨0 0 0 1 1 1 0 0]]

Vals: Template:Val list

Badness: 0.018985

Duodecic

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 81/80, 91/90, 128/125

POTE generator: ~36/35 = 37.688

Mapping: [⟨12 19 28 0 8 78], ⟨0 0 0 1 1 -1]]

Vals: Template:Val list

Badness: 0.038307

17-limit

Subgroup: 2.3.5.7.11.13.17 Comma list: 51/50, 56/55, 81/80, 91/90, 128/125

POTE generator: ~36/35 = 38.097

Mapping: [⟨12 19 28 0 8 78 49], ⟨0 0 0 1 1 -1 0]]

Vals: Template:Val list

Badness: 0.027487

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95

POTE generator: ~36/35 = 38.080

Mapping: [⟨12 19 28 0 8 78 49 51], ⟨0 0 0 1 1 -1 0 0]]

Vals: Template:Val list

Badness: 0.020939

Duodecim

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 64/63

Mapping: [⟨12 19 28 34 0], ⟨0 0 0 0 1]]

POTE generator: ~45/44 = 34.977

Template:Val list

Badness: 0.030536

Hours

Subgroup: 2.3.5.7

Comma list: 19683/19600, 33075/32768

Mapping: [⟨24 38 0 123], ⟨0 0 1 -1]]

Wedgie: ⟨⟨ 0 24 -24 38 -38 -123 ]]

POTE generator: ~5/4 = 384.033

Template:Val list

Badness: 0.116091

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 385/384, 9801/9800

Mapping: [⟨24 38 0 123 83], ⟨0 0 1 -1 0]]

POTE generator: ~5/4 = 384.054

Vals: Template:Val list

Badness: 0.036248

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 364/363, 385/384

Mapping: [⟨24 38 0 123 83 33], ⟨0 0 1 -1 0 1]]

POTE generator: ~5/4 = 384.652

Vals: Template:Val list

Badness: 0.026931

Decades

Subgroup: 2.3.5.7

Comma list: 1029/1024, 118098/117649

Mapping: [⟨36 57 0 101], ⟨0 0 1 0]]

Wedgie: ⟨⟨ 0 36 0 57 0 -101 ]]

POTE generator: ~5/4 = 384.764

Template:Val list

Badness: 0.108016

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1029/1024, 4000/3993

Mapping: [⟨36 57 0 101 41], ⟨0 0 1 0 1]]

POTE generator: ~5/4 = 384.150

Vals: Template:Val list

Badness: 0.043088

Omicronbeta

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 441/440, 4375/4356

Mapping: [⟨72 114 167 202 249 266], ⟨0 0 0 0 0 1]]

POTE generator: ~13/8 = 837.814

Template:Val list

Badness: 0.029956

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