Aberschismic temperaments: Difference between revisions

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Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168


Mapping: [<1 0 -31 -21 -14 -9 -34 -37|, <0 1 21 15 11 8 24 26|]
Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 -37 }}, {{val| 0 1 21 15 11 8 24 26 }}]


POTE generator: ~3/2 = 704.123
POTE generator: ~3/2 = 704.123
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Badness: 0.019065
Badness: 0.019065


=Mystery=
= Mystery =
Commas: 5120/5103, 50421/50000


[[POTE_tuning|POTE generator]]: ~5/4 = 388.646
Subgroup: 2.3.5.7


Map: [<29 46 0 14|, <0 0 1 1|]
[[Comma list]]: 5120/5103, 50421/50000


Wedgie: <<0 29 29 46 46 -14||
[[Mapping]]: [{{val| 29 46 0 14 }}, {{val| 0 0 1 1 }}]


EDOs: 29, 58, 87, 145
{{Multival|legend=1| 0 29 29 46 46 -14 }}


Badness: 0.1037
[[POTE generator]]: ~5/4 = 388.646


==11-limit==
{{Val list|legend=1| 29, 58, 87, 145 }}
Commas: 441/440, 896/891, 3388/3375


[[POTE_tuning|POTE generator]]: ~5/4 = 388.460
[[Badness]]: 0.1037


Map: [<29 46 0 14 33|, <0 0 1 1 1|]
== 11-limit ==
 
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 896/891, 3388/3375
 
Mapping: [{{val| 29 46 0 14 33 }}, {{val| 0 0 1 1 1 }}]


EDOs: 29, 58, 87, 145
POTE generator: ~5/4 = 388.460
 
Vals: {{Val list| 29, 58, 87, 145 }}


Badness: 0.0343
Badness: 0.0343


==13-limit==
== 13-limit ==
Commas: 196/195, 352/351, 364/363, 676/675


[[POTE_tuning|POTE generator]]: ~5/4 = 388.354
Subgroup: 2.3.5.7.11.13


Map: [<29 46 0 14 33 40|, <0 0 1 1 1 1|]
Comma list: 196/195, 352/351, 364/363, 676/675


EDOs: 29, 58, 87, 145, 232, 377
Mapping: [{{val| 29 46 0 14 33 40 }}, {{val| 0 0 1 1 1 1 }}]
 
POTE generator: ~5/4 = 388.354
 
Vals: {{Val list| 29, 58, 87, 145, 232, 377 }}


Badness: 0.0186
Badness: 0.0186


=Quanic=
= Quanic =
Commas: 5120/5103, 5832000/5764801


POTE generator: ~160/147 = 140.493
Subgroup: 2.3.5.7


Map: [<1 1 -4 0|, <0 5 54 24|]
[[Comma list]]: 5120/5103, 5832000/5764801


EDOs: 94, 111, 205
[[Mapping]]: [{{val| 1 1 -4 0 }}, {{val| 0 5 54 24 }}]


Badness: 0.1795
[[POTE generator]]: ~160/147 = 140.493


==11-limit==
{{Val list|legend=1| 94, 111, 205 }}
Commas: 540/539, 1331/1323, 5120/5103
 
[[Badness]]: 0.1795
 
== 11-limit ==
 
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 1331/1323, 5120/5103
 
Mapping: [{{val| 1 1 -4 0 1 }}, {{val| 0 5 54 24 21 }}]


POTE generator: ~88/81 = 140.489
POTE generator: ~88/81 = 140.489


Map: [<1 1 -4 0 1|, <0 5 54 24 21|]
Vals: {{Val list| 94, 111, 205 }}
 
Badness: 0.0587
 
== 13-limit ==


EDOs: 94, 111, 205
Subgroup: 2.3.5.7.11.13


Badness: 0.0587
Comma list: 352/351, 540/539, 729/728, 1331/1323


==13-limit==
Mapping: [{{val| 1 1 -4 0 1 3 }}, {{val| 0 5 54 24 21 6 }}]
Commas: 352/351, 540/539, 729/728, 1331/1323


POTE generator: ~13/12 = 140.496
POTE generator: ~13/12 = 140.496


Map: [<1 1 -4 0 1 3|, <0 5 54 24 21 6|]
Vals: {{Val list| 94, 111, 205 }}


EDOs: 94, 111, 205
Badness: 0.0325


Badness: 0.0325
== 17-limit ==
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 352/351, 442/441, 540/539, 715/714, 847/845


==17-limit==
Mapping: [{{val| 1 1 -4 0 1 3 -2 }}, {{val| 0 5 54 24 21 6 52 }}]
Commas: 352/351, 442/441, 540/539, 715/714, 847/845


POTE generator: ~13/12 = 140.497
POTE generator: ~13/12 = 140.497


Map: [<1 1 -4 0 1 3 -2|, <0 5 54 24 21 6 52|]
Vals: {{Val list| 94, 111, 205 }}
 
Badness: 0.0211
 
== 19-limit ==


EDOs: 94, 111, 205
Subgroup: 2.3.5.7.11.13.17.19


Badness: 0.0211
Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714


==19-limit==
Mapping: [{{val| 1 1 -4 0 1 3 -2 -5 }}, {{val| 0 5 54 24 21 6 52 79 }}]
Commas: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714


POTE generator: ~13/12 = 140.496
POTE generator: ~13/12 = 140.496


Map: [<1 1 -4 0 1 3 -2 -5|, <0 5 54 24 21 6 52 79|]
Vals: {{Val list| 94, 111, 205 }}
 
Badness: 0.0173
 
= Supers =


EDOs: 94, 111, 205
Subgroup: 2.3.5.7


Badness: 0.0173
[[Comma list]]: 5120/5103, 118098/117649
 
[[Mapping]]: [{{val| 2 1 -12 2 }}, {{val| 0 3 23 5 }}]
 
{{Multival|legend=1| 6 46 10 59 -1 -106 }}


=Supers=
[[POTE generator]]: ~9/7 = 434.218
Commas: 5120/5103, 118098/117649


POTE generator: ~9/7 = 434.218
{{Val list|legend=1| 58, 94, 152 }}


Map: [<2 1 -12 2|, <0 3 23 5|]
[[Badness]]: 0.092748


Wedgie: <<6 46 10 59 -1 -106||
== 11-limit ==


EDOs: {{EDOs|58, 94, 152}}
Subgroup: 2.3.5.7.11


Badness: 0.092748
Comma list: 540/539, 4000/3993, 5120/5103


==11-limit==
Mapping: [{{val| 2 1 -12 2 -9 }}, {{val| 0 3 23 5 22 }}]
Commas: 540/539, 4000/3993, 5120/5103


POTE generator: ~9/7 = 434.217
POTE generator: ~9/7 = 434.217


Map: [<2 1 -12 2 -9|, <0 3 23 5 22|]
Vals: {{Val list| 58, 94, 152 }}


EDOs: {{EDOs|58, 94, 152}}
Badness: 0.028240


Badness: 0.028240
== 13-limit ==
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 540/539, 729/728, 1575/1573


==13-limit==
Mapping: [{{val| 2 1 -12 2 -9 -2 }}, {{val| 0 3 23 5 22 13 }}]
Commas: 352/351, 540/539, 729/728, 1575/1573


POTE generator: ~9/7 = 434.221
POTE generator: ~9/7 = 434.221


Map: [<2 1 -12 2 -9 -2|, <0 3 23 5 22 13|]
Vals: {{Val list| 58, 94, 152f }}


EDOs: {{EDOs|58, 94, 152f}}
Badness: 0.021645


Badness: 0.021645
== 17-limit ==
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 170/169, 289/288, 352/351, 442/441, 561/560


==17-limit==
Mapping: [{{val| 2 1 -12 2 -9 -2 6 }}, {{val| 0 3 23 5 22 13 3 }}]
Commas: 170/169, 289/288, 352/351, 442/441, 561/560


POTE generator: ~9/7 = 434.181
POTE generator: ~9/7 = 434.181


Map: [<2 1 -12 2 -9 -2 6|, <0 3 23 5 22 13 3|]
Vals: {{Val list| 58, 94, 152f }}
 
Badness: 0.021316
 
= Alphaquarter =
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 5120/5103, 29360128/29296875


EDOs: {{EDOs|58, 94, 152f}}
[[Mapping]]: [{{val| 1 2 2 0 }}, {{val| 0 -9 7 61 }}]


Badness: 0.021316
{{Multival|legend=1| 9 -7 -61 -32 -122 -122 }}


=Alphaquarter=
[[POTE generator]]: ~16128/15625 = 55.243
Commas: 5120/5103, 29360128/29296875


POTE generator: ~16128/15625 = 55.243
{{Val list|legend=1| 87, 152, 239, 391 }}


Map: [<1 2 2 0|, <0 -9 7 61|]
[[Badness]]: 0.1166


Wedgie: <<9 -7 -61 -32 -122 -122||
== 11-limit ==


EDOs: 87, 152, 239, 391
Subgroup: 2.3.5.7.11


Badness: 0.1166
Comma list: 3025/3024, 4000/3993, 5120/5103


==11-limit==
Mapping: [{{val| 1 2 2 0 3 }}, {{val| 0 -9 7 61 10 }}]
Commas: 3025/3024, 4000/3993, 5120/5103


POTE generator: ~33/32 = 55.243
POTE generator: ~33/32 = 55.243


Map: [<1 2 2 0 3|, <0 -9 7 61 10|]
Vals: {{Val list| 87, 152, 239, 391 }}
 
EDOs: 87, 152, 239, 391


Badness: 0.0296
Badness: 0.0296


= Septiquarter =
= Septiquarter =
Commas: 5120/5103, 420175/419904


POTE generator: ~147/128 = 242.453
Subgroup: 2.3.5.7
 
[[Comma list]]: 5120/5103, 420175/419904
 
[[Mapping]]: [{{val| 1 3 10 2 }}, {{val| 0 -7 -38 4 }}]


Map: [<1 3 10 2|, <0 -7 -38 4|]
{{Multival|legend=1| 7 38 -4 44 -26 -116 }}


Wedgie: <<7 38 -4 44 -26 -116||
[[POTE generator]]: ~147/128 = 242.453


EDOs: {{EDOs|94, 99, 292, 391, 881bd, 1272bcd}}
{{Val list|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}


Badness: 0.0538
[[Badness]]: 0.0538


== Semiseptiquarter ==
== Semiseptiquarter ==
Commas: 5120/5103, 9801/9800, 14641/14580
 
Subgroup: 2.3.5.7.11
 
Comma list: 5120/5103, 9801/9800, 14641/14580
 
Mapping: [{{val| 2 6 20 4 15 }}, {{val| 0 -7 -38 4 -20 }}]


POTE generators: ~121/105 = 242.4511
POTE generators: ~121/105 = 242.4511


Map: [<2 6 20 4 15|, <0 -7 -38 4 -20|]
Vals: {{Val list| 94, 198, 292, 490 }}
 
EDOs: {{EDOs|94, 198, 292, 490}}


Badness: 0.0642
Badness: 0.0642


=== 13-limit ===
=== 13-limit ===
Commas: 352/351, 847/845, 1716/1715, 14641/14580
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 847/845, 1716/1715, 14641/14580
 
Mapping: [{{val| 2 6 20 4 15 7 }}, {{val| 0 -7 -38 4 -20 1 }}]


POTE generators: ~121/105 = 242.4448
POTE generators: ~121/105 = 242.4448


Map: [<2 6 20 4 15 7|, <0 -7 -38 4 -20 1|]
Vals: {{Val list| 94, 198, 490f }}
 
EDOs: {{EDOs|94, 198, 490f}}


Badness: 0.0348
Badness: 0.0348
Line 419: Line 470:


The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&amp;70 temperament (also known as ''trimot''), tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.
The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&amp;70 temperament (also known as ''trimot''), tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.
Subgroup: 2.3.5.7


[[Comma list]]: 2430/2401, 5120/5103
[[Comma list]]: 2430/2401, 5120/5103


[[Mapping]]: [&lt;1 0 -13 -3|, &lt;0 3 29 11|]
[[Mapping]]: [{{val| 1 0 -13 -3 }}, {{val| 0 3 29 11 }}]


[[Wedgie]]: &lt;&lt;3 29 11 39 9 -56||
{{Multival|legend=1| 3 29 11 39 9 -56 }}


[[POTE tuning|POTE generator]]: ~81/56 = 634.026
[[POTE generator]]: ~81/56 = 634.026


{{Val list|legend=1| 17c, 36c, 53, 229dd, 282dd }}
{{Val list|legend=1| 17c, 36c, 53, 229dd, 282dd }}
Line 433: Line 486:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 5120/5103
Comma list: 99/98, 121/120, 5120/5103


Mapping: [&lt;1 0 -13 -3 -5|, &lt;0 3 29 11 16|]
Mapping: [{{val| 1 0 -13 -3 -5 }}, {{val| 0 3 29 11 16 }}]


POTE generator: ~63/44 = 634.027
POTE generator: ~63/44 = 634.027
Line 444: Line 500:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 169/168, 352/351
Comma list: 99/98, 121/120, 169/168, 352/351


Mapping: [&lt;1 0 -13 -3 -5 0|, &lt;0 3 29 11 16 7|]
Mapping: [{{val| 1 0 -13 -3 -5 0 }}, {{val| 0 3 29 11 16 7 }}]


POTE generator: ~13/9 = 634.012
POTE generator: ~13/9 = 634.012
Line 455: Line 514:


= Ketchup =
= Ketchup =
Subgroup: 2.3.5.7
[[Comma list]]: 5120/5103, 1071875/1062882
[[Comma list]]: 5120/5103, 1071875/1062882


[[Mapping]]: [&lt;2 3 4 6|, &lt;0 4 15 -9|]
[[Mapping]]: [{{val| 2 3 4 6 }}, {{val| 0 4 15 -9 }}]


[[Wedgie]]: &lt;&lt;8 30 -18 29 -51 -126||
{{Multival|legend=1| 8 30 -18 29 -51 -126 }}


[[POTE tuning|POTE generator]]: ~64/63 = ~81/80 = 25.719
[[POTE generator]]: ~64/63 = ~81/80 = 25.719


{{Val list|legend=1| 46, 94, 140 }}
{{Val list|legend=1| 46, 94, 140 }}
Line 468: Line 530:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1331/1323, 2200/2187
Comma list: 385/384, 1331/1323, 2200/2187


Mapping: [&lt;2 3 4 6 7|, &lt;0 4 15 -9 -2|]
Mapping: [{{val| 2 3 4 6 7 }}, {{val| 0 4 15 -9 -2 }}]


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693
Line 479: Line 544:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 847/845, 1331/1323
Comma list: 325/324, 352/351, 847/845, 1331/1323


Mapping: [&lt;2 3 4 6 7 8|, &lt;0 4 15 -9 -2 -14|]
Mapping: [{{val| 2 3 4 6 7 8 }}, {{val| 0 4 15 -9 -2 -14 }}]


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697
Line 490: Line 558:


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560


Map: [&lt;2 3 4 6 7 8 8|, &lt;0 4 15 -9 -2 -14 4|]
Mapping: [{{val| 2 3 4 6 7 8 8 }}, {{val| 0 4 15 -9 -2 -14 4 }}]


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701
Line 501: Line 572:


== 19-limit ==
== 19-limit ==
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560


Mapping: [&lt;2 3 4 6 7 8 8 9|, &lt;0 4 15 -9 -2 -14 4 -12|]
Mapping: [{{val| 2 3 4 6 7 8 8 9 }}, {{val| 0 4 15 -9 -2 -14 4 -12 }}]


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660
Line 512: Line 586:


== 23-limit ==
== 23-limit ==
Commas: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384


Mapping: [&lt;2 3 4 6 7 8 8 9 9|, &lt;0 4 15 -9 -2 -14 4 -12 1|]
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
 
Mapping: [{{val| 2 3 4 6 7 8 8 9 9 }}, {{val| 0 4 15 -9 -2 -14 4 -12 1 }}]


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661
Line 522: Line 599:
Badness: 0.014033
Badness: 0.014033


[[Category:Temperament]]
[[Category:Regular temperament theory]]
[[Category:Temperament collection]]
[[Category:Hemifamity]]
[[Category:Hemifamity]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 07:39, 22 April 2021

The hemifamity temperaments temper out the hemifamity comma, [10 -6 1 -1⟩ = 5120/5103, dividing an exact or approximate septimal diesis, [2 2 -1 -1⟩ = 36/35 into two equal steps.

Belonging to it and considered below are buzzard, undecental, leapday, mystery, quanic and ketchup. Other hemifamity temperaments are dominant, garibaldi, hemififths, amity, misty, rodan, countercata and kwai.

Buzzard

See also: Vulture family

Subgroup: 2.3.5.7

Comma list: 1728/1715, 5120/5103

Mapping: [⟨1 0 -6 4], ⟨0 4 21 -3]]

Wedgie: ⟨⟨ 4 21 -3 24 -16 -66 ]]

POTE generator: ~21/16 = 475.636

Template:Val list

Badness: 0.047963

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 5120/5103

Mapping: [⟨1 0 -6 4 -12], ⟨0 4 21 -3 39]]

POTE generator: ~21/16 = 475.700

Vals: Template:Val list

Badness: 0.034484

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 540/539, 676/675

Mapping: [⟨1 0 -6 4 -12 -7], ⟨0 4 21 -3 39 27]]

POTE generator: ~21/16 = 475.697

Vals: Template:Val list

Badness: 0.018842

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 351/350, 442/441, 540/539

Mapping: [⟨1 0 -6 4 -12 -7 14], ⟨0 4 21 -3 39 27 -25]]

POTE generator: ~21/16 = 475.692

Vals: Template:Val list

Badness: 0.018403

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539

Mapping: [⟨1 0 -6 4 -12 -7 14 -12], ⟨0 4 21 -3 39 27 -25 41]]

POTE generator: ~21/16 = 475.679

Vals: Template:Val list

Badness: 0.015649

Buteo

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384, 2200/2187

Mapping: [⟨1 0 -6 4 9], ⟨0 4 21 -3 -14]]

POTE generator: ~21/16 = 475.436

Vals: Template:Val list

Badness: 0.060238

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 275/273, 385/384, 572/567

Mapping: [⟨1 0 -6 4 9 -7], ⟨0 4 21 -3 -14 27]]

POTE generator: ~21/16 = 475.464

Vals: Template:Val list

Badness: 0.039854

Undecental

Subgroup: 2.3.5.7

Comma list: 5120/5103, 235298/234375

Mapping: [⟨1 0 61 71], ⟨0 1 -37 -43]]

Wedgie: ⟨⟨ 1 -37 -43 -61 -71 4 ]]

POTE generator: ~3/2 = 703.039

Template:Val list

Badness: 0.094603

Leapday

Subgroup: 2.3.5

Comma list: 10737418240/10460353203

Mapping: [⟨1 0 -31], ⟨0 1 21]]

POTE generator: ~3/2 = 704.179

Template:Val list

Badness: 0.523182

7-limit

Subgroup: 2.3.5.7

Comma list: 686/675, 5120/5103

Mapping: [⟨1 0 -31 -21], ⟨0 1 21 15]]

Wedgie: ⟨⟨ 1 21 15 31 21 -24 ]]

POTE generator: ~3/2 = 704.263

Template:Val list

Badness: 0.096123

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440, 686/675

Mapping: [⟨1 0 -31 -21 -14], ⟨0 1 21 15 11]]

POTE generator: ~3/2 = 704.250

Vals: Template:Val list

Badness: 0.038624

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 121/120, 169/168, 352/351

Mapping: [⟨1 0 -31 -21 -14 -9], ⟨0 1 21 15 11 8]]

POTE generator: ~3/2 = 704.214

Vals: Template:Val list

Badness: 0.024732

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 91/90, 121/120, 136/135, 154/153, 169/168

Mapping: [⟨1 0 -31 -21 -14 -9 -34], ⟨0 1 21 15 11 8 24]]

POTE generator: ~3/2 = 704.229

Vals: Template:Val list

Badness: 0.017863

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168

Mapping: [⟨1 0 -31 -21 -14 -9 -34 9], ⟨0 1 21 15 11 8 24 -3]]

POTE generator: ~3/2 = 704.135

Vals: Template:Val list

Badness: 0.017356

Leapling

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168

Mapping: [⟨1 0 -31 -21 -14 -9 -34 -37], ⟨0 1 21 15 11 8 24 26]]

POTE generator: ~3/2 = 704.123

Vals: Template:Val list

Badness: 0.019065

Mystery

Subgroup: 2.3.5.7

Comma list: 5120/5103, 50421/50000

Mapping: [⟨29 46 0 14], ⟨0 0 1 1]]

Wedgie: ⟨⟨ 0 29 29 46 46 -14 ]]

POTE generator: ~5/4 = 388.646

Template:Val list

Badness: 0.1037

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 896/891, 3388/3375

Mapping: [⟨29 46 0 14 33], ⟨0 0 1 1 1]]

POTE generator: ~5/4 = 388.460

Vals: Template:Val list

Badness: 0.0343

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 364/363, 676/675

Mapping: [⟨29 46 0 14 33 40], ⟨0 0 1 1 1 1]]

POTE generator: ~5/4 = 388.354

Vals: Template:Val list

Badness: 0.0186

Quanic

Subgroup: 2.3.5.7

Comma list: 5120/5103, 5832000/5764801

Mapping: [⟨1 1 -4 0], ⟨0 5 54 24]]

POTE generator: ~160/147 = 140.493

Template:Val list

Badness: 0.1795

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1331/1323, 5120/5103

Mapping: [⟨1 1 -4 0 1], ⟨0 5 54 24 21]]

POTE generator: ~88/81 = 140.489

Vals: Template:Val list

Badness: 0.0587

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1331/1323

Mapping: [⟨1 1 -4 0 1 3], ⟨0 5 54 24 21 6]]

POTE generator: ~13/12 = 140.496

Vals: Template:Val list

Badness: 0.0325

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 352/351, 442/441, 540/539, 715/714, 847/845

Mapping: [⟨1 1 -4 0 1 3 -2], ⟨0 5 54 24 21 6 52]]

POTE generator: ~13/12 = 140.497

Vals: Template:Val list

Badness: 0.0211

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714

Mapping: [⟨1 1 -4 0 1 3 -2 -5], ⟨0 5 54 24 21 6 52 79]]

POTE generator: ~13/12 = 140.496

Vals: Template:Val list

Badness: 0.0173

Supers

Subgroup: 2.3.5.7

Comma list: 5120/5103, 118098/117649

Mapping: [⟨2 1 -12 2], ⟨0 3 23 5]]

Wedgie: ⟨⟨ 6 46 10 59 -1 -106 ]]

POTE generator: ~9/7 = 434.218

Template:Val list

Badness: 0.092748

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 5120/5103

Mapping: [⟨2 1 -12 2 -9], ⟨0 3 23 5 22]]

POTE generator: ~9/7 = 434.217

Vals: Template:Val list

Badness: 0.028240

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1575/1573

Mapping: [⟨2 1 -12 2 -9 -2], ⟨0 3 23 5 22 13]]

POTE generator: ~9/7 = 434.221

Vals: Template:Val list

Badness: 0.021645

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 289/288, 352/351, 442/441, 561/560

Mapping: [⟨2 1 -12 2 -9 -2 6], ⟨0 3 23 5 22 13 3]]

POTE generator: ~9/7 = 434.181

Vals: Template:Val list

Badness: 0.021316

Alphaquarter

Subgroup: 2.3.5.7

Comma list: 5120/5103, 29360128/29296875

Mapping: [⟨1 2 2 0], ⟨0 -9 7 61]]

Wedgie: ⟨⟨ 9 -7 -61 -32 -122 -122 ]]

POTE generator: ~16128/15625 = 55.243

Template:Val list

Badness: 0.1166

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4000/3993, 5120/5103

Mapping: [⟨1 2 2 0 3], ⟨0 -9 7 61 10]]

POTE generator: ~33/32 = 55.243

Vals: Template:Val list

Badness: 0.0296

Septiquarter

Subgroup: 2.3.5.7

Comma list: 5120/5103, 420175/419904

Mapping: [⟨1 3 10 2], ⟨0 -7 -38 4]]

Wedgie: ⟨⟨ 7 38 -4 44 -26 -116 ]]

POTE generator: ~147/128 = 242.453

Template:Val list

Badness: 0.0538

Semiseptiquarter

Subgroup: 2.3.5.7.11

Comma list: 5120/5103, 9801/9800, 14641/14580

Mapping: [⟨2 6 20 4 15], ⟨0 -7 -38 4 -20]]

POTE generators: ~121/105 = 242.4511

Vals: Template:Val list

Badness: 0.0642

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 847/845, 1716/1715, 14641/14580

Mapping: [⟨2 6 20 4 15 7], ⟨0 -7 -38 4 -20 1]]

POTE generators: ~121/105 = 242.4448

Vals: Template:Val list

Badness: 0.0348

Tricot (aka Trimot)

See also: Tricot family

The generator for tricot is the real cube root of third harmonic, 31/3, tuned between 63/44 and 13/9. Tricot can be described as 53&70 temperament (also known as trimot), tempering out the tricot comma, [39 -29 3⟩ in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.

Subgroup: 2.3.5.7

Comma list: 2430/2401, 5120/5103

Mapping: [⟨1 0 -13 -3], ⟨0 3 29 11]]

Wedgie: ⟨⟨ 3 29 11 39 9 -56 ]]

POTE generator: ~81/56 = 634.026

Template:Val list

Badness: 0.100127

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120, 5120/5103

Mapping: [⟨1 0 -13 -3 -5], ⟨0 3 29 11 16]]

POTE generator: ~63/44 = 634.027

Vals: Template:Val list

Badness: 0.056134

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 121/120, 169/168, 352/351

Mapping: [⟨1 0 -13 -3 -5 0], ⟨0 3 29 11 16 7]]

POTE generator: ~13/9 = 634.012

Vals: Template:Val list

Badness: 0.032102

Ketchup

Subgroup: 2.3.5.7

Comma list: 5120/5103, 1071875/1062882

Mapping: [⟨2 3 4 6], ⟨0 4 15 -9]]

Wedgie: ⟨⟨ 8 30 -18 29 -51 -126 ]]

POTE generator: ~64/63 = ~81/80 = 25.719

Template:Val list

Badness: 0.084538

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1331/1323, 2200/2187

Mapping: [⟨2 3 4 6 7], ⟨0 4 15 -9 -2]]

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693

Vals: Template:Val list

Badness: 0.039555

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 847/845, 1331/1323

Mapping: [⟨2 3 4 6 7 8], ⟨0 4 15 -9 -2 -14]]

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697

Vals: Template:Val list

Badness: 0.024824

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 289/288, 325/324, 352/351, 385/384, 561/560

Mapping: [⟨2 3 4 6 7 8 8], ⟨0 4 15 -9 -2 -14 4]]

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701

Vals: Template:Val list

Badness: 0.016591

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560

Mapping: [⟨2 3 4 6 7 8 8 9], ⟨0 4 15 -9 -2 -14 4 -12]]

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660

Vals: Template:Val list

Badness: 0.018170

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384

Mapping: [⟨2 3 4 6 7 8 8 9 9], ⟨0 4 15 -9 -2 -14 4 -12 1]]

POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661

Vals: Template:Val list

Badness: 0.014033

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