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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
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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 }}
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== 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
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== 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
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= 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 }}
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== 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
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== 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
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== 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
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== 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
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== 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
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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]]
Retrieved from "https://en.xen.wiki/w/Aberschismic_temperaments"