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[[Comma list]]: 1600000/1594323
[[Comma list]]: 1600000/1594323


[[Mapping]]: [{{val| 1 3 6 }}, {{val| 0 -5 -13 }}]
{{Mapping|legend=1| 1 3 6 | 0 -5 -13 }}


Mapping generators: ~2, ~243/200
: mapping generators: ~2, ~243/200


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.519
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.519
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Temperaments discussed elsewhere include:  
Temperaments discussed elsewhere include:  
* ''[[Chromat]]'', {10976/10935, 235298/234375} → [[Hemimage temperaments #Chromat]]
* ''[[Chromat]]'' → [[Hemimage temperaments #Chromat]] (+10976/10935)
* ''[[Witch]]'', {420175/419904, 1600000/1594323} → [[Wizmic microtemperaments #Witch]]
* ''[[Witch]]'' → [[Wizmic microtemperaments #Witch]] (+420175/419904)


== Septimal amity ==
== Septimal amity ==
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[[Comma list]]: 4375/4374, 5120/5103
[[Comma list]]: 4375/4374, 5120/5103


[[Mapping]]: [{{val| 1 3 6 -2 }}, {{val| 0 -5 -13 17 }}]
{{Mapping|legend=1| 1 3 6 -2 | 0 -5 -13 17 }}


{{Multival|legend=1| 5 13 -17 9 -41 -76 }}
{{Multival|legend=1| 5 13 -17 9 -41 -76 }}
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Comma list: 540/539, 4375/4374, 5120/5103
Comma list: 540/539, 4375/4374, 5120/5103


Mapping: [{{val| 1 3 6 -2 21 }}, {{val| 0 -5 -13 17 -62 }}]
Mapping: {{mapping| 1 3 6 -2 21 | 0 -5 -13 17 -62 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.464
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.464
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Comma list: 352/351, 540/539, 625/624, 847/845
Comma list: 352/351, 540/539, 625/624, 847/845


Mapping: [{{val| 1 3 6 -2 21 17 }}, {{val| 0 -5 -13 17 -62 -47 }}]
Mapping: {{mapping| 1 3 6 -2 21 17 | 0 -5 -13 17 -62 -47 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.481
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.481
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Comma list: 121/120, 176/175, 2200/2187
Comma list: 121/120, 176/175, 2200/2187


Mapping: [{{val| 1 3 6 -2 6 }}, {{val| 0 -5 -13 17 -9 }}]
Mapping: {{mapping| 1 3 6 -2 6 | 0 -5 -13 17 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.390
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.390
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Comma list: 121/120, 169/168, 176/175, 325/324
Comma list: 121/120, 169/168, 176/175, 325/324


Mapping: [{{val| 1 3 6 -2 6 2 }}, {{val| 0 -5 -13 17 -9 6 }}]
Mapping: {{mapping| 1 3 6 -2 6 2 | 0 -5 -13 17 -9 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.419
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.419
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Comma list: 121/120, 154/153, 169/168, 176/175, 273/272
Comma list: 121/120, 154/153, 169/168, 176/175, 273/272


Mapping: [{{val| 1 3 6 -2 6 2 -1 }}, {{val| 0 -5 -13 17 -9 6 18 }}]
Mapping: {{mapping| 1 3 6 -2 6 2 -1 | 0 -5 -13 17 -9 6 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.366
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.366
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Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189


Mapping: [{{val| 1 3 6 -2 6 2 -1 0 }}, {{val| 0 -5 -13 17 -9 6 18 15 }}]
Mapping: {{mapping| 1 3 6 -2 6 2 -1 0 | 0 -5 -13 17 -9 6 18 15 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.407
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.407
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Comma list: 441/440, 896/891, 4375/4374
Comma list: 441/440, 896/891, 4375/4374


Mapping: [{{val| 1 3 6 -2 -7 }}, {{val| 0 -5 -13 17 37 }}]
Mapping: {{mapping| 1 3 6 -2 -7 | 0 -5 -13 17 37 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.340
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.340
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Comma list: 196/195, 352/351, 364/363, 4375/4374
Comma list: 196/195, 352/351, 364/363, 4375/4374


Mapping: [{{val| 1 3 6 -2 -7 -11 }}, {{val| 0 -5 -13 17 37 52 }}]
Mapping: {{mapping| 1 3 6 -2 -7 -11 | 0 -5 -13 17 37 52 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.313
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.313
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Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155


Mapping: [{{val| 1 3 6 -2 -7 -11 -1 }}, {{val| 0 -5 -13 17 37 52 18 }}]
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 | 0 -5 -13 17 37 52 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.313
Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.313
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Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475


Mapping: [{{val| 1 3 6 -2 -7 -11 -1 -13 }}, {{val| 0 -5 -13 17 37 52 18 61 }}]
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 -13 | 0 -5 -13 17 37 52 18 61 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.325
Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.325
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Comma list: 3025/3024, 4375/4374, 5120/5103
Comma list: 3025/3024, 4375/4374, 5120/5103


Mapping: [{{val| 2 1 -1 13 13 }}, {{val| 0 5 13 -17 -14 }}]
Mapping: {{mapping| 2 1 -1 13 13 | 0 5 13 -17 -14 }}


Mapping generators: ~99/70, ~64/55
: mapping generators: ~99/70, ~64/55


Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.561
Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.561
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Comma list: 352/351, 847/845, 1716/1715, 3025/3024
Comma list: 352/351, 847/845, 1716/1715, 3025/3024


Mapping: [{{val| 2 1 -1 13 13 20 }}, {{val| 0 5 13 -17 -14 -29 }}]
Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.583
Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.583
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[[Comma list]]: 126/125, 100352/98415
[[Comma list]]: 126/125, 100352/98415


[[Mapping]]: [{{val| 1 3 6 11 }}, {{val| 0 -5 -13 -29 }}]
{{Mapping|legend=1| 1 3 6 11 | 0 -5 -13 -29 }}


{{Multival|legend=1| 5 13 29 9 32 31 }}
{{Multival|legend=1| 5 13 29 9 32 31 }}
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Comma list: 121/120, 126/125, 896/891
Comma list: 121/120, 126/125, 896/891


Mapping: [{{val| 1 3 6 11 6 }}, {{val| 0 -5 -13 -29 -9 }}]
Mapping: {{mapping| 1 3 6 11 6 | 0 -5 -13 -29 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.047
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.047
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== Houborizic ==
== Houborizic ==
The ''houborizic'' temperament (53&113) tempers out the [[marvel comma]], 225/224. It is so named because it is closely related to the '''houboriz tuning''' (generator: 339.774971 cents).
The ''houborizic'' temperament (53 & 60) tempers out the [[marvel comma]], 225/224. It is so named because it is closely related to the '''houboriz tuning''' (generator: 339.774971 cents).


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 225/224, 1250000/1240029
[[Comma list]]: 225/224, 1250000/1240029


[[Mapping]]: [{{val| 1 3 6 13 }}, {{val| 0 -5 -13 -36 }}]
{{Mapping|legend=1| 1 3 6 13 | 0 -5 -13 -36 }}


{{Multival|legend=1| 5 13 36 9 43 47 }}
{{Multival|legend=1| 5 13 36 9 43 47 }}
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Comma list: 225/224, 385/384, 1250000/1240029
Comma list: 225/224, 385/384, 1250000/1240029


Mapping: [{{val| 1 3 6 13 -9 }}, {{val| 0 -5 -13 -36 44 }}]
Mapping: {{mapping| 1 3 6 13 -9 | 0 -5 -13 -36 44 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763
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Comma list: 225/224, 325/324, 385/384, 2200/2197
Comma list: 225/224, 325/324, 385/384, 2200/2197


Mapping: [{{val| 1 3 6 13 -9 2 }}, {{val| 0 -5 -13 -36 44 6 }}]
Mapping: {{mapping| 1 3 6 13 -9 2 | 0 -5 -13 -36 44 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~39/32 = 339.764
Optimal tuning (POTE): ~2 = 1\1, ~39/32 = 339.764
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[[Comma list]]: 65625/65536, 1600000/1594323
[[Comma list]]: 65625/65536, 1600000/1594323


[[Mapping]]: [{{val|1 3 6 -17}}, {{val|0 -5 -13 70}}]
{{Mapping|legend=1|1 3 6 -17 | 0 -5 -13 70 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.553
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.553
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Comma list: 6250/6237, 19712/19683, 41503/41472
Comma list: 6250/6237, 19712/19683, 41503/41472


Mapping: [{{val| 1 3 6 -17 36 }}, {{val| 0 -5 -13 70 -115 }}]
Mapping: {{mapping| 1 3 6 -17 36 | 0 -5 -13 70 -115 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
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Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683


Mapping: [{{val| 1 3 6 -17 36 17 }}, {{val| 0 -5 -13 70 -115 -47 }}]
Mapping: {{mapping| 1 3 6 -17 36 17 | 0 -5 -13 70 -115 -47 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
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Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430


Mapping: [{{val| 1 3 6 -17 36 17 -31 }}, {{val| 0 -5 -13 70 -115 -47 124 }}]
Mapping: {{mapping| 1 3 6 -17 36 17 -31 | 0 -5 -13 70 -115 -47 124 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.555
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.555
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Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197


Mapping: [{{val| 1 3 6 -17 36 17 -31 15 }}, {{val| 0 -5 -13 70 -115 -47 124 -38 }}]
Mapping: {{mapping| 1 3 6 -17 36 17 -31 15 | 0 -5 -13 70 -115 -47 124 -38 }}


Optimal tuning (POTE): ~2 = 1\1, ~208/171 = 339.555
Optimal tuning (POTE): ~2 = 1\1, ~208/171 = 339.555
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== Bamity ==
== Bamity ==
Bamity has a period of half octave and tempers out the sensamagic comma, [[245/243]]. The name ''bamity'' is a play on the words ''bi-'' and ''amity''.
Bamity has a period of half octave and tempers out the sensamagic comma, [[245/243]]. The name ''bamity'' is a contraction of ''bi-'' and ''amity''.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 245/243, 64827/64000
[[Comma list]]: 245/243, 64827/64000


[[Mapping]]: [{{val| 2 1 -1 3 }}, {{val| 0 5 13 6 }}]
{{Mapping|legend=1| 2 1 -1 3 | 0 5 13 6 }}


Mapping generators: ~343/240, ~7/6
: mapping generators: ~343/240, ~7/6


{{Multival|legend=1| 10 26 12 18 -9 -45 }}
{{Multival|legend=1| 10 26 12 18 -9 -45 }}
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Comma list: 121/120, 245/243, 441/440
Comma list: 121/120, 245/243, 441/440


Mapping: [{{val| 2 1 -1 3 3 }}, {{val| 0 5 13 6 9 }}]
Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~7/6 = 260.393
Optimal tuning (POTE): ~99/70 = 1\2, ~7/6 = 260.393
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Comma list: 91/90, 121/120, 245/243, 441/440
Comma list: 91/90, 121/120, 245/243, 441/440


Mapping: [{{val| 2 1 -1 3 3 0 }}, {{val| 0 5 13 6 9 17 }}]
Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~7/6 = 260.618
Optimal tuning (POTE): ~55/39 = 1\2, ~7/6 = 260.618
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== Hamity ==
== Hamity ==
Hamity has a generator of about 430 cents which represents [[9/7]]. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a play on the words ''half'' and ''amity''.
Hamity has a generator of about 430 cents which represents [[9/7]]. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a contraction of ''half'' and ''amity''.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 2430/2401, 4000/3969  
[[Comma list]]: 2430/2401, 4000/3969  


[[Mapping]]: [{{val| 1 -2 -7 -4 }}, {{val| 0 10 26 19 }}]
{{Mapping|legend=1| 1 8 19 15 | 0 -10 -26 -19 }}
 
: mapping generators: ~2, ~14/9


{{Multival|legend=1| 10 26 19 18 2 -29 }}
{{Multival|legend=1| 10 26 19 18 2 -29 }}
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Comma list: 99/98, 121/120, 2200/2187
Comma list: 99/98, 121/120, 2200/2187


Mapping: [{{val| 1 -2 -7 -4 -3 }}, {{val| 0 10 26 19 18 }}]
Mapping: {{mapping| 1 8 19 15 15 | 0 -10 -26 -19 -18 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.192
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.192
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Comma list: 99/98, 121/120, 275/273, 572/567
Comma list: 99/98, 121/120, 275/273, 572/567


Mapping: [{{val| 1 -2 -7 -4 -3 -11 }}, {{val| 0 10 26 19 18 41 }}]
Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.216
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.216
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[[Comma list]]: 1029/1024, 1071875/1062882
[[Comma list]]: 1029/1024, 1071875/1062882


[[Mapping]]: [{{val| 1 -2 -7 4 }}, {{val| 0 15 39 -5 }}]
{{Mapping|legend=1| 1 13 32 -1 | 0 -15 -39 5 }}
 
: mapping generators: ~2, ~320/189


{{Multival|legend=1| 15 39 -5 27 -50 -121 }}
{{Multival|legend=1| 15 39 -5 27 -50 -121 }}
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Comma list: 385/384, 441/440, 1071875/1062882
Comma list: 385/384, 441/440, 1071875/1062882


Mapping: [{{val| 1 -2 -7 4 8 }}, {{val| 0 15 39 -5 -19 }}]
Mapping: {{mapping| 1 13 32 -1 -11 | 0 -15 -39 5 19 }}


Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 286.797
Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 286.797
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Comma list: 325/324, 364/363, 385/384, 10985/10976
Comma list: 325/324, 364/363, 385/384, 10985/10976


Mapping: [{{val| 1 -2 -7 4 8 8 }}, {{val| 0 15 39 -5 -19 -18 }}]
Mapping: {{mapping| 1 13 32 -1 -11 -10 | 0 -15 -39 5 19 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.789
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.789
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Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757


Mapping: [{{val| 1 -2 -7 4 8 8 6 }}, {{val| 0 15 39 -5 -19 -18 -8 }}]
Mapping: {{mapping| 1 13 32 -1 -11 -10 -2 | 0 -15 -39 5 19 18 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.795
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.795
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== Trinity ==
== Trinity ==
The ''trinity'' temperament (152 & 159) tempers out the [[meter]], 703125/702464. It splits the acute minor tenth (~243/100, an octave plus acute minor third) in three. It was so named for the following reason – 133\311 (133 steps of 311edo) is a possible generator, which is placed around 3\7 (1.1¢ flat), three of which makes acute minor third of ~243/200 with octave reduction.
The trinity temperament (152 & 159) tempers out the [[meter]], 703125/702464. It splits the acute minor tenth (~243/100, an octave plus acute minor third) in three. It was so named for the following reason – 133\311 (133 steps of 311edo) is a possible generator, which is placed around 3\7 (1.1¢ flat), three of which makes acute minor third of ~243/200 with octave reduction.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 703125/702464, 1600000/1594323
[[Comma list]]: 703125/702464, 1600000/1594323


[[Mapping]]: [{{val| 1 8 19 46 }}, {{val| 0 -15 -39 -101 }}]
{{Mapping|legend=1| 1 8 19 46 | 0 -15 -39 -101 }}


{{Multival|legend=1| 15 39 101 27 118 125 }}
{{Multival|legend=1| 15 39 101 27 118 125 }}
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Comma list: 3025/3024, 4000/3993, 19712/19683
Comma list: 3025/3024, 4000/3993, 19712/19683


Mapping: [{{val| 1 8 19 46 18 }}, {{val| 0 -15 -39 -101 -34 }}]
Mapping: {{mapping| 1 8 19 46 18 | 0 -15 -39 -101 -34 }}


POTE generator: ~121/90 = 513.177
Optimal tuning (POTE): ~2 = 1\1, ~121/90 = 513.177


{{Optimal ET sequence|legend=1| 152, 311, 463, 774, 1237e }}
{{Optimal ET sequence|legend=1| 152, 311, 463, 774, 1237e }}
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Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689


Mapping: [{{val| 1 8 19 46 18 64 }}, {{val| 0 -15 -39 -101 -34 -141 }}]
Mapping: {{mapping| 1 8 19 46 18 64 | 0 -15 -39 -101 -34 -141 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.182
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.182
Line 564: Line 568:
Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619


Mapping: [{{val| 1 8 19 46 18 64 -22 }}, {{val| 0 -15 -39 -101 -34 -141 61 }}]
Mapping: {{mapping| 1 8 19 46 18 64 -22 | 0 -15 -39 -101 -34 -141 61 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
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Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573


Mapping: [{{val| 1 8 19 46 18 64 -22 53 }}, {{val| 0 -15 -39 -101 -34 -141 61 -114 }}]
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 | 0 -15 -39 -101 -34 -141 61 -114 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
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Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104


Mapping: [{{val| 1 8 19 46 18 64 -22 53 49 }}, {{val| 0 -15 -39 -101 -34 -141 61 -114 -104 }}]
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 | 0 -15 -39 -101 -34 -141 61 -114 -104 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
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Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044


Mapping: [{{val| 1 8 19 46 18 64 -22 53 49 72 }}, {{val| 0 -15 -39 -101 -34 -141 61 -114 -104 -157 }}]
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 72 | 0 -15 -39 -101 -34 -141 61 -114 -104 -157 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
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While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.  
While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.  


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2401/2400, 1600000/1594323
[[Comma list]]: 2401/2400, 1600000/1594323


[[Mapping]]: [{{val| 1 3 6 5 }}, {{val| 0 -20 -52 -31 }}]
{{Mapping|legend=1| 1 3 6 5 | 0 -20 -52 -31 }}


{{Multival|legend=1| 20 52 31 36 -7 -74 }}
{{Multival|legend=1| 20 52 31 36 -7 -74 }}
Line 635: Line 639:
Comma list: 2401/2400, 131072/130977, 1600000/1594323
Comma list: 2401/2400, 131072/130977, 1600000/1594323


Mapping: [{{val| 1 3 6 5 -8 }}, {{val| 0 -20 -52 -31 162 }}]
Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8843
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8843
Line 648: Line 652:
Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206


Mapping: [{{val| 1 3 6 5 -8 -5 }}, {{val| 0 -20 -52 -31 162 123 }}]
Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8838
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8838
Line 661: Line 665:
Comma list: 2401/2400, 6250/6237, 19712/19683
Comma list: 2401/2400, 6250/6237, 19712/19683


Mapping: [{{val| 1 3 6 5 14 }}, {{val| 0 -20 -52 -31 -149 }}]
Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8896
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8896
Line 674: Line 678:
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647


Mapping: [{{val| 1 3 6 5 14 17 }}, {{val| 0 -20 -52 -31 -149 -188 }}]
Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8910
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8910
Line 687: Line 691:
Comma list: 385/384, 1375/1372, 1600000/1594323
Comma list: 385/384, 1375/1372, 1600000/1594323


Mapping: [{{val| 1 3 6 5 -1 }}, {{val| 0 -20 -52 -31 63 }}]
Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9091
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9091
Line 700: Line 704:
Comma list: 325/324, 385/384, 1375/1372, 19773/19712
Comma list: 325/324, 385/384, 1375/1372, 19773/19712


Mapping: [{{val| 1 3 6 5 -1 2 }}, {{val| 0 -20 -52 -31 63 24 }}]
Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9127
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9127
Line 713: Line 717:
Comma list: 243/242, 441/440, 980000/970299
Comma list: 243/242, 441/440, 980000/970299


Mapping: [{{val| 1 3 6 5 7 }}, {{val| 0 -20 -52 -31 -50 }}]
Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8917
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8917
Line 726: Line 730:
Comma list: 243/242, 364/363, 441/440, 1875/1859
Comma list: 243/242, 364/363, 441/440, 1875/1859


Mapping: [{{val| 1 3 6 5 7 10 }}, {{val| 0 -20 -52 -31 -50 -89 }}]
Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9164
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9164
Line 739: Line 743:
Comma list: 2401/2400, 9801/9800, 14641/14580
Comma list: 2401/2400, 9801/9800, 14641/14580


Mapping: [{{val| 2 6 12 10 13 }}, {{val| 0 -20 -52 -31 -43 }}]
Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8788
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8788
Line 752: Line 756:
Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580


Mapping: [{{val| 2 6 12 10 13 19 }}, {{val| 0 -20 -52 -31 -43 -82 }}]
Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8750
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8750
Line 765: Line 769:
Comma list: 2401/2400, 3025/3024, 1600000/1594323
Comma list: 2401/2400, 3025/3024, 1600000/1594323


Mapping: [{{val| 1 3 6 5 3 }}, {{val| 0 -40 -104 -62 13 }}]
Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}


Optimal tuning (POTE): ~2 = 1\1, ~4096/3993 = 42.4391
Optimal tuning (POTE): ~2 = 1\1, ~4096/3993 = 42.4391
Line 778: Line 782:
Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024


Mapping: [{{val| 1 3 6 5 3 6 }}, {{val| 0 -40 -104 -62 13 -65 }}]
Mapping: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}


Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 42.4391
Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 42.4391
Line 793: Line 797:
[[Comma list]]: 16875/16807, 1600000/1594323
[[Comma list]]: 16875/16807, 1600000/1594323


[[Mapping]]: [{{val| 1 8 19 20 }}, {{val| 0 -25 -65 -67 }}]
{{Mapping|legend=1| 1 8 19 20 | 0 -25 -65 -67 }}


{{Multival|legend=1| 25 65 67 45 36 -27 }}
{{Multival|legend=1| 25 65 67 45 36 -27 }}
Line 808: Line 812:
Comma list: 540/539, 1375/1372, 1600000/1594323
Comma list: 540/539, 1375/1372, 1600000/1594323


Mapping: [{{val| 1 8 19 20 5 }}, {{val| 0 -25 -65 -67 -6 }}]
Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3200/2673 = 307.906
Optimal tuning (POTE): ~2 = 1\1, ~3200/2673 = 307.906
Line 821: Line 825:
Comma list: 540/539, 729/728, 1375/1372, 2205/2197
Comma list: 540/539, 729/728, 1375/1372, 2205/2197


Mapping: [{{val| 1 8 19 20 5 25 }}, {{val| 0 -25 -65 -67 -6 -83 }}]
Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}


Optimal tuning (POTE): ~2 = 1\1, ~143/120 = 307.913
Optimal tuning (POTE): ~2 = 1\1, ~143/120 = 307.913
Line 831: Line 835:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Amity family| ]] <!-- main article -->
[[Category:Amity family| ]] <!-- main article -->
[[Category:Amity|#]] <!-- key article -->
[[Category:Amity| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Amity_family"