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Amity family: Difference between revisions

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The '''amity family''' tempers out the 5-limit [[amity comma]], 1600000/1594323. The generator for the [[amity]] temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It can also be described as the 46&53 temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo|99EDO]] is a good tuning for amity, with generator 28\99, and MOS of 11, 18, 25, 32, 39, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.
The '''amity family''' tempers out the 5-limit [[amity comma]], 1600000/1594323. The generator for the [[amity]] temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. If you are looking for a different kind of neutral third this could be the temperament for you.


== Amity ==
== Amity ==
{{Main| Amity }}
{{Main| Amity }}
{{See also| Ragismic microtemperaments #Amity }}
 
In the 5-limit amity is a genuine [[microtemperament]], with 58\205 being a possible tuning. Another good choice is (64/5)<sup>1/13</sup>, which gives a pure classical major third. [[Mos scale]]s of 11, 18, 25, 32, 39, 46 or 53 notes are available.


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
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== Septimal amity ==
== Septimal amity ==
{{Main| Amity }}
Septimal amity can be described as the 46 &amp; 53 temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo]] is a good tuning, with generator 28\99.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


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


{{Multival|legend=1|20 52 31 36 -7 -74}}
{{Multival|legend=1| 20 52 31 36 -7 -74 }}


[[POTE generator]]: ~21/20 = 84.880
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 84.880


{{Val list|legend=1| 99, 212, 311, 410, 1131, 1541b }}
{{Val list|legend=1| 99, 212, 311, 410, 1131, 1541b }}
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Mapping: [{{val| 1 3 6 5 -8 }}, {{val| 0 -20 -52 -31 162 }}]
Mapping: [{{val| 1 3 6 5 -8 }}, {{val| 0 -20 -52 -31 162 }}]


POTE generator: ~21/20 = 84.8843
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8843


Optimal GPV sequence: {{val list| 99, 212e, 311, 410, 721, 1032, 1343 }}
Optimal GPV sequence: {{val list| 99, 212e, 311, 410, 721, 1032, 1343 }}
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Mapping: [{{val| 1 3 6 5 -8 -5 }}, {{val| 0 -20 -52 -31 162 123 }}]
Mapping: [{{val| 1 3 6 5 -8 -5 }}, {{val| 0 -20 -52 -31 162 123 }}]


POTE generator: ~21/20 = 84.8838
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8838


Optimal GPV sequence: {{val list| 99, 212ef, 311, 410, 721, 1032 }}
Optimal GPV sequence: {{val list| 99, 212ef, 311, 410, 721, 1032 }}
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Mapping: [{{val| 1 3 6 5 14 }}, {{val| 0 -20 -52 -31 -149 }}]
Mapping: [{{val| 1 3 6 5 14 }}, {{val| 0 -20 -52 -31 -149 }}]


POTE generator: ~21/20 = 84.8896
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8896


Optimal GPV sequence: {{val list| 99e, 212, 311, 1145c, 1456cd }}
Optimal GPV sequence: {{val list| 99e, 212, 311, 1145c, 1456cd }}
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Mapping: [{{val| 1 3 6 5 14 17 }}, {{val| 0 -20 -52 -31 -149 -188 }}]
Mapping: [{{val| 1 3 6 5 14 17 }}, {{val| 0 -20 -52 -31 -149 -188 }}]


POTE generator: ~21/20 = 84.8910
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8910


Optimal GPV sequence: {{val list| 99ef, 212, 311, 834, 1145c }}
Optimal GPV sequence: {{val list| 99ef, 212, 311, 834, 1145c }}
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Mapping: [{{val| 1 3 6 5 -1 }}, {{val| 0 -20 -52 -31 63 }}]
Mapping: [{{val| 1 3 6 5 -1 }}, {{val| 0 -20 -52 -31 63 }}]


POTE generator: ~21/20 = 84.9091
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9091


Optimal GPV sequence: {{val list| 99, 113, 212, 961ccdeee }}
Optimal GPV sequence: {{val list| 99, 113, 212, 961ccdeee }}
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Mapping: [{{val| 1 3 6 5 -1 2 }}, {{val| 0 -20 -52 -31 63 24 }}]
Mapping: [{{val| 1 3 6 5 -1 2 }}, {{val| 0 -20 -52 -31 63 24 }}]


POTE generator: ~21/20 = 84.9127
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9127


Optimal GPV sequence: {{val list| 99, 113, 212, 537cdeff, 749ccdeefff }}
Optimal GPV sequence: {{val list| 99, 113, 212, 537cdeff, 749ccdeefff }}
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Mapping: [{{val| 1 3 6 5 7 }}, {{val| 0 -20 -52 -31 -50 }}]
Mapping: [{{val| 1 3 6 5 7 }}, {{val| 0 -20 -52 -31 -50 }}]


POTE generator: ~21/20 = 84.8917
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8917


Optimal GPV sequence: {{val list| 99e, 212e }}
Optimal GPV sequence: {{val list| 99e, 212e }}
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Mapping: [{{val| 1 3 6 5 7 10 }}, {{val| 0 -20 -52 -31 -50 -89 }}]
Mapping: [{{val| 1 3 6 5 7 10 }}, {{val| 0 -20 -52 -31 -50 -89 }}]


POTE generator: ~21/20 = 84.9164
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9164


Optimal GPV sequence: {{val list| 99ef, 113, 212ef }}
Optimal GPV sequence: {{val list| 99ef, 113, 212ef }}
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Mapping: [{{val| 2 6 12 10 13 }}, {{val| 0 -20 -52 -31 -43 }}]
Mapping: [{{val| 2 6 12 10 13 }}, {{val| 0 -20 -52 -31 -43 }}]


POTE generator: ~21/20 = 84.8788
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8788


Optimal GPV sequence: {{val list| 198, 212, 410 }}
Optimal GPV sequence: {{val list| 198, 212, 410 }}
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Mapping: [{{val| 2 6 12 10 13 19 }}, {{val| 0 -20 -52 -31 -43 -82 }}]
Mapping: [{{val| 2 6 12 10 13 19 }}, {{val| 0 -20 -52 -31 -43 -82 }}]


POTE generator: ~21/20 = 84.8750
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8750


Optimal GPV sequence: {{val list| 198, 410 }}
Optimal GPV sequence: {{val list| 198, 410 }}
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Mapping: [{{val| 1 3 6 5 3 }}, {{val| 0 -40 -104 -62 13 }}]
Mapping: [{{val| 1 3 6 5 3 }}, {{val| 0 -40 -104 -62 13 }}]


POTE generator: ~4096/3993 = 42.4391
Optimal tuning (POTE): ~2 = 1\1, ~4096/3993 = 42.4391


Optimal GPV sequence: {{val list| 85c, 113, 198, 311, 509, 820 }}
Optimal GPV sequence: {{val list| 85c, 113, 198, 311, 509, 820 }}
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Mapping: [{{val| 1 3 6 5 3 6 }}, {{val| 0 -40 -104 -62 13 -65 }}]
Mapping: [{{val| 1 3 6 5 3 6 }}, {{val| 0 -40 -104 -62 13 -65 }}]


POTE generator: ~40/39 = 42.4391
Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 42.4391


Optimal GPV sequence: {{val list| 85c, 113, 198, 311, 509, 820f }}
Optimal GPV sequence: {{val list| 85c, 113, 198, 311, 509, 820f }}
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