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Minortonic family: Difference between revisions

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== Minortone ==
== Minortone ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: {{monzo| -16 35 -17 }}
[[Comma list]]: {{monzo| -16 35 -17 }}


[[Mapping]]: [{{val| 1 -1 -3 }}, {{val| 0 17 35 }}]
[[Mapping]]: [{{val| 1 -1 -3 }}, {{val| 0 17 35 }}]


[[POTE generator]]: ~10/9 = 182.466
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.466


{{Val list|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}
{{Val list|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}
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However, as noted before, 32/21 is only a ragisma shy of (10/9)<sup>4</sup>, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. 21 generators gives a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.
However, as noted before, 32/21 is only a ragisma shy of (10/9)<sup>4</sup>, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. 21 generators gives a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4375/4374, 2100875/2097152
[[Comma list]]: 4375/4374, 2100875/2097152
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{{Multival|legend=1| 17 35 -21 16 -81 -147 }}
{{Multival|legend=1| 17 35 -21 16 -81 -147 }}


[[POTE generator]]: ~10/9 = 182.458
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.458


{{Val list|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}
{{Val list|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}
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Mapping: [{{val| 1 -1 -3 6 10 }}, {{val| 0 17 35 -21 -43 }}]
Mapping: [{{val| 1 -1 -3 6 10 }}, {{val| 0 17 35 -21 -43 }}]


POTE generator: ~10/9 = 182.482
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.482


Optimal GPV sequence: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
Optimal GPV sequence: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
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Mapping: [{{val| 1 -1 -3 6 10 11 }}, {{val| 0 17 35 -21 -43 -48 }}]
Mapping: [{{val| 1 -1 -3 6 10 11 }}, {{val| 0 17 35 -21 -43 -48 }}]


POTE generator: ~10/9 = 182.481
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481


Optimal GPV sequence: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
Optimal GPV sequence: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
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Mapping: [{{val| 1 -1 -3 6 10 11 5 }}, {{val| 0 17 35 -21 -43 -48 -6 }}]
Mapping: [{{val| 1 -1 -3 6 10 11 5 }}, {{val| 0 17 35 -21 -43 -48 -6 }}]


POTE generator: ~10/9 = 182.481
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481


Optimal GPV sequence: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
Optimal GPV sequence: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
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Mapping: [{{val| 1 -1 -3 6 3 }}, {{val| 0 17 35 -21 3 }}]
Mapping: [{{val| 1 -1 -3 6 3 }}, {{val| 0 17 35 -21 3 }}]


POTE generator: ~10/9 = 182.449
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.449


Optimal GPV sequence: {{Val list| 46, 125, 171e }}
Optimal GPV sequence: {{Val list| 46, 125, 171e }}
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Mapping: [{{val| 1 -1 -3 6 3 11 }}, {{val| 0 17 35 -21 3 -48 }}]
Mapping: [{{val| 1 -1 -3 6 3 11 }}, {{val| 0 17 35 -21 3 -48 }}]


POTE generator: ~10/9 = 182.470
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.470


Optimal GPV sequence: {{Val list| 46, 125, 171e, 388ee }}
Optimal GPV sequence: {{Val list| 46, 125, 171e, 388ee }}
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Mapping: [{{val| 1 -1 -3 6 3 11 5 }}, {{val| 0 17 35 -21 3 -48 -6 }}]
Mapping: [{{val| 1 -1 -3 6 3 11 5 }}, {{val| 0 17 35 -21 3 -48 -6 }}]


POTE generator: ~10/9 = 182.471
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.471


Optimal GPV sequence: {{Val list| 46, 125, 171e, 388ee }}
Optimal GPV sequence: {{Val list| 46, 125, 171e, 388ee }}
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Mapping: [{{val| 1 -1 -3 6 3 4 }}, {{val| 0 17 35 -21 3 -2 }}]
Mapping: [{{val| 1 -1 -3 6 3 4 }}, {{val| 0 17 35 -21 3 -2 }}]


POTE generator: ~10/9 = 182.437
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.437


Optimal GPV sequence: {{Val list| 46, 79, 125f, 171ef, 296eff }}
Optimal GPV sequence: {{Val list| 46, 79, 125f, 171ef, 296eff }}
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Mapping: [{{val| 1 -1 -3 6 3 4 5 }}, {{val| 0 17 35 -21 3 -2 -6 }}]
Mapping: [{{val| 1 -1 -3 6 3 4 5 }}, {{val| 0 17 35 -21 3 -2 -6 }}]


POTE generator: ~10/9 = 182.444
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.444


Optimal GPV sequence: {{Val list| 46, 125f, 171ef }}
Optimal GPV sequence: {{Val list| 46, 125f, 171ef }}
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Mapping: [{{val| 2 -2 -6 12 13 }}, {{val| 0 17 35 -21 -20 }}]
Mapping: [{{val| 2 -2 -6 12 13 }}, {{val| 0 17 35 -21 -20 }}]


POTE generator: ~10/9 = 182.457
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.457


Optimal GPV sequence: {{Val list| 46, 204c, 250, 296, 342 }}
Optimal GPV sequence: {{Val list| 46, 204c, 250, 296, 342 }}
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== Domain ==
== Domain ==
''Not to be confused with [[domain]] as in basis mapping.''
{{See also| Landscape microtemperaments #Domain }}


Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Chromatic pairs #Terrain|terrain]].
''Domain'' adds the [[landscape comma]], 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Chromatic pairs #Terrain|terrain]].


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 250047/250000, 645700815/645657712
[[Comma list]]: 250047/250000, 645700815/645657712
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[[Mapping]]: [{{val| 3 -3 -9 -8 }}, {{val| 0 17 35 36 }}]
[[Mapping]]: [{{val| 3 -3 -9 -8 }}, {{val| 0 17 35 36 }}]


[[POTE generator]]: ~10/9 = 182.467
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467


{{Val list|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}
{{Val list|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}
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