Porwell family: Difference between revisions
Cmloegcmluin (talk | contribs) adding parenthetical "(unchanged intervals)" to eigenmonzo lists |
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The '''porwell family''' of rank-3 temperaments tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} = [[6144/6125]]. | |||
The '''porwell family''' of rank | |||
== Hewuermity == | == Hewuermity == | ||
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Mapping generators: ~2, ~3, ~35/32 | Mapping generators: ~2, ~3, ~35/32 | ||
[[POTE generator]]s: ~3/2 = 702.3482, ~35/32 = 157.4677 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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[[Mapping]]: [{{val| 1 0 1 4 2 }}, {{val| 0 1 1 -1 1 }}, {{val| 0 0 -2 3 1 }}] | [[Mapping]]: [{{val| 1 0 1 4 2 }}, {{val| 0 1 1 -1 1 }}, {{val| 0 0 -2 3 1 }}] | ||
Mapping generators: 2, 3, 11/10 | Mapping generators: ~2, ~3, ~11/10 | ||
Map to lattice: [{{val| 0 1 -1 2 0 }}, {{val| 0 1 1 -1 1 }}] | Map to lattice: [{{val| 0 1 -1 2 0 }}, {{val| 0 1 1 -1 1 }}] | ||
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: 11/10, 11/8 | : 11/10, 11/8 | ||
: Angle (11/10, 11/8) = 87.464 degrees | : Angle (11/10, 11/8) = 87.464 degrees | ||
[[POTE generator]]s: ~3/2 = 702.1530, ~11/10 = 157.0881 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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Mapping: [{{val| 1 0 1 4 2 7 }}, {{val| 0 1 1 -1 1 -2 }}, {{val| 0 0 -2 3 -1 -1 }}] | Mapping: [{{val| 1 0 1 4 2 7 }}, {{val| 0 1 1 -1 1 -2 }}, {{val| 0 0 -2 3 -1 -1 }}] | ||
Map to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}] | Map to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}] | ||
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: 11/10 length = 0.7898, 11/8 length = 1.002 | : 11/10 length = 0.7898, 11/8 length = 1.002 | ||
: Angle (11/10, 11/8) = 106.7439 degrees | : Angle (11/10, 11/8) = 106.7439 degrees | ||
POTE generators: ~3/2 = 701.8679, ~11/10 = 156.9582 | |||
Minimax tuning: | Minimax tuning: | ||
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Mapping: [{{val| 1 0 1 4 2 2 }}, {{val| 0 1 1 -1 1 1 }}, {{val| 0 0 -2 3 -1 -1 }}] | Mapping: [{{val| 1 0 1 4 2 2 }}, {{val| 0 1 1 -1 1 1 }}, {{val| 0 0 -2 3 -1 -1 }}] | ||
POTE generators: ~3/2 = 699.3420, ~11/10 = 155.3666 | |||
Vals: {{Val list| 7, 9, 15, 22f, 24, 31 }} | Vals: {{Val list| 7, 9, 15, 22f, 24, 31 }} | ||
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Badness: 0.808 × 10<sup>-3</sup> | Badness: 0.808 × 10<sup>-3</sup> | ||
== Jupiter | == Jupiter == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 540/539, 5632/5625 | [[Comma list]]: 540/539, 5632/5625 | ||
[[Mapping]]: [{{val| 1 0 1 4 -5 }}, {{val| 0 1 1 -1 6 }}, {{val| 0 0 2 - | [[Mapping]]: [{{val| 1 0 1 4 -5 }}, {{val| 0 1 1 -1 6 }}, {{val| 0 0 -2 3 -8 }}] | ||
Mapping generators: ~2, ~3, ~35/32 | |||
{{Val list|legend=1| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }} | {{Val list|legend=1| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }} | ||
[[Badness]]: 0.562 × 10<sup>-3</sup> | [[Badness]]: 0.562 × 10<sup>-3</sup> | ||
== Semiporwell == | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 6144/6125, 9801/9800 | |||
[[Mapping]]: [{{val| 2 0 0 11 14 }}, {{val| 0 1 1 -1 -2 }}, {{val| 0 0 2 -3 -1 }}] | |||
Mapping generators: ~99/70, ~3/2, ~128/99 | |||
[[POTE generator]]s: ~3/2 = 702.4613, ~128/99 = 442.4903 | |||
{{Val list|legend=1| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }} | |||
[[Badness]]: 1.253 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1716/1715, 2080/2079, 3584/3575 | |||
Mapping: [{{val| 2 0 0 11 14 15 }}, {{val| 0 1 1 -1 -2 -1 }}, {{val| 0 0 2 -3 -1 -6 }}] | |||
POTE generators: ~3/2 = 702.3964, ~128/99 = 442.5902 | |||
Vals: {{Val list| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }} | |||
Badness: 1.220 × 10<sup>-3</sup> | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||