Gamelismic family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
"Gamelan" -> "gamelismic" (cuz "gamelan" needs to go) |
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The '''gamelismic family''' of temperaments are rank-3 temperaments tempering out [[1029/1024]]. | The '''gamelismic family''' of temperaments are rank-3 temperaments tempering out [[1029/1024]]. | ||
== | == Gamelismic == | ||
{{Main| Portent }} | {{Main| Portent }} | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 1029/1024 | [[Comma list]]: 1029/1024 | ||
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: Angle (8/7, 5/4) = 90 degrees | : Angle (8/7, 5/4) = 90 degrees | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 233.6875, ~5/4 = 385.1853 | ||
[[Minimax tuning]]: c = 1029/1024 | [[Minimax tuning]]: c = 1029/1024 | ||
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Portent has a [[Normal lists #normal interval list|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440. | Portent has a [[Normal lists #normal interval list|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440. | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 385/384, 441/440 | [[Comma list]]: 385/384, 441/440 | ||
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: Angle (8/7, 12/11) = 86.657 degrees | : Angle (8/7, 12/11) = 86.657 degrees | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 233.6884, ~5/4 = 385.1618 | ||
[[Minimax tuning]]: c = 1029/1024, e = 385/384 | [[Minimax tuning]]: c = 1029/1024, e = 385/384 | ||
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Mapping: [{{val| 1 1 0 3 5 6 }}, {{val| 0 3 0 -1 4 12 }}, {{val| 0 0 1 0 -1 -2 }}] | Mapping: [{{val| 1 1 0 3 5 6 }}, {{val| 0 3 0 -1 4 12 }}, {{val| 0 0 1 0 -1 -2 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.9128, ~5/4 = 384.7278 | ||
{{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 159, 477cdf }} | {{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 159, 477cdf }} | ||
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Mapping: [{{val| 1 1 0 3 5 -5 }}, {{val| 0 3 0 -1 4 -3 }}, {{val| 0 0 1 0 -1 4 }}] | Mapping: [{{val| 1 1 0 3 5 -5 }}, {{val| 0 3 0 -1 4 -3 }}, {{val| 0 0 1 0 -1 4 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6843, ~5/4 = 384.9830 | ||
{{Optimal ET sequence|legend=1| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }} | {{Optimal ET sequence|legend=1| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }} | ||
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Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 -10 }}, {{val| 0 0 1 0 -1 2 }}] | Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 -10 }}, {{val| 0 0 1 0 -1 2 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4088, ~5/4 = 385.3825 | ||
{{Optimal ET sequence|legend=1| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }} | {{Optimal ET sequence|legend=1| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }} | ||
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: Angle (8/7, 6/5) = 98.6015 | : Angle (8/7, 6/5) = 98.6015 | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4313, ~5/4 = 385.2890 | ||
Minimax tuning: | Minimax tuning: | ||
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Mapping: [{{val| 1 1 0 3 5 7 }}, {{val| 0 3 0 -4 1 -5 }}, {{val| 0 0 1 0 -1 -1 }}] | Mapping: [{{val| 1 1 0 3 5 7 }}, {{val| 0 3 0 -4 1 -5 }}, {{val| 0 0 1 0 -1 -1 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4088, ~5/4 = 385.3825 | ||
{{Optimal ET sequence|legend=1| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }} | {{Optimal ET sequence|legend=1| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }} | ||
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Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 2 }}, {{val| 0 0 1 0 -1 1 }}] | Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 2 }}, {{val| 0 0 1 0 -1 1 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.3664, ~5/4 = 382.3425 | ||
{{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72f, 185cf }} | {{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72f, 185cf }} | ||
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Mapping: [{{val| 1 1 2 3 3 4 }}, {{val| 0 3 0 -1 4 -1 }}, {{val| 0 0 3 0 -3 -1 }}] | Mapping: [{{val| 1 1 2 3 3 4 }}, {{val| 0 3 0 -1 4 -1 }}, {{val| 0 0 3 0 -3 -1 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6434, ~14/13 = 128.3440 | ||
{{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }} | {{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }} | ||
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Mapping: [{{val| 1 1 2 3 3 4 4 }}, {{val| 0 3 0 -1 4 -1 1 }}, {{val| 0 0 3 0 -3 -1 -1 }}] | Mapping: [{{val| 1 1 2 3 3 4 4 }}, {{val| 0 3 0 -1 4 -1 1 }}, {{val| 0 0 3 0 -3 -1 -1 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6803, ~14/13 = 128.4149 | ||
{{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }} | {{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }} | ||
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== Gamel == | == Gamel == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 540/539, 1029/1024 | [[Comma list]]: 540/539, 1029/1024 | ||
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[[Mapping]]: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 0 -1 11 }}, {{val| 0 0 1 0 1 }}] | [[Mapping]]: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 0 -1 11 }}, {{val| 0 0 1 0 1 }}] | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 233.2909, ~5/4 = 384.2120 | ||
{{Optimal ET sequence|legend=1| 10, 31, 41, 72 }} | {{Optimal ET sequence|legend=1| 10, 31, 41, 72 }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Gamelismic family| ]] <!-- main article --> | [[Category:Gamelismic family| ]] <!-- main article --> | ||
[[Category:Gamelismic| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||