Meantone family: Difference between revisions
m Remove originator of temperaments |
mNo edit summary |
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[[POTE generator]]: ~3/2 = 696.239 | [[POTE generator]]: ~3/2 = 696.239 | ||
[[Minimax tuning]]: | |||
* 5-odd-limit minimax: ~3/2 = {{ 0 0 1/4 }} | |||
: [[Eigenmonzo]]s: 2, 5 | |||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* [[ | * [[Diamond monotone]] range: [685.714, 720.000] (4\7 to 3\5) | ||
* [[ | * [[Diamond tradeoff]] range: [694.786, 701.955] (1/3 comma to Pythagorean) | ||
* | * Diamond monotone and tradeoff: [694.786, 701.955] | ||
{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }} | {{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }} | ||
| Line 64: | Line 68: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and | * 7- and 9-odd-limit: ~3/2 = {{ 0 0 1/4 }} | ||
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}] | : [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}] | ||
: [[Eigenmonzo]]s: 2, 5 | : [[Eigenmonzo]]s: 2, 5 | ||
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Minimax tuning: | Minimax tuning: | ||
* | * 11-odd-limit: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }} | ||
: [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 25/16 -1/8 0 0 1/16 }}, {{Monzo| 9/4 -1/2 0 0 1/4 }}, {{Monzo| 21/8 -5/4 0 0 5/8 }}, {{Monzo| 25/8 -9/4 0 0 9/8 }}] | : [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 25/16 -1/8 0 0 1/16 }}, {{Monzo| 9/4 -1/2 0 0 1/4 }}, {{Monzo| 21/8 -5/4 0 0 5/8 }}, {{Monzo| 25/8 -9/4 0 0 9/8 }}] | ||
: | : Eigenmonzos: 2, 11/9 | ||
Tuning ranges: | Tuning ranges: | ||
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POTE generator: ~3/2 = 696.642 | POTE generator: ~3/2 = 696.642 | ||
Minimax tuning: | |||
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }} | |||
: Eigenmonzos: 2, 11/9 | |||
Vals: {{Val list| 12f, 19e, 31 }} | Vals: {{Val list| 12f, 19e, 31 }} | ||
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POTE generator: ~3/2 = 697.264 | POTE generator: ~3/2 = 697.264 | ||
Minimax tuning: | |||
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 8/13 0 0 1/26 0 -1/26 }} | |||
: Eigenmonzos: 2, 14/13 | |||
Tuning ranges: | |||
* Diamond monotone range: [696.774, 697.674] (18\31 to 25\43) | |||
* Diamond tradeoff range: [691.202, 701.955] | |||
* Diamond monotone and tradeoff: [696.774, 697.674] | |||
Vals: {{Val list| 12, 19ef, 31, 43, 74 }} | Vals: {{Val list| 12, 19ef, 31, 43, 74 }} | ||
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Minimax tuning: | Minimax tuning: | ||
* | * 11-odd-limit: ~3/2 = {{Monzo| 0 0 1/4 }} | ||
: [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 1 0 1/4 0 0 }}, {{Monzo| 0 0 1 0 0 }}, {{Monzo| -3 0 5/2 0 0 }}, {{Monzo| 11 0 -13/4 0 0 }}] | : [{{Monzo| 1 0 0 0 0 }}, {{Monzo| 1 0 1/4 0 0 }}, {{Monzo| 0 0 1 0 0 }}, {{Monzo| -3 0 5/2 0 0 }}, {{Monzo| 11 0 -13/4 0 0 }}] | ||
: | : Eigenmonzos: 2, 5 | ||
Tuning ranges: | Tuning ranges: | ||
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POTE generator: ~3/2 = 696.211 | POTE generator: ~3/2 = 696.211 | ||
Minimax tuning: | |||
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 4/7 0 0 0 -1/28 1/28 }} | |||
: Eigenmonzos: 2, 13/11 | |||
Tuning ranges: | Tuning ranges: | ||
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POTE generator: ~3/2 = 696.250 | POTE generator: ~3/2 = 696.250 | ||
Tuning ranges: | |||
* Diamond monotone range: [694.737, 700.000] (11\19 to 7\12) | |||
* Diamond tradeoff range: [682.502, 704.377] | |||
* Diamond monotone and tradeoff: [694.737, 700.000] | |||
Vals: {{Val list| 7d, 12, 19, 31e, 50ee }} | Vals: {{Val list| 7d, 12, 19, 31e, 50ee }} | ||