Meantone family: Difference between revisions
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 5-odd-limit | * [[5-odd-limit]]: ~3/2 = {{Monzo| 0 0 1/4 }} | ||
: [[Eigenmonzo]]s: 2, 5 | : [[Eigenmonzo]]s: 2, 5 | ||
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[[Comma list]]: 81/80, 126/125 | [[Comma list]]: 81/80, 126/125 | ||
[[Mapping]]: [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}] | [[Mapping]]: [{{val| 1 0 -4 -13 }}, {{val| 0 1 4 10 }}] | ||
{{Multival|legend=1| 1 4 10 4 13 12 }} | {{Multival|legend=1| 1 4 10 4 13 12 }} | ||
| Line 68: | Line 68: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and 9-odd-limit: ~3/2 = {{ 0 0 1/4 }} | * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~3/2 = {{Monzo| 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 | ||
| Line 97: | Line 97: | ||
Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }} | * [[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 | : Eigenmonzos: 2, 11/9 | ||
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Minimax tuning: | Minimax tuning: | ||
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }} | * [[13-odd-limit|13-]] and [[15-odd-limit]]: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }} | ||
: Eigenmonzos: 2, 11/9 | : Eigenmonzos: 2, 11/9 | ||
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POTE generator: ~3/2 = 697.529 | POTE generator: ~3/2 = 697.529 | ||
Minimax tuning: | |||
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 14/25 -2/25 0 0 0 1/25 }} | |||
: Eigenmonzos: 2, 18/13 | |||
Vals: {{Val list| 12f, 31f, 43 }} | Vals: {{Val list| 12f, 31f, 43 }} | ||
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* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | ||
==== Tridecimal | ==== Tridecimal meanpop ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generator: ~3/2 = 696.202 | POTE generator: ~3/2 = 696.202 | ||
Minimax tuning: | |||
* 13- and 15-odd-limit: ~3/2 = {{Monzo| 11/13 0 0 0 -1/13 }} | |||
: Eigenmonzos: 2, 11 | |||
Vals: {{Val list| 12e, 19, 31f, 50ff, 81fff }} | Vals: {{Val list| 12e, 19, 31f, 50ff, 81fff }} | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] | * [[7-odd-limit]]: ~3/2 = {{Monzo| 8/13 0 1/13 -1/13 }} | ||
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 21/13 0 1/13 -1/13 }}, {{Monzo| 32/13 0 4/13 -4/13 }}, {{Monzo| 32/13 0 -9/13 9/13 }}] | : [{{Monzo| 1 0 0 0 }}, {{Monzo| 21/13 0 1/13 -1/13 }}, {{Monzo| 32/13 0 4/13 -4/13 }}, {{Monzo| 32/13 0 -9/13 9/13 }}] | ||
: [[Eigenmonzo]]s: 2, 7/5 | : [[Eigenmonzo]]s: 2, 7/5 | ||
* [[9-odd-limit]] | * [[9-odd-limit]]: ~3/2 = {{Monzo| 6/11 2/11 0 -1/11 }} | ||
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 17/11 2/11 0 -1/11 }}, {{Monzo| 24/11 8/11 0 -4/11 }}, {{Monzo| 34/11 -18/11 0 9/11 }}] | : [{{Monzo| 1 0 0 0 }}, {{Monzo| 17/11 2/11 0 -1/11 }}, {{Monzo| 24/11 8/11 0 -4/11 }}, {{Monzo| 34/11 -18/11 0 9/11 }}] | ||
: Eigenmonzos: 2, 9/7 | : Eigenmonzos: 2, 9/7 | ||
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Comma list: 81/80, 121/120, 176/175 | Comma list: 81/80, 121/120, 176/175 | ||
Mapping: [{{val|1 1 0 6 2}}, {{val|0 2 8 -11 5}}] | Mapping: [{{val| 1 1 0 6 2 }}, {{val| 0 2 8 -11 5 }}] | ||
Mapping generators: ~2, ~11/9 | Mapping generators: ~2, ~11/9 | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]]: 1/ | * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{Monzo| 0 0 1/12 }} | ||
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3 0 -1/12 0 }}] | : [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3 0 -1/12 0 }}] | ||
: [[Eigenmonzo]]s: 2, 5 | : [[Eigenmonzo]]s: 2, 5 | ||
| Line 1,596: | Line 1,604: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and 9-odd-limit: 1/ | * 7- and 9-odd-limit: ~9/7 = {{Monzo| 1/2 0 -1/16 }} | ||
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3/2 0 9/16 0 }}] | : [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3/2 0 9/16 0 }}] | ||
: [[Eigenmonzo]]s: 2, 5 | : [[Eigenmonzo]]s: 2, 5 | ||
| Line 1,731: | Line 1,739: | ||
Minimax tuning: | Minimax tuning: | ||
* 7- and 9-odd-limit: 1/ | * 7- and 9-odd-limit: ~10/7 = {{Monzo| 1/3 0 1/12 }} | ||
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 2/3 0 11/12 0 }}] | : [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 2/3 0 11/12 0 }}] | ||
: [[Eigenmonzo]]s: 2, 5 | : [[Eigenmonzo]]s: 2, 5 | ||