Meantone family: Difference between revisions

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Xenllium (talk | contribs)
Fixed typo
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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 5-odd-limit minimax: ~3/2 = {{ 0 0 1/4 }}
* [[5-odd-limit]]: ~3/2 = {{Monzo| 0 0 1/4 }}
: [[Eigenmonzo]]s: 2, 5
: [[Eigenmonzo]]s: 2, 5


Line 61: Line 61:
[[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 }}
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[[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
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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 Meanpop ====
==== 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 }}
Line 543: Line 551:


[[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
Line 1,293: Line 1,301:
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
Line 1,479: Line 1,487:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: 1/4 comma
* [[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: 1/4 comma
* 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: 1/4 comma
* 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