Meantone family: Difference between revisions
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Tags: Mobile edit Mobile web edit |
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<span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span> | ||
[[ | [[Comma]]s: 81/80, 686/675 | ||
Liese, with wedgie <<3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[ | Liese, with wedgie <<3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo]] makes for a good liese tuning, though [[19edo]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55. | ||
7 and 9 limit minimax 1/4 comma | 7 and 9 limit minimax 1/4 comma | ||
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[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |2/3 0 11/12 0>] | [|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |2/3 0 11/12 0>] | ||
[[ | [[Eigenmonzo]]s: 2, 5 | ||
[[POTE_tuning|POTE generator]]: ~10/7 = 632.406 | [[POTE_tuning|POTE generator]]: ~10/7 = 632.406 | ||
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Map: [<1 0 -4 -3|, <0 3 12 11|] | Map: [<1 0 -4 -3|, <0 3 12 11|] | ||
[[ | [[Generator]]s: 2, 10/7 | ||
EDOs: [[17edo| | EDOs: [[17edo|17c]], [[19edo|19]], [[36edo|36]], [[55edo|55]], [[74edo|74d]] | ||
[[ | [[Badness]]: 0.0467 | ||
==Liesel== | ==Liesel== | ||
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Map: [<1 0 -4 -3 4|, <0 3 12 11 -1|] | Map: [<1 0 -4 -3 4|, <0 3 12 11 -1|] | ||
EDOs: 17c, 19, 36, | EDOs: 17c, 19, 36, 55e, 91cee | ||
Badness: 0.0407 | Badness: 0.0407 | ||
==13-limit== | ===13-limit=== | ||
Liesel is a very natural 13-limit tuning, given the generator is so near 13/9. | Liesel is a very natural 13-limit tuning, given the generator is so near 13/9. | ||
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Map: [<1 0 -4 -3 4 0|, <0 3 12 11 -1 7|] | Map: [<1 0 -4 -3 4 0|, <0 3 12 11 -1 7|] | ||
EDOs: 17c, 19, 36, | EDOs: 17c, 19, 36, 55ef, 91ceef | ||
Badness: 0.0273 | Badness: 0.0273 | ||
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Map: [<1 0 -4 -3 -5|, <0 3 12 11 16|] | Map: [<1 0 -4 -3 -5|, <0 3 12 11 16|] | ||
EDOs: 19e, 36e | EDOs: 17c, 19e, 36e | ||
Badness: 0.0416 | Badness: 0.0416 | ||
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Badness: 0.0548 | Badness: 0.0548 | ||
==13-limit== | ===13-limit=== | ||
Commas: 45/44, 81/80, 91/88, 147/143 | Commas: 45/44, 81/80, 91/88, 147/143 | ||
POTE generator: ~10/7 = 631.221 | POTE generator: ~10/7 = 631.221 | ||
Map: [<1 0 -4 -3 -6 0|, <0 3 12 11 18 7|] | Map: [<1 0 -4 -3 -6 0|, <0 3 12 11 18 7|] | ||