Meantone family: Difference between revisions
→Dominant: maqamic > neutrominant, see the main article for details |
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Badness: 0.021565 | Badness: 0.021565 | ||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 45/44, 50/49, 78/77, 81/80, 85/84 | |||
Mapping: [{{val| 2 0 -8 -7 -12 -21 5 }}, {{val| 0 1 4 4 6 9 1 }}] | |||
POTE generator: ~3/2 = 692.487 | |||
Vals: {{Val list| 12f, 14cf, 26 }} | |||
Badness: 0.018358 | |||
===== 19-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 45/44, 50/49, 57/56, 78/77, 81/80, 85/84 | |||
Mapping: [{{val| 2 0 -8 -7 -12 -21 5 -1 }}, {{val| 0 1 4 4 6 9 1 3 }}] | |||
POTE generator: ~3/2 = 692.299 | |||
Vals: {{Val list| 12f, 14cf, 26 }} | |||
Badness: 0.015118 | |||
==== Enjera ==== | ==== Enjera ==== | ||
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Vals: {{Val list| 24d, 26, 50d }} | Vals: {{Val list| 24d, 26, 50d }} | ||
Badness: 0. | Badness: 0.070689 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
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Vals: {{Val list| 24d, 26, 50d }} | Vals: {{Val list| 24d, 26, 50d }} | ||
Badness: 0. | Badness: 0.040047 | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
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Vals: {{Val list| 24d, 26 }} | Vals: {{Val list| 24d, 26 }} | ||
Badness: 0. | Badness: 0.029499 | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
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Vals: {{Val list| 24d, 26 }} | Vals: {{Val list| 24d, 26 }} | ||
Badness: 0. | Badness: 0.023133 | ||
== Pombe == | == Pombe == | ||
Pombe (named after the African millet beer) is a variant of [[#Teff]] by Kaiveran Lugheidh that eschews the tempering of 50/49 to attain more accuracy in the 7-limit. Oddly, the 7th harmonic has a lesser generator distance than in teff (-5 vs +8), but this combined with the fact that other harmonics are in the opposite direction means that the 7-limit diamond is more complex overall. | Pombe (named after the African millet beer) is a variant of [[#Teff]] by Kaiveran Lugheidh that eschews the tempering of 50/49 to attain more accuracy in the 7-limit. Oddly, the 7th harmonic has a lesser generator distance than in teff (-5 vs +8), but this combined with the fact that other harmonics are in the opposite direction means that the 7-limit diamond is more complex overall. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
[[Comma list]]: 81/80, 300125/294912 | [[Comma list]]: 81/80, 300125/294912 | ||
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{{Val list|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }} | {{Val list|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.116104 | ||
=== 11-limit === | === 11-limit === | ||
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Vals: {{Val list| 24, 26, 50 }} | Vals: {{Val list| 24, 26, 50 }} | ||
Badness: 0. | Badness: 0.052099 | ||
=== 13-limit === | === 13-limit === | ||
| Line 1,332: | Line 1,358: | ||
Vals: {{Val list| 24, 26, 50 }} | Vals: {{Val list| 24, 26, 50 }} | ||
Badness: 0. | Badness: 0.031039 | ||
=== 17-limit === | === 17-limit === | ||
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Vals: {{Val list| 24, 26, 50 }} | Vals: {{Val list| 24, 26, 50 }} | ||
Badness: 0. | Badness: 0.021260 | ||
=== 19-limit === | === 19-limit === | ||
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Vals: {{Val list| 24, 26, 50 }} | Vals: {{Val list| 24, 26, 50 }} | ||
Badness: 0. | Badness: 0.016548 | ||
== Mohaha == | == Mohaha == | ||
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* 7- and 9-odd-limit [[diamond monotone]]: ~128/105 = [347.368, 350.000] (11\38 to 7\24) | * 7- and 9-odd-limit [[diamond monotone]]: ~128/105 = [347.368, 350.000] (11\38 to 7\24) | ||
* 7-odd-limit [[diamond tradeoff]]: ~128/105 = [347.393, 350.978] | * 7-odd-limit [[diamond tradeoff]]: ~128/105 = [347.393, 350.978] | ||
* 9-odd-limit | * 9-odd-limit diamond tradeoff: ~128/105 = [345.601, 350.978] | ||
* 7-odd-limit diamond monotone and tradeoff: ~128/105 = [347.393, 350.000] | * 7-odd-limit diamond monotone and tradeoff: ~128/105 = [347.393, 350.000] | ||
* 9-odd-limit diamond monotone and tradeoff: ~128/105 = [347.368, 350.000] | * 9-odd-limit diamond monotone and tradeoff: ~128/105 = [347.368, 350.000] | ||