Breedsmic temperaments: Difference between revisions
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== Neominor == | == Neominor == | ||
The generator for neominor temperament is tridecimal minor third [[13/11]], also known as ''Neo-gothic minor third''. | The generator for neominor temperament is tridecimal minor third [[13/11]], also known as ''Neo-gothic minor third''. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Emmthird == | == Emmthird == | ||
The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935. | The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.016736 | [[Badness]]: 0.016736 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 243/242, 441/440, 1792000/1771561 | |||
Mapping: [{{val|1 -3 -17 -8 -8}}, {{val|0 14 59 33 35}}] | |||
POTE generator: ~1372/1089 = 392.991 | |||
Vals: {{Val list| 58, 113, 171 }} | |||
Badness: 0.052358 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 243/242, 364/363, 441/440, 2200/2197 | |||
Mapping: [{{val|1 -3 -17 -8 -8 -13}}, {{val|0 14 59 33 35 51}}] | |||
POTE generator: ~180/143 = 392.989 | |||
Vals: {{Val list| 58, 113, 171 }} | |||
Badness: 0.026974 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 243/242, 364/363, 441/440, 595/594, 2200/2197 | |||
Mapping: [{{val|1 -3 -17 -8 -8 -13 9}}, {{val|0 14 59 33 35 51 -15}}] | |||
POTE generator: ~64/51 = 392.985 | |||
Vals: {{Val list| 58, 113, 171 }} | |||
Badness: 0.023205 | |||
== Quinmite == | == Quinmite == | ||
The generator for quinmite is quasi-tempered minor third 25/21, flatter than 6/5 by the starling comma, 126/125. It is also generated by 1/5 of minor tenth 12/5, and its name is a play on the words "quintans" (Latin for "one fifth") and "minor tenth". | The generator for quinmite is quasi-tempered minor third 25/21, flatter than 6/5 by the starling comma, 126/125. It is also generated by 1/5 of minor tenth 12/5, and its name is a play on the words "quintans" (Latin for "one fifth") and "minor tenth". | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Unthirds == | == Unthirds == | ||
The generator for unthirds temperament is undecimal major third, 14/11. | The generator for unthirds temperament is undecimal major third, 14/11. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Newt == | == Newt == | ||
This temperament has a generator of neutral third (0.2 cents flat of [[49/40]]) and tempers out the [[garischisma]]. | This temperament has a generator of neutral third (0.2 cents flat of [[49/40]]) and tempers out the [[garischisma]]. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||