Breedsmic temperaments: Difference between revisions
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'''Breedsmic temperaments''' are rank two temperaments tempering out the [[breedsma]], |-5 -1 -2 4> = [[2401/2400]]. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma. | '''Breedsmic temperaments''' are rank two temperaments tempering out the [[breedsma]], |-5 -1 -2 4> = [[2401/2400]]. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma. | ||
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Badness: 0.0235 | Badness: 0.0235 | ||
==13-limit== | === 13-limit === | ||
Commas: 144/143, 196/195, 243/242, 364/363 | Commas: 144/143, 196/195, 243/242, 364/363 | ||
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Badness: 0.0191 | Badness: 0.0191 | ||
=Semihemi= | == Semihemi == | ||
Commas: 2401/2400, 3388/3375, 9801/9800 | Commas: 2401/2400, 3388/3375, 9801/9800 | ||
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Badness: 0.042487 | Badness: 0.042487 | ||
==13-limit== | === 13-limit === | ||
Commas: 352/351, 676/675, 847/845, 1716/1715 | Commas: 352/351, 676/675, 847/845, 1716/1715 | ||
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Badness: 0.0356 | Badness: 0.0356 | ||
==13-limit== | === 13-limit === | ||
Commas: 243/242, 441/440, 625/624, 3584/3575 | Commas: 243/242, 441/440, 625/624, 3584/3575 | ||
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Badness: 0.0369 | Badness: 0.0369 | ||
==17-limit== | === 17-limit === | ||
Commas: 243/242, 375/374, 441/440, 625/624, 3584/3575 | Commas: 243/242, 375/374, 441/440, 625/624, 3584/3575 | ||
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Badness: 0.0302 | Badness: 0.0302 | ||
=Hemitert= | == Hemitert == | ||
Commas: 2401/2400 3025/3024 65625/65536 | Commas: 2401/2400, 3025/3024, 65625/65536 | ||
POTE generator: ~45/44 = 38.596 | POTE generator: ~45/44 = 38.596 | ||
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{{main|Harry}} | {{main|Harry}} | ||
{{see also|Gravity family #Harry}} | {{see also|Gravity family #Harry}} | ||
Harry adds cataharry, 19683/19600, to the set of commas. It may be described as the 58&72 temperament, with wedgie <<12 34 20 26 -2 -49||. The period is half an octave, and the generator 21/20, with generator tunings of 9\130 or 14\202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices. | Harry adds cataharry, 19683/19600, to the set of commas. It may be described as the 58&72 temperament, with wedgie <<12 34 20 26 -2 -49||. The period is half an octave, and the generator 21/20, with generator tunings of 9\130 or 14\202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices. | ||
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Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with <<12 34 20 30 52 ...|| as the octave wedgie. [[130edo]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies. | Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with <<12 34 20 30 52 ...|| as the octave wedgie. [[130edo]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies. | ||
Commas: 2401/2400, 19683/19600 | |||
[[POTE_tuning|POTE generator]]: ~21/20 = 83.156 | [[POTE_tuning|POTE generator]]: ~21/20 = 83.156 | ||