Hemimage temperaments: Difference between revisions
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= Chromat = | = Chromat = | ||
The chromat temperament has a period of 1/3 octave and tempers out the hemimage (10976/10935) and the triwellisma (235298/234375). It is also described as [[Amity family|amity extension]] with third-octave period. | The chromat temperament has a period of 1/3 octave and tempers out the hemimage (10976/10935) and the triwellisma (235298/234375). It is also described as an [[Amity family|amity extension]] with third-octave period. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[POTE generator]]: ~28/27 = 60.528 | [[POTE generator]]: ~28/27 = 60.528 | ||
{{Val list|legend=1| 60, 99, 258, 357, 456 }} | {{Val list|legend=1| 39d, 60, 99, 258, 357, 456 }} | ||
[[Badness]]: 0.057499 | [[Badness]]: 0.057499 | ||
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POTE generator: ~3/2 = 703.231 | POTE generator: ~3/2 = 703.231 | ||
Vals: {{Val list| 80, 140, 360, 500be, 860bde }} | Vals: {{Val list| 60e, 80, 140, 360, 500be, 860bde }} | ||
Badness: 0.046770 | Badness: 0.046770 | ||
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[[POTE generator]]: ~192/175 = 162.8061 | [[POTE generator]]: ~192/175 = 162.8061 | ||
{{Val list|legend=1| 22, 74d, 96d, 118, 140, 258, 398 }} | {{Val list|legend=1| 22, 74d, 96d, 118, 140, 258, 398, 656d }} | ||
[[Badness]]: 0.065492 | [[Badness]]: 0.065492 | ||
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= Cotoneum = | = Cotoneum = | ||
{{Main|Cotoneum}} | {{Main| Cotoneum }} | ||
The ''cotoneum'' temperament (41&217, named by [[User:Xenllium|Xenllium]] after the Latin for "quince") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41]], [[176edo|176]], [[217edo|217]], and [[258edo|258]] EDOs, and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order. | The ''cotoneum'' temperament (41&217, named by [[User:Xenllium|Xenllium]] after the Latin for "quince") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41]], [[176edo|176]], [[217edo|217]], and [[258edo|258]] EDOs, and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order. | ||
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POTE generator: ~3/2 = 702.303 | POTE generator: ~3/2 = 702.303 | ||
Vals: {{Val list| 41, 176, 217 }} | Vals: {{Val list| 41, 135c, 176, 217 }} | ||
Badness: 0.050966 | Badness: 0.050966 | ||