Quintile family: Difference between revisions
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== Septimal pental == | == Septimal pental == | ||
The pental temperament can be described as 5&60 temperament (also known as ''pentacloud''), tempering out the [[cloudy comma]], 16807/16384 and the [[245/243|sensamagic comma]], 245/243 in the 7-limit. | The pental temperament can be described as 5&60 temperament (also known as ''pentacloud''), tempering out the [[cloudy comma]], 16807/16384 and the [[245/243|sensamagic comma]], 245/243 in the 7-limit. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~3/2 = 701.377 | POTE generator: ~3/2 = 701.377 | ||
Optimal GPV sequence: {{Val list| 5, 60, 65 }} | |||
Badness: 0.093248 | Badness: 0.093248 | ||
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POTE generator: ~3/2 = 700.996 | POTE generator: ~3/2 = 700.996 | ||
Optimal GPV sequence: {{Val list| 5, 60, 65, 125de, 190ddef }} | |||
Badness: 0.067549 | Badness: 0.067549 | ||
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== Hemipental == | == Hemipental == | ||
The ''hemipental'' temperament (125&130) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 ([[Hewuermera temperaments|hewuermera]], satribiru-agu) and 5250987/5242880 ([[Mitonismic temperaments|mitonisma]], laquadzo-agu). | The ''hemipental'' temperament (125&130) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 ([[Hewuermera temperaments|hewuermera]], satribiru-agu) and 5250987/5242880 ([[Mitonismic temperaments|mitonisma]], laquadzo-agu). | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~8/7 = 230.634 | POTE generator: ~8/7 = 230.634 | ||
Optimal GPV sequence: {{Val list| 5e, 125, 130, 255, 385, 640, 1025b }} | |||
Badness: 0.047624 | Badness: 0.047624 | ||
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POTE generator: ~8/7 = 230.668 | POTE generator: ~8/7 = 230.668 | ||
Optimal GPV sequence: {{Val list| 5ef, 125, 130, 255, 385, 515, 900ef }} | |||
Badness: 0.041043 | Badness: 0.041043 | ||
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== Decal == | == Decal == | ||
The decal temperament (130&190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 (sesquiquartisma, laquadru-atriyo), and the [[15/14ths equal temperament|linus comma]], {{Monzo|11 -10 -10 10}}. | The decal temperament (130&190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 (sesquiquartisma, laquadru-atriyo), and the [[15/14ths equal temperament|linus comma]], {{Monzo|11 -10 -10 10}}. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~3/2 = 701.240 | POTE generator: ~3/2 = 701.240 | ||
Optimal GPV sequence: {{Val list| 60e, 130, 190, 320 }} | |||
Badness: 0.040633 | Badness: 0.040633 | ||
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POTE generator: ~3/2 = 701.252 | POTE generator: ~3/2 = 701.252 | ||
Optimal GPV sequence: {{Val list| 60e, 130, 190, 320 }} | |||
Badness: 0.023948 | Badness: 0.023948 | ||