Quintile family: Difference between revisions
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Cleanup, temperament maps reviewed, +mapping generators |
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The pental family tempers out the pental comma, 847288609443/838860800000 = {{Monzo|-28 25 -5}}. | The '''pental family''' tempers out the pental comma, 847288609443/838860800000 = {{Monzo|-28 25 -5}}. | ||
== Pental == | == Pental == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
[[Comma]]: 847288609443/838860800000 | [[Comma list]]: 847288609443/838860800000 | ||
[[Mapping]]: [{{val|5 0 -28}}, {{val|0 1 5}}] | [[Mapping]]: [{{val| 5 0 -28 }}, {{val| 0 1 5 }}] | ||
Mapping generators: ~59049/51200, ~3 | |||
[[POTE generator]]: ~3/2 = 701.210 | [[POTE generator]]: ~3/2 = 701.210 | ||
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[[Badness]]: 0.240050 | [[Badness]]: 0.240050 | ||
== | == 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. | ||
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[[Comma list]]: 19683/19600, 589824/588245 | [[Comma list]]: 19683/19600, 589824/588245 | ||
[[Mapping]]: [{{val|5 | [[Mapping]]: [{{val| 5 0 -28 18 }}, {{val| 0 2 10 -1 }}] | ||
Mapping generators: ~147/128, ~140/81 | |||
[[POTE generator]]: ~8/7 = 230.654 | [[POTE generator]]: ~8/7 = 230.654 | ||
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Comma list: 540/539, 8019/8000, 180224/180075 | Comma list: 540/539, 8019/8000, 180224/180075 | ||
Mapping: [{{val|5 | Mapping: [{{val| 5 0 -28 18 -54 }}, {{val| 0 2 10 -1 18 }}] | ||
POTE generator: ~8/7 = 230.634 | POTE generator: ~8/7 = 230.634 | ||
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Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000 | Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000 | ||
Mapping: [{{val|5 | Mapping: [{{val| 5 0 -28 18 -54 34 }}, {{val| 0 2 10 -1 18 -13 }}] | ||
POTE generator: ~8/7 = 230.668 | POTE generator: ~8/7 = 230.668 | ||
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[[Comma list]]: 235298/234375, 321489/320000 | [[Comma list]]: 235298/234375, 321489/320000 | ||
[[Mapping]]: [{{val|10 0 -56 -67}}, {{val|0 1 5 6}}] | [[Mapping]]: [{{val| 10 0 -56 -67 }}, {{val| 0 1 5 6 }}] | ||
Mapping generators: ~15/14, ~3 | |||
[[POTE generator]]: ~3/2 = 701.303 | [[POTE generator]]: ~3/2 = 701.303 | ||
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Comma list: 441/440, 8019/8000, 234375/234256 | Comma list: 441/440, 8019/8000, 234375/234256 | ||
Mapping: [{{val|10 0 -56 -67 -108}}, {{val|0 1 5 6 9}}] | Mapping: [{{val| 10 0 -56 -67 -108 }}, {{val| 0 1 5 6 9 }}] | ||
POTE generator: ~3/2 = 701.240 | POTE generator: ~3/2 = 701.240 | ||
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Comma list: 441/440, 729/728, 1001/1000, 4225/4224 | Comma list: 441/440, 729/728, 1001/1000, 4225/4224 | ||
Mapping: [{{val|10 0 -56 -67 -108 37}}, {{val|0 1 5 6 9 0}}] | Mapping: [{{val| 10 0 -56 -67 -108 37 }}, {{val| 0 1 5 6 9 0 }}] | ||
POTE generator: ~3/2 = 701.252 | POTE generator: ~3/2 = 701.252 | ||
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Badness: 0.023948 | Badness: 0.023948 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Pental]] | [[Category:Pental family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | |||