Quintile family: Difference between revisions
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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 | |||
[[Comma]]: 847288609443/838860800000 | [[Comma]]: 847288609443/838860800000 | ||
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[[Badness]]: 0.240050 | [[Badness]]: 0.240050 | ||
=== 7-limit | === 7-limit === | ||
The pental temperament can be described as 5&60 temperament (''pentacloud'' | 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 | |||
[[Comma list]]: 245/243, 16807/16384 | [[Comma list]]: 245/243, 16807/16384 | ||
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[[Badness]]: 0.120942 | [[Badness]]: 0.120942 | ||
=== 11-limit | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 245/243, 385/384, 3087/3025 | Comma list: 245/243, 385/384, 3087/3025 | ||
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Badness: 0.093248 | Badness: 0.093248 | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 105/104, 144/143, 245/243, 3087/3025 | Comma list: 105/104, 144/143, 245/243, 3087/3025 | ||
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Badness: 0.067549 | Badness: 0.067549 | ||
== Hemipental | == Hemipental == | ||
The ''hemipental'' temperament (125&130 | 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 (laquadzo-agu). | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 19683/19600, 589824/588245 | [[Comma list]]: 19683/19600, 589824/588245 | ||
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[[Badness]]: 0.104163 | [[Badness]]: 0.104163 | ||
=== 11-limit | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 540/539, 8019/8000, 180224/180075 | Comma list: 540/539, 8019/8000, 180224/180075 | ||
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Badness: 0.047624 | Badness: 0.047624 | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000 | Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000 | ||
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Badness: 0.041043 | Badness: 0.041043 | ||
== 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 | |||
[[Comma list]]: 235298/234375, 321489/320000 | [[Comma list]]: 235298/234375, 321489/320000 | ||
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[[Badness]]: 0.104859 | [[Badness]]: 0.104859 | ||
=== 11-limit | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 8019/8000, 234375/234256 | Comma list: 441/440, 8019/8000, 234375/234256 | ||
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Badness: 0.040633 | Badness: 0.040633 | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 441/440, 729/728, 1001/1000, 4225/4224 | Comma list: 441/440, 729/728, 1001/1000, 4225/4224 | ||
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[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Pental]] | |||