Quintosec family: Difference between revisions
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The '''qintosec family''' tempers out the qintosec comma, 140737488355328/140126044921875 = |47 -15 -10>. | The '''qintosec family''' tempers out the qintosec comma, 140737488355328/140126044921875 = |47 -15 -10>. | ||
= Qintosec = | == Qintosec == | ||
[[Comma]]: 140737488355328/140126044921875 | [[Comma]]: 140737488355328/140126044921875 | ||
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[[Badness]]: 0.139191 | [[Badness]]: 0.139191 | ||
== 7-limit == | === 7-limit === | ||
The qintosec temperament can be described as 10&65d temperament, tempering out the [[225/224|marvel comma]], 225/224 in the 7-limit. | The qintosec temperament can be described as 10&65d temperament, tempering out the [[225/224|marvel comma]], 225/224 in the 7-limit. | ||
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[[Badness]]: 0.156764 | [[Badness]]: 0.156764 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 225/224, 243/242, 3840/3773 | Comma list: 225/224, 243/242, 3840/3773 | ||
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Badness: 0.077907 | Badness: 0.077907 | ||
== Qinto == | === Qinto === | ||
Comma list: 225/224, 385/384, 332750/321489 | Comma list: 225/224, 385/384, 332750/321489 | ||
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Badness: 0.127732 | Badness: 0.127732 | ||
= Sengasec = | == Sengasec == | ||
The ''sengasec'' temperament (10&55, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit. | The ''sengasec'' temperament (10&55, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit. | ||
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[[Badness]]: 0.156259 | [[Badness]]: 0.156259 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 243/242, 385/384, 686/675 | Comma list: 243/242, 385/384, 686/675 | ||
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Badness: 0.081607 | Badness: 0.081607 | ||
== 13-limit == | === 13-limit === | ||
Comma list: 105/104, 144/143, 243/242, 686/675 | Comma list: 105/104, 144/143, 243/242, 686/675 | ||
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Badness: 0.056390 | Badness: 0.056390 | ||
= Decoid = | == Decoid == | ||
{{See also|Breedsmic temperaments #Decoid}} | {{See also|Breedsmic temperaments #Decoid}} | ||
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[[Badness]]: 0.033902 | [[Badness]]: 0.033902 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 2401/2400, 5632/5625, 9801/9800 | Comma list: 2401/2400, 5632/5625, 9801/9800 | ||
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Badness: 0.018735 | Badness: 0.018735 | ||
== 13-limit == | === 13-limit === | ||
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095 | Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095 | ||
Revision as of 21:39, 1 June 2021
The qintosec family tempers out the qintosec comma, 140737488355328/140126044921875 = |47 -15 -10>.
Qintosec
Comma: 140737488355328/140126044921875
POTE generator: ~16/15 = 111.105
Map: [<5 7 13|, <0 2 -3|]
Optimal ET sequence: 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc
Badness: 0.139191
7-limit
The qintosec temperament can be described as 10&65d temperament, tempering out the marvel comma, 225/224 in the 7-limit.
Comma list: 225/224, 2560000/2470629
POTE generator: ~15/14 = 111.553
Map: [<5 7 13 15|, <0 2 -3 -2|]
Optimal ET sequence: 10, 55d, 65d, 75, 140d, 215dd
Badness: 0.156764
11-limit
Comma list: 225/224, 243/242, 3840/3773
POTE generator: ~15/14 = 111.311
Map: [<5 7 13 15 15|, <0 2 -3 -2 5|]
Vals: 10, 55d, 65d, 140de, 205dde
Badness: 0.077907
Qinto
Comma list: 225/224, 385/384, 332750/321489
POTE generator: ~15/14 = 112.448
Map: [<5 7 13 15 14|, <0 2 -3 -2 7|]
Badness: 0.127732
Sengasec
The sengasec temperament (10&55, named by Xenllium) tempers out the cloudy comma, 16807/16384 and the sengic comma, 686/675 in the 7-limit.
Comma list: 686/675, 16807/16384
POTE generator: ~16/15 = 111.113
Map: [<5 7 13 14|, <0 2 -3 0|]
Optimal ET sequence: 10, 55, 65, 140dd, 205ddd, 270ddd
Badness: 0.156259
11-limit
Comma list: 243/242, 385/384, 686/675
POTE generator: ~16/15 = 110.659
Map: [<5 7 13 14 15|, <0 2 -3 0 5|]
Badness: 0.081607
13-limit
Comma list: 105/104, 144/143, 243/242, 686/675
POTE generator: ~16/15 = 110.910
Map: [<5 7 13 14 15 19|, <0 2 -3 0 5 -1|]
Badness: 0.056390
Decoid
Comma list: 2401/2400, 67108864/66976875
POTE generator: ~16/15 = 111.099
Map: [<10 0 47 36|, <0 2 -3 -1|]
Optimal ET sequence: 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc
Badness: 0.033902
11-limit
Comma list: 2401/2400, 5632/5625, 9801/9800
POTE generator: ~16/15 = 111.070
Map: [<10 0 47 36 98|, <0 2 -3 -1 -8|]
Vals: 10e, 130, 270, 670, 940, 1210, 2150c
Badness: 0.018735
13-limit
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
POTE generator: ~16/15 = 111.083
Map: [<10 0 47 36 98 37|, <0 2 -3 -1 -8 0|]
Vals: 10e, 130, 270, 940, 1210f, 1480cf
Badness: 0.013475