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
[[POTE tuning|POTE generator]]: ~16/15 = 111.105


POTE generator: ~16/15 = 111.105
[[Map]]: [<5 1 22|, <0 2 -3|]


Map: [<5 1 22|, <0 2 -3|]
{{Vals|legend=1| 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}


EDOs: {{EDOs| 10, 55, 65, 75, 140, 205, 270, 335, 400, 530, 605, 875, 940, 1145, 1415 }}
[[Badness]]: 0.139191


Badness: 0.1392
== 7-limit ==
In the 7-limit, the qintosec temperament (10&75) tempers out the [[225/224|marvel comma]], 225/224.


=== 7-limit ===
[[Comma list]]: 225/224, 2560000/2470629


Commas: 225/224, 2560000/2470629
[[POTE tuning|POTE generator]]: ~16/15 = 111.553


POTE generator: ~16/15 = 111.553
[[Map]]: [<5 1 22 21|, <0 2 -3 -2|]


Map: [<5 1 22 21|, <0 2 -3 -2|]
{{Vals|legend=1| 10, 55d, 65d, 75, 140d, 215dd }}


EDOs: {{EDOs| 10, 55d, 65d, 75, 140d }}
[[Badness]]: 0.156764
 
Badness: 0.1568
 
== Decoid ==


= Decoid =
{{See also|Breedsmic temperaments #Decoid}}
{{See also|Breedsmic temperaments #Decoid}}


Commas: 2401/2400, 67108864/66976875
[[Comma list]]: 2401/2400, 67108864/66976875
 
POTE generator: ~16/15 = 111.099


Map: [<10 0 47 36|, <0 2 -3 -1|]
[[POTE tuning|POTE generator]]: ~16/15 = 111.099


EDOs: {{EDOs| 10, 130, 140, 270, 400, 410, 530, 550 }}
[[Map]]: [<10 0 47 36|, <0 2 -3 -1|]


Badness: 0.0339
{{Vals|legend=1| 10, 130, 140, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}


=== 11-limit ===
[[Badness]]: 0.033902


Commas: 2401/2400, 5632/5625, 9801/9800
== 11-limit ==
Comma list: 2401/2400, 5632/5625, 9801/9800


POTE generator: ~16/15 = 111.070
POTE generator: ~16/15 = 111.070
Line 47: Line 45:
Map: [<10 0 47 36 98|, <0 2 -3 -1 -8|]
Map: [<10 0 47 36 98|, <0 2 -3 -1 -8|]


EDOs: {{EDOs| 10e, 130, 140, 270, 400, 410, 530e }}
Vals: {{Vals| 10e, 130, 270, 670, 940, 1210, 2150c }}
 
Badness: 0.0187


=== 13-limit ===
Badness: 0.018735


Commas: 676/675, 1001/1000, 1716/1715, 4096/4095
== 13-limit ==
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095


POTE generator: ~16/15 = 111.083
POTE generator: ~16/15 = 111.083
Line 59: Line 56:
Map: [<10 0 47 36 98 37|, <0 2 -3 -1 -8 0|]
Map: [<10 0 47 36 98 37|, <0 2 -3 -1 -8 0|]


EDOs: {{EDOs| 10e, 130, 140, 270, 400, 410, 530e }}
Vals: {{Vals| 10e, 130, 270, 940, 1210f, 1480cf }}


Badness: 0.0135
Badness: 0.013475


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Qintosec]]
[[Category:Qintosec]]

Revision as of 07:29, 3 April 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 1 22|, <0 2 -3|]

Optimal ET sequence: 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc

Badness: 0.139191

7-limit

In the 7-limit, the qintosec temperament (10&75) tempers out the marvel comma, 225/224.

Comma list: 225/224, 2560000/2470629

POTE generator: ~16/15 = 111.553

Map: [<5 1 22 21|, <0 2 -3 -2|]

Optimal ET sequence: 10, 55d, 65d, 75, 140d, 215dd

Badness: 0.156764

Decoid

See also: Breedsmic temperaments § 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, 130, 140, 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

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