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 = {{monzo|47 -15 -10}}.
 
== Qintosec ==
Subgroup: 2.3.5


== Qintosec  ==
[[Comma]]: 140737488355328/140126044921875
[[Comma]]: 140737488355328/140126044921875


[[POTE tuning|POTE generator]]: ~16/15 = 111.105
[[Mapping]]: [{{val|5 7 13}}, {{val|0 2 -3}}]


[[Map]]: [<5 7 13|, <0 2 -3|]
[[POTE generator]]: ~16/15 = 111.105


{{Vals|legend=1| 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}
{{Val list|legend=1| 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}


[[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.
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 2560000/2470629
[[Comma list]]: 225/224, 2560000/2470629


[[POTE tuning|POTE generator]]: ~15/14 = 111.553
[[Mapping]]: [{{val|5 7 13 15}}, {{val|0 2 -3 -2}}]
 
{{Multival|legend=1|10 -15 -10 -47 -44 19}}


[[Map]]: [<5 7 13 15|, <0 2 -3 -2|]
[[POTE generator]]: ~15/14 = 111.553


{{Vals|legend=1| 10, 55d, 65d, 75, 140d, 215dd }}
{{Val list|legend=1| 10, 55d, 65d, 75, 140d, 215dd }}


[[Badness]]: 0.156764
[[Badness]]: 0.156764


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 243/242, 3840/3773
Comma list: 225/224, 243/242, 3840/3773
Mapping: [{{val|5 7 13 15 15}}, {{val|0 2 -3 -2 5}}]


POTE generator: ~15/14 = 111.311
POTE generator: ~15/14 = 111.311


Map: [<5 7 13 15 15|, <0 2 -3 -2 5|]
Vals: {{Val list| 10, 55d, 65d, 140de, 205dde }}


Vals: {{Vals| 10, 55d, 65d, 140de, 205dde }}
Badness: 0.077907


Badness: 0.077907
=== Qinto ===
Subgroup: 2.3.5.7.11


=== Qinto  ===
Comma list: 225/224, 385/384, 332750/321489
Comma list: 225/224, 385/384, 332750/321489
Mapping: [{{val|5 7 13 15 14}}, {{val|0 2 -3 -2 7}}]


POTE generator: ~15/14 = 112.448
POTE generator: ~15/14 = 112.448


Map: [<5 7 13 15 14|, <0 2 -3 -2 7|]
Vals: {{Val list| 10, 75, 160cde }}


Vals: {{Vals| 10, 75, 160cde }}
Badness: 0.127732


Badness: 0.127732
== Sengasec ==
The ''sengasec'' temperament (10&55) tempers out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.


== Sengasec  ==
Subgroup: 2.3.5.7
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.


[[Comma list]]: 686/675, 16807/16384
[[Comma list]]: 686/675, 16807/16384


[[POTE tuning|POTE generator]]: ~16/15 = 111.113
[[Mapping]]: [{{val|5 7 13 14}}, {{val|0 2 -3 0}}]


[[Map]]: [<5 7 13 14|, <0 2 -3 0|]
[[POTE generator]]: ~16/15 = 111.113


{{Vals|legend=1| 10, 55, 65, 140dd, 205ddd, 270ddd }}
{{Val list|legend=1| 10, 55, 65, 140dd, 205ddd, 270ddd }}


[[Badness]]: 0.156259
[[Badness]]: 0.156259


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 243/242, 385/384, 686/675
Comma list: 243/242, 385/384, 686/675
Mapping: [{{val|5 7 13 14 15}}, {{val|0 2 -3 0 5}}]


POTE generator: ~16/15 = 110.659
POTE generator: ~16/15 = 110.659


Map: [<5 7 13 14 15|, <0 2 -3 0 5|]
Vals: {{Val list| 10, 55, 65 }}


Vals: {{Vals| 10, 55, 65 }}
Badness: 0.081607


Badness: 0.081607
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 105/104, 144/143, 243/242, 686/675
Comma list: 105/104, 144/143, 243/242, 686/675
Mapping: [{{val|5 7 13 14 15 19}}, {{val|0 2 -3 0 5 -1}}]


POTE generator: ~16/15 = 110.910
POTE generator: ~16/15 = 110.910


Map: [<5 7 13 14 15 19|, <0 2 -3 0 5 -1|]
Vals: {{Val list| 10, 55, 65 }}
 
Vals: {{Vals| 10, 55, 65 }}


Badness: 0.056390
Badness: 0.056390


== Decoid ==
== Decoid ==
{{See also|Breedsmic temperaments #Decoid}}
{{See also|Breedsmic temperaments #Decoid}}
Subgroup: 2.3.5.7


[[Comma list]]: 2401/2400, 67108864/66976875
[[Comma list]]: 2401/2400, 67108864/66976875


[[POTE tuning|POTE generator]]: ~16/15 = 111.099
[[Mapping]]: [{{val|10 0 47 36}}, {{val|0 2 -3 -1}}]


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


{{Vals|legend=1| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
{{Val list|legend=1| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}


[[Badness]]: 0.033902
[[Badness]]: 0.033902


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 5632/5625, 9801/9800
Comma list: 2401/2400, 5632/5625, 9801/9800
Mapping: [{{val|10 0 47 36 98}}, {{val|0 2 -3 -1 -8}}]


POTE generator: ~16/15 = 111.070
POTE generator: ~16/15 = 111.070


Map: [<10 0 47 36 98|, <0 2 -3 -1 -8|]
Vals: {{Val list| 10e, 130, 270, 670, 940, 1210, 2150c }}


Vals: {{Vals| 10e, 130, 270, 670, 940, 1210, 2150c }}
Badness: 0.018735


Badness: 0.018735
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
Mapping: [{{val|10 0 47 36 98 37}}, {{val|0 2 -3 -1 -8 0}}]


POTE generator: ~16/15 = 111.083
POTE generator: ~16/15 = 111.083


Map: [<10 0 47 36 98 37|, <0 2 -3 -1 -8 0|]
Vals: {{Val list| 10e, 130, 270, 940, 1210f, 1480cf }}
 
Vals: {{Vals| 10e, 130, 270, 940, 1210f, 1480cf }}


Badness: 0.013475
Badness: 0.013475

Revision as of 04:12, 5 June 2021

The qintosec family tempers out the qintosec comma, 140737488355328/140126044921875 = [47 -15 -10⟩.

Qintosec

Subgroup: 2.3.5

Comma: 140737488355328/140126044921875

Mapping: [⟨5 7 13], ⟨0 2 -3]]

POTE generator: ~16/15 = 111.105

Template:Val list

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.

Subgroup: 2.3.5.7

Comma list: 225/224, 2560000/2470629

Mapping: [⟨5 7 13 15], ⟨0 2 -3 -2]]

Wedgie: ⟨⟨ 10 -15 -10 -47 -44 19 ]]

POTE generator: ~15/14 = 111.553

Template:Val list

Badness: 0.156764

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 3840/3773

Mapping: [⟨5 7 13 15 15], ⟨0 2 -3 -2 5]]

POTE generator: ~15/14 = 111.311

Vals: Template:Val list

Badness: 0.077907

Qinto

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 332750/321489

Mapping: [⟨5 7 13 15 14], ⟨0 2 -3 -2 7]]

POTE generator: ~15/14 = 112.448

Vals: Template:Val list

Badness: 0.127732

Sengasec

The sengasec temperament (10&55) tempers out the cloudy comma, 16807/16384 and the sengic comma, 686/675 in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 686/675, 16807/16384

Mapping: [⟨5 7 13 14], ⟨0 2 -3 0]]

POTE generator: ~16/15 = 111.113

Template:Val list

Badness: 0.156259

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 385/384, 686/675

Mapping: [⟨5 7 13 14 15], ⟨0 2 -3 0 5]]

POTE generator: ~16/15 = 110.659

Vals: Template:Val list

Badness: 0.081607

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 243/242, 686/675

Mapping: [⟨5 7 13 14 15 19], ⟨0 2 -3 0 5 -1]]

POTE generator: ~16/15 = 110.910

Vals: Template:Val list

Badness: 0.056390

Decoid

See also: Breedsmic temperaments § Decoid

Subgroup: 2.3.5.7

Comma list: 2401/2400, 67108864/66976875

Mapping: [⟨10 0 47 36], ⟨0 2 -3 -1]]

POTE generator: ~16/15 = 111.099

Template:Val list

Badness: 0.033902

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 5632/5625, 9801/9800

Mapping: [⟨10 0 47 36 98], ⟨0 2 -3 -1 -8]]

POTE generator: ~16/15 = 111.070

Vals: Template:Val list

Badness: 0.018735

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095

Mapping: [⟨10 0 47 36 98 37], ⟨0 2 -3 -1 -8 0]]

POTE generator: ~16/15 = 111.083

Vals: Template:Val list

Badness: 0.013475

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