Quintosec family: Difference between revisions

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Line 6: Line 6:
[[Comma]]: 140737488355328/140126044921875
[[Comma]]: 140737488355328/140126044921875


[[Mapping]]: [{{val|5 7 13}}, {{val|0 2 -3}}]
[[Mapping]]: [{{val| 5 1 22 }}, {{val| 0 2 -3 }}]
 
Mapping generators: ~524288/455625, ~16384/10125


[[POTE generator]]: ~16/15 = 111.105
[[POTE generator]]: ~16/15 = 111.105
Line 14: Line 16:
[[Badness]]: 0.139191
[[Badness]]: 0.139191


=== 7-limit ===
== Septimal qintosec ==
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 [[marvel comma]], 225/224 in the 7-limit.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 21: Line 23:
[[Comma list]]: 225/224, 2560000/2470629
[[Comma list]]: 225/224, 2560000/2470629


[[Mapping]]: [{{val|5 7 13 15}}, {{val|0 2 -3 -2}}]
[[Mapping]]: [{{val| 5 1 22 21 }}, {{val| 0 2 -3 -2 }}]


{{Multival|legend=1|10 -15 -10 -47 -44 19}}
{{Multival|legend=1| 10 -15 -10 -47 -44 19 }}


[[POTE generator]]: ~15/14 = 111.553
[[POTE generator]]: ~15/14 = 111.553
Line 36: Line 38:
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}}]
Mapping: [{{val| 5 1 22 21 0 }}, {{val| 0 2 -3 -2 5 }}]


POTE generator: ~15/14 = 111.311
POTE generator: ~15/14 = 111.311
Line 49: Line 51:
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}}]
Mapping: [{{val| 5 1 22 21 -7 }}, {{val|0 2 -3 -2 7 }}]


POTE generator: ~15/14 = 112.448
POTE generator: ~15/14 = 112.448
Line 64: Line 66:
[[Comma list]]: 686/675, 16807/16384
[[Comma list]]: 686/675, 16807/16384


[[Mapping]]: [{{val|5 7 13 14}}, {{val|0 2 -3 0}}]
[[Mapping]]: [{{val| 5 1 22 14 }}, {{val| 0 2 -3 0 }}]


[[POTE generator]]: ~16/15 = 111.113
[[POTE generator]]: ~16/15 = 111.113
Line 77: Line 79:
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}}]
Mapping: [{{val| 5 1 22 14 0 }}, {{val| 0 2 -3 0 5 }}]


POTE generator: ~16/15 = 110.659
POTE generator: ~16/15 = 110.659
Line 90: Line 92:
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}}]
Mapping: [{{val| 5 1 22 14 0 22 }}, {{val| 0 2 -3 0 5 -1 }}]


POTE generator: ~16/15 = 110.910
POTE generator: ~16/15 = 110.910
Line 99: Line 101:


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


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 105: Line 107:
[[Comma list]]: 2401/2400, 67108864/66976875
[[Comma list]]: 2401/2400, 67108864/66976875


[[Mapping]]: [{{val|10 0 47 36}}, {{val|0 2 -3 -1}}]
[[Mapping]]: [{{val| 10 0 47 36 }}, {{val| 0 2 -3 -1 }}]
 
Mapping generators: ~15/14, ~8192/4725


[[POTE generator]]: ~16/15 = 111.099
[[POTE generator]]: ~16/15 = 111.099
Line 118: Line 122:
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}}]
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
Line 131: Line 135:
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}}]
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
Line 139: Line 143:
Badness: 0.013475
Badness: 0.013475


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Qintosec]]
[[Category:Qintosec family| ]] <!-- main article -->
[[Category:Rank 2]]

Revision as of 06:17, 28 July 2021

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

Qintosec

Subgroup: 2.3.5

Comma: 140737488355328/140126044921875

Mapping: [⟨5 1 22], ⟨0 2 -3]]

Mapping generators: ~524288/455625, ~16384/10125

POTE generator: ~16/15 = 111.105

Template:Val list

Badness: 0.139191

Septimal qintosec

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 1 22 21], ⟨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 1 22 21 0], ⟨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 1 22 21 -7], ⟨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 1 22 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 1 22 14 0], ⟨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 1 22 14 0 22], ⟨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]]

Mapping generators: ~15/14, ~8192/4725

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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