Gravity family: Difference between revisions

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= Gravity =
= Gravity =
Subgroup: 2.3.5
[[Comma]]: 129140163/128000000
[[Comma]]: 129140163/128000000


Line 73: Line 75:
Badness: 0.012657
Badness: 0.012657


=Gravid=
= Gravid =
Commas: 126/125, 1605632/1594323
Subgroup: 2.3.5.7
 
[[Comma list]]: 126/125, 1605632/1594323
 
[[Mapping]]: [{{val|1 -1 -5 -14}}, {{val|0 6 17 39}}]
 
[[Wedgie]]: {{multival|6 17 39 13 45 43}}


POTE generator: ~27/20 = 517.140
[[POTE generator]]: ~27/20 = 517.140


Map: [<1 -1 -5 -14|, <0 6 17 39|]
{{Val list|legend=1| 7d, 58, 65, 123, 181c }}


Wedgie: <<6 17 39 13 45 43||
[[Badness]]: 0.131153


EDOs: 7d, 58, 65, 123, 181c
== 11-limit ==
Subgroup: 2.3.5.7.11


Badness: 0.1312
Comma list: 126/125, 243/242, 896/891


==11-limit==
Mapping: [{{val|1 -1 -5 -14 -3}}, {{val|0 6 17 39 15}}]
Commas: 126/125, 243/242, 896/891


POTE generator: ~27/20 = 517.155
POTE generator: ~27/20 = 517.155


Map: [<1 -1 -5 -14 -3|, <0 6 17 39 15|]
Vals: {{Val list| 7d, 58, 65, 123, 181ce }}
 
Badness: 0.047283
 
= Zarvo =
Subgroup: 2.3.5.7


EDOs: 7d, 58, 65, 123, 181ce
[[Comma list]]: 4375/4374, 33075/32768


Badness: 0.0473
[[Mapping]]: [{{val|1 -1 -5 14}}, {{val|0 6 17 -26}}]


=Zarvo=
[[Wedgie]]: {{multival|6 17 -26 13 -58 -108}}
Commas: 4375/4374, 33075/32768


POTE generator: ~27/20 = 516.702
[[POTE generator]]: ~27/20 = 516.702


Map: [<1 -1 -5 14|, <0 6 17 -26|]
{{Val list|lenegd=1| 7, 65, 72 }}


Wedgie: <<6 17 -26 13 -58 -108||
[[Badness]]: 0.096840


EDOs: 7, 65, 72
== 11-limit ==
Subgroup: 2.3.5.7.11


Badness: 0.0968
Comma list: 243/242, 385/384, 4000/3993


==11-limit==
Mapping: [{{val|1 -1 -5 14 -3}}, {{val|0 6 17 -26 15}}]
Commas: 243/242, 385/384, 4000/3993


POTE generator: ~27/20 = 516.691
POTE generator: ~27/20 = 516.691


Map: [<1 -1 -5 14 -3|, <0 6 17 -26 15|]
Vals: {{Val list| 7, 65, 72 }}
 
Badness: 0.034773


EDOs: 7, 65, 72
== 13-limit ==
Subgroup: 2.3.5.7.11.13


Badness: 0.0348
Comma list: 169/168, 243/242, 325/324, 385/384


==13-limit==
Mapping: [{{val|1 -1 -5 14 -3 8}}, {{val|0 6 17 -26 15 -10}}]
Commas: 169/168, 243/242, 325/324, 385/384


POTE generator: ~27/20 = 516.667
POTE generator: ~27/20 = 516.667


Map: [<1 -1 -5 14 -3 8|, <0 6 17 -26 15 -10|]
Vals: {{Val list| 7, 65f, 72, 79 }}
 
EDOs: 7, 65f, 72, 79


Badness: 0.0276
Badness: 0.027584


[[Category:Theory]]
[[Category:Theory]]

Revision as of 16:39, 4 May 2021

The gravity family tempers out graviton, the 5-limit comma 129140163/128000000 = [-13 17 -6⟩. The graviton equals (81/80)4/(25/24), so that four 81/80 commas come to a classic chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the syntonic-chromatic equivalence continuum, whereby (81/80)k = 25/24.

Temperaments not discussed here include marvo.

Gravity

Subgroup: 2.3.5

Comma: 129140163/128000000

Mapping: [⟨1 5 12], ⟨0 -6 -17]]

POTE generator: ~40/27 = 683.156

Template:Val list

Badness: 0.093184

Harry

Main article: Harry
See also: Breedsmic temperaments § Harry

Harry temperament can be described as 58&72 temperament, tempering out 7-limit commas 2401/2400 and 19683/19600; 11-limit commas 243/242, 441/440 and 4000/3993, leading to a period of a half octave and a generator of minor semitone tempered between 21/20 and 22/21. Harry temperament also equates 14/13 with 27/25 in the 13-limit, 17/16 with 18/17 and 13/11 with 20/17 in the 17-limit.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 19683/19600

Mapping: [⟨2 4 7 7], ⟨0 -6 -17 -10]]

Wedgie: ⟨⟨ 12 34 20 26 -2 -49 ]]

POTE generator: ~21/20 = 83.156

Template:Val list

Badness: 0.034077

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 4000/3993

Mapping: [⟨2 4 7 7 9], ⟨0 -6 -17 -10 -15]]

POTE generator: ~21/20 = 83.167

Vals: Template:Val list

Badness: 0.015867

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 441/440, 676/675

Mapping: [⟨2 4 7 7 9 11], ⟨0 -6 -17 -10 -15 -26]]

POTE generator: ~21/20 = 83.116

Vals: Template:Val list

Badness: 0.013046

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 243/242, 289/288, 351/350, 441/440

Mapping: [⟨2 4 7 7 9 11 9], ⟨0 -6 -17 -10 -15 -26 -6]]

POTE generator: ~21/20 = 83.168

Vals: Template:Val list

Badness: 0.012657

Gravid

Subgroup: 2.3.5.7

Comma list: 126/125, 1605632/1594323

Mapping: [⟨1 -1 -5 -14], ⟨0 6 17 39]]

Wedgie: ⟨⟨ 6 17 39 13 45 43 ]]

POTE generator: ~27/20 = 517.140

Template:Val list

Badness: 0.131153

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 243/242, 896/891

Mapping: [⟨1 -1 -5 -14 -3], ⟨0 6 17 39 15]]

POTE generator: ~27/20 = 517.155

Vals: Template:Val list

Badness: 0.047283

Zarvo

Subgroup: 2.3.5.7

Comma list: 4375/4374, 33075/32768

Mapping: [⟨1 -1 -5 14], ⟨0 6 17 -26]]

Wedgie: ⟨⟨ 6 17 -26 13 -58 -108 ]]

POTE generator: ~27/20 = 516.702

Template:Val list

Badness: 0.096840

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 385/384, 4000/3993

Mapping: [⟨1 -1 -5 14 -3], ⟨0 6 17 -26 15]]

POTE generator: ~27/20 = 516.691

Vals: Template:Val list

Badness: 0.034773

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 243/242, 325/324, 385/384

Mapping: [⟨1 -1 -5 14 -3 8], ⟨0 6 17 -26 15 -10]]

POTE generator: ~27/20 = 516.667

Vals: Template:Val list

Badness: 0.027584

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