Gravity family: Difference between revisions

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Badness: 0.0932
Badness: 0.0932


=Harry=
= Harry =
{{main|Harry}}
{{main|Harry}}
{{see also|Breedsmic temperaments #Harry}}
{{see also|Breedsmic temperaments #Harry}}
Line 21: Line 21:
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.
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.


Commas: 2401/2400, 19683/19600
Subgroup: 2.3.5.7


POTE generator: ~21/20 = 83.156
[[Comma list]]: 2401/2400, 19683/19600


Map: [<2 4 7 7|, <0 -6 -17 -10|]
[[Mapping]]: [{{val| 2 4 7 7 }}, {{val| 0 -6 -17 -10 }}]


Wedgie: <<12 34 20 26 -2 -49||
{{Multival|legend=1| 12 34 20 26 -2 -49 }}


EDOs: 58, 72, 130, 202, 534
[[POTE generator]]: ~21/20 = 83.156


Badness: 0.0341
{{Val list|legend=1| 14c, 58, 72, 130, 202, 534, 736b, 938b }}


==11-limit==
[[Badness]]: 0.034077
Commas: 243/242, 441/440, 4000/3993
 
== 11-limit ==
Subgroup: 2.3.5.7.11
 
Comma list: 243/242, 441/440, 4000/3993
 
Mapping: [{{val| 2 4 7 7 9 }}, {{val| 0 -6 -17 -10 -15 }}]


POTE generator: ~21/20 = 83.167
POTE generator: ~21/20 = 83.167


Map: [<2 4 7 7 9|, <0 -6 -17 -10 -15|]
Vals: {{Val list| 14c, 58, 72, 130, 202 }}
 
Badness: 0.015867


EDOs: 58, 72, 130, 202
== 13-limit ==
Subgroup: 2.3.5.7.11.13


Badness: 0.0159
Comma list: 243/242, 351/350, 441/440, 676/675


==13-limit==
Mapping: [{{val| 2 4 7 7 9 11 }}, {{val| 0 -6 -17 -10 -15 -26 }}]
Commas: 243/242, 351/350, 364/363, 441/440


POTE generator: ~21/20 = 83.116
POTE generator: ~21/20 = 83.116


Map: [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|]
Vals: {{Val list| 58, 72, 130, 332f, 462ef }}


EDOs: 58, 72, 130
Badness: 0.013046


Badness: 0.0130
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17


==17-limit==
Comma list: 221/220, 243/242, 289/288, 351/350, 441/440
Commas: 221/220, 243/242, 289/288, 351/350, 441/440
 
Mapping: [{{val| 2 4 7 7 9 11 9 }}, {{val| 0 -6 -17 -10 -15 -26 -6 }}]


POTE generator: ~21/20 = 83.168
POTE generator: ~21/20 = 83.168


Map: [<2 4 7 7 9 11 9|, <0 -6 -17 -10 -15 -26 -6|]
Vals: {{Val list| 58, 72, 130, 202g }}
 
EDOs: 58, 72, 130


Badness: 0.0127
Badness: 0.012657


=Gravid=
=Gravid=

Revision as of 16:21, 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

Comma: 129140163/128000000

POTE generator: ~40/27 = 683.156

Map: [<1 5 12|, <0 -6 -17|]

EDOs: 7, 58, 65, 137, 202, 267, 469

Badness: 0.0932

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

Commas: 126/125, 1605632/1594323

POTE generator: ~27/20 = 517.140

Map: [<1 -1 -5 -14|, <0 6 17 39|]

Wedgie: <<6 17 39 13 45 43||

EDOs: 7d, 58, 65, 123, 181c

Badness: 0.1312

11-limit

Commas: 126/125, 243/242, 896/891

POTE generator: ~27/20 = 517.155

Map: [<1 -1 -5 -14 -3|, <0 6 17 39 15|]

EDOs: 7d, 58, 65, 123, 181ce

Badness: 0.0473

Zarvo

Commas: 4375/4374, 33075/32768

POTE generator: ~27/20 = 516.702

Map: [<1 -1 -5 14|, <0 6 17 -26|]

Wedgie: <<6 17 -26 13 -58 -108||

EDOs: 7, 65, 72

Badness: 0.0968

11-limit

Commas: 243/242, 385/384, 4000/3993

POTE generator: ~27/20 = 516.691

Map: [<1 -1 -5 14 -3|, <0 6 17 -26 15|]

EDOs: 7, 65, 72

Badness: 0.0348

13-limit

Commas: 169/168, 243/242, 325/324, 385/384

POTE generator: ~27/20 = 516.667

Map: [<1 -1 -5 14 -3 8|, <0 6 17 -26 15 -10|]

EDOs: 7, 65f, 72, 79

Badness: 0.0276

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