Gravity family: Difference between revisions
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The '''gravity family''' tempers out [[graviton]], the 5-limit comma 129140163/128000000 = {{monzo| -13 17 -6 }}. The graviton equals (81/80)<sup>4</sup>/(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)<sup>''k''</sup> = 25/24. | |||
Temperaments not discussed here include [[Marvel temperaments #marvo|marvo]]. | |||
= Gravity = | = Gravity = | ||
Comma: 129140163/128000000 | Comma: 129140163/128000000 | ||
Revision as of 08:22, 22 February 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
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
POTE generator: ~21/20 = 83.156
Map: [<2 4 7 7|, <0 -6 -17 -10|]
Wedgie: <<12 34 20 26 -2 -49||
EDOs: 58, 72, 130, 202, 534
Badness: 0.0341
11-limit
Commas: 243/242, 441/440, 4000/3993
POTE generator: ~21/20 = 83.167
Map: [<2 4 7 7 9|, <0 -6 -17 -10 -15|]
EDOs: 58, 72, 130, 202
Badness: 0.0159
13-limit
Commas: 243/242, 351/350, 364/363, 441/440
POTE generator: ~21/20 = 83.116
Map: [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|]
EDOs: 58, 72, 130
Badness: 0.0130
17-limit
Commas: 221/220, 243/242, 289/288, 351/350, 441/440
POTE generator: ~21/20 = 83.168
Map: [<2 4 7 7 9 11 9|, <0 -6 -17 -10 -15 -26 -6|]
EDOs: 58, 72, 130
Badness: 0.0127
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