Gravity family

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Gravity

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 chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the Whitewood -> Mavila -> Dicot -> Porcupine -> Tetracot -> Amity -> ..... (Meantone) continuum, whereby (81/80)^n = 25/24.

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