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. | 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. | ||
== Gravity | Full 7-limit extensions of gravity include gravid (58 & 65), marvo (65d & 72), zarvo (65 & 72), and harry (58 & 72), all considered below. A notable subgroup extension is larry. | ||
== Gravity == | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 7: | Line 9: | ||
[[Mapping]]: [{{val| 1 5 12 }}, {{val| 0 -6 -17 }}] | [[Mapping]]: [{{val| 1 5 12 }}, {{val| 0 -6 -17 }}] | ||
Mapping generators: ~2, ~40/27 | |||
[[POTE generator]]: ~40/27 = 683.156 | [[POTE generator]]: ~40/27 = 683.156 | ||
| Line 14: | Line 18: | ||
[[Badness]]: 0.093184 | [[Badness]]: 0.093184 | ||
=== | === Larry === | ||
Subgroup: 2.3.5.11 | |||
Comma list: 243/242, 4000/3993 | |||
Sval mapping: [{{val| 1 5 12 12 }}, {{val| 0 -6 -17 -15 }}] | |||
Gencom mapping: [{{val| 1 5 12 0 12 }}, {{val| 0 -6 -17 0 -15 }}] | |||
Gencom: [2 40/27; 243/242 4000/3993] | |||
POTE generator: ~40/27 = 683.166 | |||
Vals: {{Val list| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }} | |||
Badness: 0.0125 | |||
== Harry == | == Harry == | ||
Revision as of 17:07, 26 September 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.
Full 7-limit extensions of gravity include gravid (58 & 65), marvo (65d & 72), zarvo (65 & 72), and harry (58 & 72), all considered below. A notable subgroup extension is larry.
Gravity
Subgroup: 2.3.5
Comma list: 129140163/128000000
Mapping: [⟨1 5 12], ⟨0 -6 -17]]
Mapping generators: ~2, ~40/27
POTE generator: ~40/27 = 683.156
Badness: 0.093184
Larry
Subgroup: 2.3.5.11
Comma list: 243/242, 4000/3993
Sval mapping: [⟨1 5 12 12], ⟨0 -6 -17 -15]]
Gencom mapping: [⟨1 5 12 0 12], ⟨0 -6 -17 0 -15]]
Gencom: [2 40/27; 243/242 4000/3993]
POTE generator: ~40/27 = 683.166
Vals: Template:Val list
Badness: 0.0125
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
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, 364/363, 441/440
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
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
Marvo
Subgroup: 2.3.5.7
Comma list: 225/224, 78125000/78121827
Mapping: [⟨1 5 12 29], ⟨0 -6 -17 -46]]
Wedgie: ⟨⟨ 6 17 46 13 56 59 ]]
POTE generator: ~27/20 = 516.694
Badness: 0.097627
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 4000/3993
Mapping: [⟨1 5 12 29 12], ⟨0 -6 -17 -46 -15]]
POTE generator: ~27/20 = 516.699
Vals: Template:Val list
Badness: 0.031685
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 351/350, 1625/1617
Mapping: [⟨1 5 12 29 12 39], ⟨0 -6 -17 -46 -15 -62]]
POTE generator: ~27/20 = 516.730
Vals: Template:Val list
Badness: 0.026882
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
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