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 | ||
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[[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 | ||
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[[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 == | ||