Gravity family: Difference between revisions

m Comma list
+larry (a way to address 2.3.5.11 subgroup temps)
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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


=== Extensions ===
=== Larry ===
Extensions of gravity include gravid (58 & 65), marvo (65d & 72), zarvo (65 & 72), and harry (58 & 72), all considered below.  
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 ==