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.

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.

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 ==

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POTE generator: ~40/27 = 683.166

~~Vals~~: {{Val list| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }}

Optimal GPV sequence: {{Val list| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }}

Badness: 0.0125

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POTE generator: ~21/20 = 83.167

~~Vals~~: {{Val list| 14c, 58, 72, 130, 202 }}

Optimal GPV sequence: {{Val list| 14c, 58, 72, 130, 202 }}

Badness: 0.015867

Line 77:

POTE generator: ~21/20 = 83.116

~~Vals~~: {{Val list| 14cf, 58, 72, 130, 332f, 462ef }}

Optimal GPV sequence: {{Val list| 14cf, 58, 72, 130, 332f, 462ef }}

Badness: 0.013046

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POTE generator: ~21/20 = 83.168

~~Vals~~: {{Val list| 14cf, 58, 72, 130, 202g }}

Optimal GPV sequence: {{Val list| 14cf, 58, 72, 130, 202g }}

Badness: 0.012657

Line 118:

POTE generator: ~27/20 = 517.155

~~Vals~~: {{Val list| 58, 123, 181ce }}

Optimal GPV sequence: {{Val list| 58, 123, 181ce }}

Badness: 0.047283

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POTE generator: ~27/20 = 516.699

~~Vals~~: {{Val list| 65d, 72, 281, 353c, 425bc, 497bc }}

Optimal GPV sequence: {{Val list| 65d, 72, 281, 353c, 425bc, 497bc }}

Badness: 0.031685

Line 159:

POTE generator: ~27/20 = 516.730

~~Vals~~: {{Val list| 65d, 72, 137, 209, 281f, 490bcf }}

Optimal GPV sequence: {{Val list| 65d, 72, 137, 209, 281f, 490bcf }}

Badness: 0.026882

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POTE generator: ~27/20 = 516.691

~~Vals~~: {{Val list| 65, 72, 353cd }}

Optimal GPV sequence: {{Val list| 65, 72, 353cd }}

Badness: 0.034773

Line 200:

POTE generator: ~27/20 = 516.667

~~Vals~~: {{Val list| 65f, 72 }}

Optimal GPV sequence: {{Val list| 65f, 72 }}

Badness: 0.027584

@@ Line 1: / Line 1: @@
 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.
-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.
+Full 7-limit extensions of gravity include gravid (58&amp;65), marvo (65d&amp;72), zarvo (65&amp;72), and harry (58&amp;72), all considered below. A notable subgroup extension is larry.
 == Gravity ==
@@ Line 31: / Line 31: @@
 POTE generator: ~40/27 = 683.166
-Vals: {{Val list| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }}
+Optimal GPV sequence: {{Val list| 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202 }}
 Badness: 0.0125
@@ Line 64: / Line 64: @@
 POTE generator: ~21/20 = 83.167
-Vals: {{Val list| 14c, 58, 72, 130, 202 }}
+Optimal GPV sequence: {{Val list| 14c, 58, 72, 130, 202 }}
 Badness: 0.015867
@@ Line 77: / Line 77: @@
 POTE generator: ~21/20 = 83.116
-Vals: {{Val list| 14cf, 58, 72, 130, 332f, 462ef }}
+Optimal GPV sequence: {{Val list| 14cf, 58, 72, 130, 332f, 462ef }}
 Badness: 0.013046
@@ Line 90: / Line 90: @@
 POTE generator: ~21/20 = 83.168
-Vals: {{Val list| 14cf, 58, 72, 130, 202g }}
+Optimal GPV sequence: {{Val list| 14cf, 58, 72, 130, 202g }}
 Badness: 0.012657
@@ Line 118: / Line 118: @@
 POTE generator: ~27/20 = 517.155
-Vals: {{Val list| 58, 123, 181ce }}
+Optimal GPV sequence: {{Val list| 58, 123, 181ce }}
 Badness: 0.047283
@@ Line 146: / Line 146: @@
 POTE generator: ~27/20 = 516.699
-Vals: {{Val list| 65d, 72, 281, 353c, 425bc, 497bc }}
+Optimal GPV sequence: {{Val list| 65d, 72, 281, 353c, 425bc, 497bc }}
 Badness: 0.031685
@@ Line 159: / Line 159: @@
 POTE generator: ~27/20 = 516.730
-Vals: {{Val list| 65d, 72, 137, 209, 281f, 490bcf }}
+Optimal GPV sequence: {{Val list| 65d, 72, 137, 209, 281f, 490bcf }}
 Badness: 0.026882
@@ Line 187: / Line 187: @@
 POTE generator: ~27/20 = 516.691
-Vals: {{Val list| 65, 72, 353cd }}
+Optimal GPV sequence: {{Val list| 65, 72, 353cd }}
 Badness: 0.034773
@@ Line 200: / Line 200: @@
 POTE generator: ~27/20 = 516.667
-Vals: {{Val list| 65f, 72 }}
+Optimal GPV sequence: {{Val list| 65f, 72 }}
 Badness: 0.027584