Hemifamity temperaments: Difference between revisions
+semiseptiquarter |
→Tricot: edo list reviewed (tbh this 7-limit extension looks poor) |
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Badness: 0.0348 | Badness: 0.0348 | ||
=Tricot= | = Tricot = | ||
The generator for tricot temperament is the real cube root of third harmonic, 3 | The generator for tricot temperament is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit. | ||
==5-limit== | == 5-limit == | ||
Comma: |39 -29 3 | Comma: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | ||
POTE generator: ~59049/40960 = 634.012 | POTE generator: ~59049/40960 = 634.012 | ||
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Wedgie: <<3 29 39|| | Wedgie: <<3 29 39|| | ||
EDOs: 53, 335, 388, 441, | EDOs: {{EDOs| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }} | ||
Badness: 0.0461 | Badness: 0.0461 | ||
==7-limit== | == 7-limit == | ||
Commas: 2430/2401, 5120/5103 | Commas: 2430/2401, 5120/5103 | ||
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Wedgie: <<3 29 11 39 9 -56|| | Wedgie: <<3 29 11 39 9 -56|| | ||
EDOs: 17c, 36c, 53, | EDOs: {{EDOs| 17c, 36c, 53, 229dd, 282dd }} | ||
Badness: 0.1001 | Badness: 0.1001 | ||
==11-limit== | == 11-limit == | ||
Commas: 99/98, 121/120, 5120/5103 | Commas: 99/98, 121/120, 5120/5103 | ||
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Map: [<1 0 -13 -3 -5|, <0 3 29 11 16|] | Map: [<1 0 -13 -3 -5|, <0 3 29 11 16|] | ||
EDOs: 17c, 36ce, 53, | EDOs: {{EDOs| 17c, 36ce, 53, 176de, 229ddee, 282ddeee }} | ||
Badness: 0.0561 | Badness: 0.0561 | ||
==13-limit== | == 13-limit == | ||
Commas: 99/98, 121/120, 169/168, 352/351 | Commas: 99/98, 121/120, 169/168, 352/351 | ||
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Map: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|] | Map: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|] | ||
EDOs: 17c, 36ce, 53 | EDOs: {{EDOs| 17c, 36ce, 53 }} | ||
Badness: 0.0321 | Badness: 0.0321 | ||