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Aberschismic temperaments: Difference between revisions

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Line 42: Line 42:
POTE generator: ~21/16 = 475.700
POTE generator: ~21/16 = 475.700


Vals: {{Val list| 53, 58, 111, 280cd, 391cd }}
Optimal GPV sequence: {{Val list| 53, 58, 111, 280cd, 391cd }}


Badness: 0.034484
Badness: 0.034484
Line 55: Line 55:
POTE generator: ~21/16 = 475.697
POTE generator: ~21/16 = 475.697


Vals: {{Val list| 53, 58, 111, 280cdf, 391cdf }}
Optimal GPV sequence: {{Val list| 53, 58, 111, 280cdf, 391cdf }}


Badness: 0.018842
Badness: 0.018842
Line 68: Line 68:
POTE generator: ~21/16 = 475.692
POTE generator: ~21/16 = 475.692


Vals: {{Val list| 53, 58, 111, 321cdfg }}
Optimal GPV sequence: {{Val list| 53, 58, 111, 321cdfg }}


Badness: 0.018403
Badness: 0.018403
Line 81: Line 81:
POTE generator: ~21/16 = 475.679
POTE generator: ~21/16 = 475.679


Vals: {{Val list| 53, 58h, 111 }}
Optimal GPV sequence: {{Val list| 53, 58h, 111 }}


Badness: 0.015649
Badness: 0.015649
Line 94: Line 94:
POTE generator: ~21/16 = 475.436
POTE generator: ~21/16 = 475.436


Vals: {{Val list| 5, 48, 53 }}
Optimal GPV sequence: {{Val list| 5, 48, 53 }}


Badness: 0.060238
Badness: 0.060238
Line 107: Line 107:
POTE generator: ~21/16 = 475.464
POTE generator: ~21/16 = 475.464


Vals: {{Val list| 5, 48f, 53 }}
Optimal GPV sequence: {{Val list| 5, 48f, 53 }}


Badness: 0.039854
Badness: 0.039854
Line 156: Line 156:
POTE generator: ~3/2 = 704.250
POTE generator: ~3/2 = 704.250


Vals: {{Val list| 17c, 29, 46, 167de, 213de, 259cdde }}
Optimal GPV sequence: {{Val list| 17c, 29, 46, 167de, 213de, 259cdde }}


Badness: 0.038624
Badness: 0.038624
Line 169: Line 169:
POTE generator: ~3/2 = 704.214
POTE generator: ~3/2 = 704.214


Vals: {{Val list| 17c, 29, 46, 121def, 167def, 213deff }}
Optimal GPV sequence: {{Val list| 17c, 29, 46, 121def, 167def, 213deff }}


Badness: 0.024732
Badness: 0.024732
Line 182: Line 182:
POTE generator: ~3/2 = 704.229
POTE generator: ~3/2 = 704.229


Vals: {{Val list| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}
Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}


Badness: 0.017863
Badness: 0.017863
Line 195: Line 195:
POTE generator: ~3/2 = 704.135
POTE generator: ~3/2 = 704.135


Vals: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}
Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}


Badness: 0.017356
Badness: 0.017356
Line 208: Line 208:
POTE generator: ~3/2 = 704.123
POTE generator: ~3/2 = 704.123


Vals: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}
Optimal GPV sequence: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}


Badness: 0.019065
Badness: 0.019065
Line 239: Line 239:
POTE generator: ~5/4 = 388.460
POTE generator: ~5/4 = 388.460


Vals: {{Val list| 29, 58, 87, 145 }}
Optimal GPV sequence: {{Val list| 29, 58, 87, 145 }}


Badness: 0.034291
Badness: 0.034291
Line 252: Line 252:
POTE generator: ~5/4 = 388.354
POTE generator: ~5/4 = 388.354


Vals: {{Val list| 29, 58, 87, 145, 232, 377cef }}
Optimal GPV sequence: {{Val list| 29, 58, 87, 145, 232, 377cef }}


Badness: 0.018591
Badness: 0.018591
Line 278: Line 278:
POTE generator: ~88/81 = 140.489
POTE generator: ~88/81 = 140.489


Vals: {{Val list| 94, 111, 205 }}
Optimal GPV sequence: {{Val list| 94, 111, 205 }}


Badness: 0.058678
Badness: 0.058678
Line 291: Line 291:
POTE generator: ~13/12 = 140.496
POTE generator: ~13/12 = 140.496


Vals: {{Val list| 94, 111, 205 }}
Optimal GPV sequence: {{Val list| 94, 111, 205 }}


Badness: 0.032481
Badness: 0.032481
Line 304: Line 304:
POTE generator: ~13/12 = 140.497
POTE generator: ~13/12 = 140.497


Vals: {{Val list| 94, 111, 205 }}
Optimal GPV sequence: {{Val list| 94, 111, 205 }}


Badness: 0.021112
Badness: 0.021112
Line 317: Line 317:
POTE generator: ~13/12 = 140.496
POTE generator: ~13/12 = 140.496


Vals: {{Val list| 94, 111, 205 }}
Optimal GPV sequence: {{Val list| 94, 111, 205 }}


Badness: 0.017273
Badness: 0.017273
Line 345: Line 345:
POTE generators: ~121/105 = 242.4511
POTE generators: ~121/105 = 242.4511


Vals: {{Val list| 94, 198, 292, 490 }}
Optimal GPV sequence: {{Val list| 94, 198, 292, 490 }}


Badness: 0.064160
Badness: 0.064160
Line 358: Line 358:
POTE generators: ~121/105 = 242.4448
POTE generators: ~121/105 = 242.4448


Vals: {{Val list| 94, 198, 490f }}
Optimal GPV sequence: {{Val list| 94, 198, 490f }}


Badness: 0.034834
Badness: 0.034834


== Tricot (aka trimot) ==
== Tricot ==
{{see also| Tricot family }}
{{see also| Tricot family }}


The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&amp;70 temperament (also known as ''trimot''), 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.
The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&amp;70 temperament (also called as "trimot'", as confirmed by the data from [http://x31eq.com/cgi-bin/rt.cgi?ets=53_17c&limit=7 x31eq]), 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.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 390: Line 390:
POTE generator: ~63/44 = 634.027
POTE generator: ~63/44 = 634.027


Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
Optimal GPV sequence: {{Val list| 17c, 36ce, 53, 70, 123de }}


Badness: 0.056134
Badness: 0.056134
Line 403: Line 403:
POTE generator: ~13/9 = 634.012
POTE generator: ~13/9 = 634.012


Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
Optimal GPV sequence: {{Val list| 17c, 36ce, 53, 70, 123de }}


Badness: 0.032102
Badness: 0.032102
== Countriton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Countriton]].''
Subgroup: 2.3.5.7
[[Comma list]]: 5120/5103, 7558272/7503125
[[Mapping]]: [{{val|1 6 19 -7}}, {{val|0 -9 -34 20}}]
[[POTE generator]]: ~1728/1225 = 588.582
{{Val list|legend=1| 53, 157, 210 }}
[[Badness]]: 0.131191
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 176/175, 5120/5103, 41503/41472
Mapping: [{{val|1 6 19 -7 27}}, {{val|0 -9 -34 20 -48}}]
POTE generator: ~108/77 = 588.545
Optimal GPV sequence: {{Val list| 53, 104c, 157 }}
Badness: 0.084782
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 847/845, 2197/2187
Mapping: [{{val|1 6 19 -7 27 14}}, {{val|0 -9 -34 20 -48 -21}}]
POTE generator: ~108/77 = 588.544
Optimal GPV sequence: {{Val list| 53, 104c, 157 }}
Badness: 0.042321


== Ketchup ==
== Ketchup ==
Line 431: Line 472:
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693


Vals: {{Val list| 46, 94, 140 }}
Optimal GPV sequence: {{Val list| 46, 94, 140 }}


Badness: 0.039555
Badness: 0.039555
Line 444: Line 485:
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697


Vals: {{Val list| 46, 94, 140 }}
Optimal GPV sequence: {{Val list| 46, 94, 140 }}


Badness: 0.024824
Badness: 0.024824
Line 457: Line 498:
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701


Vals: {{Val list| 46, 94, 140 }}
Optimal GPV sequence: {{Val list| 46, 94, 140 }}


Badness: 0.016591
Badness: 0.016591
Line 470: Line 511:
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660


Vals: {{Val list| 46, 94, 140h, 234eh }}
Optimal GPV sequence: {{Val list| 46, 94, 140h, 234eh }}


Badness: 0.018170
Badness: 0.018170
Line 483: Line 524:
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661


Vals: {{Val list| 46, 94, 140h, 234ehi }}
Optimal GPV sequence: {{Val list| 46, 94, 140h, 234ehi }}


Badness: 0.014033
Badness: 0.014033
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