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Aberschismic temperaments: Difference between revisions

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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 35: Line 34:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 49: Line 47:


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 63: Line 60:


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 77: Line 73:


== Buteo ==
== Buteo ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 91: Line 86:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 105: Line 99:


= Undecental =
= Undecental =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 121: Line 114:


= Leapday =
= Leapday =
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 135: Line 127:


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 151: Line 142:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 165: Line 155:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 179: Line 168:


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 193: Line 181:


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 207: Line 194:


=== Leapling ===
=== Leapling ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 223: Line 209:
{{main| Mystery }}
{{main| Mystery }}


== 5-limit ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 251: Line 236:
{{Val list|legend=1| 29, 58, 87, 145 }}
{{Val list|legend=1| 29, 58, 87, 145 }}


[[Badness]]: 0.1037
[[Badness]]: 0.103734


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 265: Line 249:
Vals: {{Val list| 29, 58, 87, 145 }}
Vals: {{Val list| 29, 58, 87, 145 }}


Badness: 0.0343
Badness: 0.034291


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 279: Line 262:
Vals: {{Val list| 29, 58, 87, 145, 232, 377cef }}
Vals: {{Val list| 29, 58, 87, 145, 232, 377cef }}


Badness: 0.0186
Badness: 0.018591


= Quanic =
= Quanic =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 293: Line 275:
{{Val list|legend=1| 94, 111, 205 }}
{{Val list|legend=1| 94, 111, 205 }}


[[Badness]]: 0.1795
[[Badness]]: 0.179475


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 307: Line 288:
Vals: {{Val list| 94, 111, 205 }}
Vals: {{Val list| 94, 111, 205 }}


Badness: 0.0587
Badness: 0.058678


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 321: Line 301:
Vals: {{Val list| 94, 111, 205 }}
Vals: {{Val list| 94, 111, 205 }}


Badness: 0.0325
Badness: 0.032481


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 335: Line 314:
Vals: {{Val list| 94, 111, 205 }}
Vals: {{Val list| 94, 111, 205 }}


Badness: 0.0211
Badness: 0.021112


== 19-limit ==
== 19-limit ==
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 349: Line 327:
Vals: {{Val list| 94, 111, 205 }}
Vals: {{Val list| 94, 111, 205 }}


Badness: 0.0173
Badness: 0.017273


= Supers =
= Supers =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 368: Line 345:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 382: Line 358:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 396: Line 371:


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 410: Line 384:


= Alphaquarter =
= Alphaquarter =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 423: Line 396:
{{Val list|legend=1| 87, 152, 239, 391 }}
{{Val list|legend=1| 87, 152, 239, 391 }}


[[Badness]]: 0.1166
[[Badness]]: 0.116594


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 437: Line 409:
Vals: {{Val list| 87, 152, 239, 391 }}
Vals: {{Val list| 87, 152, 239, 391 }}


Badness: 0.0296
Badness: 0.029638


= Septiquarter =
= Septiquarter =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 453: Line 424:
{{Val list|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}
{{Val list|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}


[[Badness]]: 0.0538
[[Badness]]: 0.053760


== Semiseptiquarter ==
== Semiseptiquarter ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 467: Line 437:
Vals: {{Val list| 94, 198, 292, 490 }}
Vals: {{Val list| 94, 198, 292, 490 }}


Badness: 0.0642
Badness: 0.064160


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 481: Line 450:
Vals: {{Val list| 94, 198, 490f }}
Vals: {{Val list| 94, 198, 490f }}


Badness: 0.0348
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 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.


Subgroup: 2.3.5
[[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883
[[Mapping]]: [&lt;1 0 -13|, &lt;0 3 29|]
[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012
{{Val list|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
[[Badness]]: 0.046093
== 7-limit (aka Trimot) ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 503: Line 485:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 517: Line 498:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 531: Line 511:


= Ketchup =
= Ketchup =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 547: Line 526:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 561: Line 539:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 575: Line 552:


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 589: Line 565:


== 19-limit ==
== 19-limit ==
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 603: Line 578:


== 23-limit ==
== 23-limit ==
Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7.11.13.17.19.23


Line 615: Line 589:


Badness: 0.014033
Badness: 0.014033
= Undim =
Subgroup: 2.3.5
[[Comma list]]: {{monzo| 41 -20 -4 }} = 2199023255552/2179240250625
[[Mapping]]: [{{val| 4 0 41 }}, {{val| 0 1 -5 }}]
Mapping generators: ~1215/1024, ~3
[[POTE generator]]: ~3/2 = 702.736
{{Val list|legend=1| 12, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }}
[[Badness]]: 0.241703
== 7-limit ==
Subgroup: 2.3.5.7
[[Comma list]]: 5120/5103, 390625/388962
[[Mapping]]: [{{val| 4 0 41 81 }}, {{val| 0 1 -5 -11 }}]
{{Multival|legend=1| 4 -20 -44 -41 -81 -46 }}
[[POTE generator]]: ~3/2 = 702.736
{{Val list|legend=1| 12, 128, 140, 152, 292 }}
[[Badness]]: 0.062754
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 5120/5103, 5632/5625
Mapping: [{{val| 4 0 41 81 128 }}, {{val| 0 1 -5 -11 -18 }}]
POTE generator: ~3/2 = 702.689
Vals: {{Val list| 12, 128e, 140, 152, 292, 444d, 596d }}
Badness: 0.034837


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
Retrieved from "https://en.xen.wiki/w/Aberschismic_temperaments"