Very high accuracy temperaments: Difference between revisions

Line 377:

= Rank-3 temperaments =

== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: 282475249000/282429536481

[[Comma list]]: {{monzo| 3 -24 3 10 }} = 282475249000/282429536481

Mapping: [{{val| 1 0 9 -3 }}, {{val| 0 1 8 0 }}, {{val| 0 0 10 -3 }}]

[[Mapping]]: [{{val| 1 0 9 -3 }}, {{val| 0 1 8 0 }}, {{val| 0 0 10 -3 }}]

{{Optimal ET sequence|legend=1| 171, 935, 1106, 1277, 2289, 2460, 3395, 3566, ~~3737~~}}

{{Optimal ET sequence|legend=1| 171, 764, 935, 1106, 1277, 2118, 2289, 2460, 3224, 3395, 3566, 26068, 26239, 29634, 29805, 33200, 33371, 36937, 40503, 44069 }}

Badness: 0.~~000281~~

[[Badness]]: 0.281 × 10-3

== Saquadtrizo-asepgu (171 & 2019 & 3566) ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: 13841287201/13839609375

[[Comma list]]: {{monzo| 0 -11 -7 12 }} = 13841287201/13839609375

Mapping: [{{val| 1 0 0 0 }}, {{val| 0 1 7 5 }}, {{val| 0 0 12 7 }}]

[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 7 5 }}, {{val| 0 0 12 7 }}]

{{Optimal ET sequence|legend=1| 171, 1547~~, 1677~~, 1718, 1848, 2019, 3395, 3566, ~~3737~~}}

{{Optimal ET sequence|legend=1| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}

Badness: 0.~~000135~~

[[Badness]]: 0.135 × 10-3

== Laquinzo-aquadquadgu (171 & 441 & 4973) ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000

[[Comma list]]: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000

Mapping: [{{val| 1 0 3 11 }}, {{val| 0 1 4 9 }}, {{val| 0 0 5 16 }}]

[[Mapping]]: [{{val| 1 0 3 11 }}, {{val| 0 1 4 9 }}, {{val| 0 0 5 16 }}]

{{Optimal ET sequence|legend=1| 171~~, 270~~, 441, 612, ~~783~~, 4802, 4973, 5144}}

{{Optimal ET sequence|legend=1| 171, 441, 612, 2696, 2795, 2867, 2966, 3137, 3308, 3407, 3479, 3578, 3749, 3920, 4091, 4190, 4361, 4532, 4703, 4802, 4973, 5144, 10117, 10558, 15531, 15702, 52079, 62637, 67781, 78339 }}

Badness: 0.~~000297~~

[[Badness]]: 0.297 × 10-3

== Laleruyo (171 & 1547 & 3125) ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: 3955078125/3954653486

[[Comma list]]: {{monzo| -1 4 11 -11 }} = 3955078125/3954653486

Mapping: [{{val| 1 3 0 1 }}, {{val| 0 11 0 4 }}, {{val| 0 0 1 1 }}]

[[Mapping]]: [{{val| 1 3 0 1 }}, {{val| 0 11 0 4 }}, {{val| 0 0 1 1 }}]

{{Optimal ET sequence|legend=1| 171, 1407, 1547, 1578, 1718, 2783, 2954, 3125, ~~3296~~}}

{{Optimal ET sequence|legend=1| 171, 863, 894, 1034, 1065, 1205, 1236, 1376, 1407, 1547, 1578, 1718, 2612, 2783, 2954, 3125, 12329, 15454, 18579, 21704, 40283, 61987 }}

Badness: 0.~~000114~~

[[Badness]]: 0.114 × 10-3

== Starscape or Latritriru-ayo ==

Line 427:

[[Mapping]]: [{{val| 1 0 4 0 }}, {{val| 0 1 1 2 }}, {{val| 0 0 9 1 }}]

{{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634, }} …

{{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634 }}

[[Badness]]: 0.~~000545~~

[[Badness]]: 0.545 × 10-3

== Sepbizo-asegu (171 & 3566 & 4973) ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: 6104007655641/6103515625000

[[Comma list]]: {{monzo| -3 2 -17 14 }} = 6104007655641/6103515625000

Mapping: [{{val| 1 0 13 16 }}, {{val| 0 1 10 12 }}, {{val| 0 0 14 17 }}]

[[Mapping]]: [{{val| 1 0 13 16 }}, {{val| 0 1 10 12 }}, {{val| 0 0 14 17 }}]

{{Optimal ET sequence|legend=1| 171, 1236, 1407, ~~3566~~, ~~3737~~, ~~3908~~, ~~4802~~, ~~4973~~, 8539, 8710}}

{{Optimal ET sequence|legend=1| 171, 894, 1065, 1236, 1407, 1578, 3053, 3224, 3395, 3566, 5144, 8368, 8539, 8710, 17249, 20815, 29525, 38064, 67589, 105653 }}

Badness: 0.~~000223~~

[[Badness]]: 0.223 × 10-3

== Euzenius or Sabiruquinyo ==

[[Subgroup]]: 2.3.5.7

Line 449:

Line 451:

[[Mapping]]: [{{val| 1 0 0 -5 }}, {{val| 0 2 0 -13 }}, {{val| 0 0 1 5 }}]

{{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654, }} …

{{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654 }}

[[Badness]]: 0.~~000205~~

[[Badness]]: 0.205 × 10-3

== Quinla-zoyoyo (612 & 1848 & 3125) ==

Line 462:

Line 464:

{{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795 }}

[[Badness]]: 0.~~000366~~

[[Badness]]: 0.366 × 10-3

== Satwethezo-atritribigu (171 & 1547 & 4973) ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: {{monzo| 1 -15 -18 23 }}

[[Comma list]]: {{monzo| 1 -15 -18 23 }}

Mapping: [{{val| 1 0 9 7 }}, {{val| 0 1 3 3 }}, {{val| 0 0 23 18 }}]

[[Mapping]]: [{{val| 1 0 9 7 }}, {{val| 0 1 3 3 }}, {{val| 0 0 23 18 }}]

{{Optimal ET sequence|legend=1| 171, 1547, 4802, 4973, 5144, 6520, 6691~~, 6862, 11493~~, 11664~~, 11835, 18184~~, 18355, ~~18526~~, ~~25046~~, ~~30019~~, ~~30190~~, ~~48545~~}}

{{Optimal ET sequence|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 3255, 3426, 3597, 4460, 4631, 4802, 4973, 5144, 6520, 6691, 11664, 18355, 48374, 48545, 66900, 145464, }} …

Badness: 0.~~000114~~

[[Badness]]: 0.114 × 10-3

== Trisa-quinbiru-agu (441 & 1848 & 3125) ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: {{monzo| 51 -13 -1 -10 }}

[[Comma list]]: {{monzo| 51 -13 -1 -10 }}

Mapping: [{{val| 1 0 1 5 }}, {{val| 0 1 7 -2 }}, {{val| 0 0 10 -1 }}]

[[Mapping]]: [{{val| 1 0 1 5 }}, {{val| 0 1 7 -2 }}, {{val| 0 0 10 -1 }}]

{{Optimal ET sequence|legend=1| 441, ~~1848~~, ~~3125~~, ~~3566~~, ~~4973~~, ~~6691~~, ~~8098~~, ~~8539~~, 9816, 11664, 14789~~, 15230~~, 18355, ~~21480~~, ~~30019~~, ~~33144~~, ~~39835~~, ~~51499~~}}

{{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …

Badness: 0.~~000263~~

[[Badness]]: 0.263 × 10-3

== Quinbisa-quinbizo-alegu (1848 & 11664 & 21480) ==

[[Subgroup]]: 2.3.5.7

~~== Quinbisa~~-~~quinbizo~~-~~alegu (21480 & 33144 & 103169) ==~~

[[Comma list]]: {{monzo| 110 -71 -11 10 }}

~~Subgroup: 2.3.5.7~~

~~Comma list~~: {{~~monzo~~| ~~110~~ -71 -11 10 }}

[[Mapping]]: [{{val| 1 0 0 -11 }}, {{val| 0 1 -1 6 }}, {{val| 0 0 10 11 }}]

~~Mapping: [~~{{~~val~~| 1 ~~0 0 -11 }}~~, ~~{{val| 0 1 -1 6 }}~~, ~~{{val| 0 0 10 11~~ }}]

{{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …

~~{{Optimal ET sequence|legend=1| 11664, 21480, 33144, 36881, 48545, 54624, 70025, 81689, 91505, 103169}}~~

[[Badness]]: 0.122 × 10-3

[[Category:Temperament collections]]

@@ Line 377: / Line 377: @@
 = Rank-3 temperaments =
 == Sasaquinbizo-atriyo (171 &amp; 1106 &amp; 3566) ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: 282475249000/282429536481
+[[Comma list]]: {{monzo| 3 -24 3 10 }} = 282475249000/282429536481
-Mapping: [{{val| 1 0 9 -3 }}, {{val| 0 1 8 0 }}, {{val| 0 0 10 -3 }}]
+[[Mapping]]: [{{val| 1 0 9 -3 }}, {{val| 0 1 8 0 }}, {{val| 0 0 10 -3 }}]
-{{Optimal ET sequence|legend=1| 171, 935, 1106, 1277, 2289, 2460, 3395, 3566, 3737}}
+{{Optimal ET sequence|legend=1| 171, 764, 935, 1106, 1277, 2118, 2289, 2460, 3224, 3395, 3566, 26068, 26239, 29634, 29805, 33200, 33371, 36937, 40503, 44069 }}
-Badness: 0.000281
+[[Badness]]: 0.281 × 10<sup>-3</sup>
 == Saquadtrizo-asepgu (171 &amp; 2019 &amp; 3566) ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: 13841287201/13839609375
+[[Comma list]]: {{monzo| 0 -11 -7 12 }} = 13841287201/13839609375
-Mapping: [{{val| 1 0 0 0 }}, {{val| 0 1 7 5 }}, {{val| 0 0 12 7 }}]
+[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 7 5 }}, {{val| 0 0 12 7 }}]
-{{Optimal ET sequence|legend=1| 171, 1547, 1677, 1718, 1848, 2019, 3395, 3566, 3737}}
+{{Optimal ET sequence|legend=1| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}
-Badness: 0.000135
+[[Badness]]: 0.135 × 10<sup>-3</sup>
 == Laquinzo-aquadquadgu (171 &amp; 441 &amp; 4973) ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000
+[[Comma list]]: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000
-Mapping: [{{val| 1 0 3 11 }}, {{val| 0 1 4 9 }}, {{val| 0 0 5 16 }}]
+[[Mapping]]: [{{val| 1 0 3 11 }}, {{val| 0 1 4 9 }}, {{val| 0 0 5 16 }}]
-{{Optimal ET sequence|legend=1| 171, 270, 441, 612, 783, 4802, 4973, 5144}}
+{{Optimal ET sequence|legend=1| 171, 441, 612, 2696, 2795, 2867, 2966, 3137, 3308, 3407, 3479, 3578, 3749, 3920, 4091, 4190, 4361, 4532, 4703, 4802, 4973, 5144, 10117, 10558, 15531, 15702, 52079, 62637, 67781, 78339 }}
-Badness: 0.000297
+[[Badness]]: 0.297 × 10<sup>-3</sup>
 == Laleruyo (171 &amp; 1547 &amp; 3125) ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: 3955078125/3954653486
+[[Comma list]]: {{monzo| -1 4 11 -11 }} = 3955078125/3954653486
-Mapping: [{{val| 1 3 0 1 }}, {{val| 0 11 0 4 }}, {{val| 0 0 1 1 }}]
+[[Mapping]]: [{{val| 1 3 0 1 }}, {{val| 0 11 0 4 }}, {{val| 0 0 1 1 }}]
-{{Optimal ET sequence|legend=1| 171, 1407, 1547, 1578, 1718, 2783, 2954, 3125, 3296}}
+{{Optimal ET sequence|legend=1| 171, 863, 894, 1034, 1065, 1205, 1236, 1376, 1407, 1547, 1578, 1718, 2612, 2783, 2954, 3125, 12329, 15454, 18579, 21704, 40283, 61987 }}
-Badness: 0.000114
+[[Badness]]: 0.114 × 10<sup>-3</sup>
 == Starscape or Latritriru-ayo ==
@@ Line 427: / Line 427: @@
 [[Mapping]]: [{{val| 1 0 4 0 }}, {{val| 0 1 1 2 }}, {{val| 0 0 9 1 }}]
-{{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634, }} …
+{{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634 }}
-[[Badness]]: 0.000545
+[[Badness]]: 0.545 × 10<sup>-3</sup>
 == Sepbizo-asegu (171 &amp; 3566 &amp; 4973) ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: 6104007655641/6103515625000
+[[Comma list]]: {{monzo| -3 2 -17 14 }} = 6104007655641/6103515625000
-Mapping: [{{val| 1 0 13 16 }}, {{val| 0 1 10 12 }}, {{val| 0 0 14 17 }}]
+[[Mapping]]: [{{val| 1 0 13 16 }}, {{val| 0 1 10 12 }}, {{val| 0 0 14 17 }}]
-{{Optimal ET sequence|legend=1| 171, 1236, 1407, 3566, 3737, 3908, 4802, 4973, 8539, 8710}}
+{{Optimal ET sequence|legend=1| 171, 894, 1065, 1236, 1407, 1578, 3053, 3224, 3395, 3566, 5144, 8368, 8539, 8710, 17249, 20815, 29525, 38064, 67589, 105653 }}
-Badness: 0.000223
+[[Badness]]: 0.223 × 10<sup>-3</sup>
 == Euzenius or Sabiruquinyo ==
+{{See also| Euzenius comma }}
 [[Subgroup]]: 2.3.5.7
@@ Line 449: / Line 451: @@
 [[Mapping]]: [{{val| 1 0 0 -5 }}, {{val| 0 2 0 -13 }}, {{val| 0 0 1 5 }}]
-{{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654, }} …
+{{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654 }}
-[[Badness]]: 0.000205
+[[Badness]]: 0.205 × 10<sup>-3</sup>
 == Quinla-zoyoyo (612 &amp; 1848 &amp; 3125) ==
@@ Line 462: / Line 464: @@
 {{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795 }}
-[[Badness]]: 0.000366
+[[Badness]]: 0.366 × 10<sup>-3</sup>
 == Satwethezo-atritribigu (171 &amp; 1547 &amp; 4973)  ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: {{monzo| 1 -15 -18 23 }}
+[[Comma list]]: {{monzo| 1 -15 -18 23 }}
-Mapping: [{{val| 1 0 9 7 }}, {{val| 0 1 3 3 }}, {{val| 0 0 23 18 }}]
+[[Mapping]]: [{{val| 1 0 9 7 }}, {{val| 0 1 3 3 }}, {{val| 0 0 23 18 }}]
-{{Optimal ET sequence|legend=1| 171, 1547, 4802, 4973, 5144, 6520, 6691, 6862, 11493, 11664, 11835, 18184, 18355, 18526, 25046, 30019, 30190, 48545}}
+{{Optimal ET sequence|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 3255, 3426, 3597, 4460, 4631, 4802, 4973, 5144, 6520, 6691, 11664, 18355, 48374, 48545, 66900, 145464, }} …
-Badness: 0.000114
+[[Badness]]: 0.114 × 10<sup>-3</sup>
 == Trisa-quinbiru-agu (441 &amp; 1848 &amp; 3125) ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: {{monzo| 51 -13 -1 -10 }}
+[[Comma list]]: {{monzo| 51 -13 -1 -10 }}
-Mapping: [{{val| 1 0 1 5 }}, {{val| 0 1 7 -2 }}, {{val| 0 0 10 -1 }}]
+[[Mapping]]: [{{val| 1 0 1 5 }}, {{val| 0 1 7 -2 }}, {{val| 0 0 10 -1 }}]
-{{Optimal ET sequence|legend=1| 441, 1848, 3125, 3566, 4973, 6691, 8098, 8539, 9816, 11664, 14789, 15230, 18355, 21480, 30019, 33144, 39835, 51499}}
+{{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …
-Badness: 0.000263
+[[Badness]]: 0.263 × 10<sup>-3</sup>
+== Quinbisa-quinbizo-alegu (1848 &amp; 11664 &amp; 21480) ==
+[[Subgroup]]: 2.3.5.7
-== Quinbisa-quinbizo-alegu (21480 &amp; 33144 &amp; 103169) ==
+[[Comma list]]: {{monzo| 110 -71 -11 10 }}
-Subgroup: 2.3.5.7
-Comma list: {{monzo| 110 -71 -11 10 }}
+[[Mapping]]: [{{val| 1 0 0 -11 }}, {{val| 0 1 -1 6 }}, {{val| 0 0 10 11 }}]
-Mapping: [{{val| 1 0 0 -11 }}, {{val| 0 1 -1 6 }}, {{val| 0 0 10 11 }}]
+{{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …
-{{Optimal ET sequence|legend=1| 11664, 21480, 33144, 36881, 48545, 54624, 70025, 81689, 91505, 103169}}
+[[Badness]]: 0.122 × 10<sup>-3</sup>
 [[Category:Temperament collections]]