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Very high accuracy temperaments: Difference between revisions

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= Rank-3 temperaments =
= Rank-3 temperaments =
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


{{Mapping|legend=1| 1 0 9 -3 | 0 1 8 0 | 0 0 10 -3 }}
{{Mapping|legend=1| 1 0 9 -3 | 0 1 8 0 | 0 0 10 -3 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9624, ~6561/3430 = 1122.9387
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9624, ~6561/3430 = 1122.9387


{{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 }}
{{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]]: 0.281 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.24


== Saquadtrizo-asepgu (171 &amp; 2019 &amp; 3566) ==
== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 -12 -7 }}
{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 -12 -7 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9584, ~16807/10125 = 877.2825
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9584, ~16807/10125 = 877.2825


{{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 }}
{{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]]: 0.135 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.595


== Laquinzo-aquadquadgu (171 &amp; 441 &amp; 4973) ==
== 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|legend=1| 1 0 3 11 | 0 1 4 9 | 0 0 5 16 }}
{{Mapping|legend=1| 1 0 3 11 | 0 1 4 9 | 0 0 5 16 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9501, ~250/189 = 484.2956
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9501, ~250/189 = 484.2956


{{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 }}
{{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]]: 0.297 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.31


== Laleruyo (171 &amp; 1547 &amp; 3125) ==
== Laleruyo (171 & 1547 & 3125) ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


{{Mapping|legend=1| 1 3 0 1 | 0 -11 0 -4 | 0 0 1 1 }}
{{Mapping|legend=1| 1 3 0 1 | 0 -11 0 -4 | 0 0 1 1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~375/343 = 154.3678, ~5/4 = 386.3070
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~375/343 = 154.3678, ~5/4 = 386.3070


{{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 }}
{{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]]: 0.114 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.501


== Starscape or Latritriru-ayo ==
== Starscape or Latritriru-ayo ==
Line 512: Line 512:
{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 -9 -1 }}
{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 -9 -1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9514, ~9/7 = 435.0709
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9514, ~9/7 = 435.0709


{{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]]: 0.545 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.240


== Sepbizo-asegu (171 &amp; 3566 &amp; 4973) ==
== Sepbizo-asegu (171 & 3566 & 4973) ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 -14 -17 }}
{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 -14 -17 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9548, ~31250/16807 = 1073.8021
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9548, ~31250/16807 = 1073.8021


{{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 }}
{{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]]: 0.223 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.982


== Euzenius or Sabiruquinyo ==
== Euzenius or Sabiruquinyo ==
Line 540: Line 540:
{{Mapping|legend=1| 1 1 0 -5 | 0 2 0 -13 | 0 0 1 5 }}
{{Mapping|legend=1| 1 1 0 -5 | 0 2 0 -13 | 0 0 1 5 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6250/5103 = 350.9787, ~5/4 = 386.3099
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~6250/5103 = 350.9787, ~5/4 = 386.3099


{{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]]: 0.205 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.0902


== Nommismic or Quinla-zoyoyo ==
== Nommismic or Quinla-zoyoyo ==
Line 555: Line 555:
{{Mapping|legend=1| 1 0 0 55 | 0 1 0 -30 | 0 0 1 -2 }}
{{Mapping|legend=1| 1 0 0 55 | 0 1 0 -30 | 0 0 1 -2 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9516, ~5/4 = 386.3132
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9516, ~5/4 = 386.3132


{{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …
{{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …


[[Badness]]: 0.366 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.62


== Satwethezo-atritribigu (171 &amp; 1547 &amp; 4973)  ==
== Satwethezo-atritribigu (171 & 1547 & 4973)  ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 568: Line 568:
{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 -23 -18 }}
{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 -23 -18 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9551, ~56953125/40353607 = 596.5022
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9551, ~56953125/40353607 = 596.5022


{{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, }} …
{{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]]: 0.114 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.505


== Technologismic or Trisa-quinbiru-agu (441 &amp; 1848 &amp; 3125)  ==
== Technologismic or Trisa-quinbiru-agu ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 581: Line 581:
{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 -10 1 }}
{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 -10 1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9553, ~63/32 = 1172.7374
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9553, ~63/32 = 1172.7374


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


[[Badness]]: 0.263 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.116


== Quinbisa-quinbizo-alegu (1848 &amp; 11664 &amp; 21480) ==
== Quinbisa-quinbizo-alegu (1848 & 11664 & 21480) ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 594: Line 594:
{{Mapping|legend=1| 1 0 0 -11 | 0 1 9 17 | 0 0 -10 -11 }}
{{Mapping|legend=1| 1 0 0 -11 | 0 1 9 17 | 0 0 -10 -11 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.955, ~32805/28672 = 233.128
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.955, ~32805/28672 = 233.128


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


[[Badness]]: 0.122 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.538


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
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