Very high accuracy temperaments: Difference between revisions
→Atomic: correct link |
+optimal tunings for rank-3 temps, by request from FB |
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{{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 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 }} | ||
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[[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 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 }} | ||
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{{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 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 }} | ||
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[[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 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 }} | ||
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[[Comma list]]: 645700815/645657712 | [[Comma list]]: 645700815/645657712 | ||
{{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 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 }} | ||
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[[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 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 }} | ||
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{{Mapping|legend=1| 1 0 0 -5 | 0 2 0 -13 | 0 0 1 5 }} | {{Mapping|legend=1| 1 0 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 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 }} | ||
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[[Comma list]]: {{monzo| 1 -15 -18 23 }} | [[Comma list]]: {{monzo| 1 -15 -18 23 }} | ||
{{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 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, }} … | ||
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[[Comma list]]: {{monzo| 51 -13 -1 -10 }} | [[Comma list]]: {{monzo| 51 -13 -1 -10 }} | ||
{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 10 | {{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 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, }} … | ||
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[[Comma list]]: {{monzo| 110 -71 -11 10 }} | [[Comma list]]: {{monzo| 110 -71 -11 10 }} | ||
{{Mapping|legend=1| 1 0 0 -11 | 0 1 -1 6 | 0 0 10 11 }} | {{Mapping|legend=1| 1 0 0 -11 | 0 1 -1 6 | 0 0 -10 -11 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~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, }} … | ||