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Very high accuracy temperaments: Difference between revisions

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→Atomic: Moved information from Map of Rank 2 Temps page
Restore POTE tuning by request
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: mapping generators: ~94921875/67108864, ~1125/1024
: mapping generators: ~94921875/67108864, ~1125/1024


[[Optimal tuning]] ([[CTE]]): ~94921875/67108864 = 1\2, ~1125/1024 = 162.7433
[[Optimal tuning]]s:
* [[CTE]]: ~94921875/67108864 = 1\2, ~1125/1024 = 162.7433
* [[POTE]]: ~94921875/67108864 = 1\2, ~1125/1024 = 162.742626


{{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}
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: mapping generators: ~2, ~{{monzo| -38 5 13 }}
: mapping generators: ~2, ~{{monzo| -38 5 13 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| -38 5 13 }} = 132.1949
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~{{monzo| -38 5 13 }} = 132.1949
* [[POTE]]: ~2 = 1\1, ~{{monzo| -38 5 13 }} = 132.194668


{{Optimal ET sequence|legend=1| 9, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}
{{Optimal ET sequence|legend=1| 9, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}
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: mapping generators: ~2, ~{{monzo| 19 -19 5 }}
: mapping generators: ~2, ~{{monzo| 19 -19 5 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 19 -19 5 }} = 594.6345
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~{{monzo| 19 -19 5 }} = 594.6345
* [[POTE]]: ~2 = 1\1, ~{{monzo| 19 -19 5 }} = 594.634565


{{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}
{{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}
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: mapping generators: ~2, ~864/625
: mapping generators: ~2, ~864/625


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~864/625 = 560.546826
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~864/625 = 560.5470
* [[POTE]]: ~2 = 1\1, ~864/625 = 560.546826


{{Optimal ET sequence|legend=1| 15, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
{{Optimal ET sequence|legend=1| 15, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
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: mapping generators: ~2, ~{{monzo| 27 -18 1 }}
: mapping generators: ~2, ~{{monzo| 27 -18 1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 27 -18 1 }} = 950.9814
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~{{monzo| 27 -18 1 }} = 950.9814
* [[POTE]]: ~2 = 1\1, ~{{monzo| 27 -18 1 }} = 950.981594


{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
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: mapping generators: ~2, ~6/5
: mapping generators: ~2, ~6/5


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 315.6479
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~6/5 = 315.6479
* [[POTE]]: ~2 = 1\1, ~6/5 = 315.647919


{{Optimal ET sequence|legend=1| 19, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
{{Optimal ET sequence|legend=1| 19, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
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Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}
Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}


Optimal tuning (CTE): ~2 = 1\1, ~36756909/33554432 = 157.8240
Optimal tunings:
* CTE: ~2 = 1\1, ~36756909/33554432 = 157.8240


{{Optimal ET sequence|legend=1| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
{{Optimal ET sequence|legend=1| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
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: mapping generators: ~2, 7381125/4194304
: mapping generators: ~2, 7381125/4194304


Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5679
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~8388608/7381125 = 221.5679
* [[POTE]]: ~2 = 1\1, ~8388608/7381125 = 221.567899


{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
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Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}
Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}


Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5680
Optimal tunings:
* CTE: ~2 = 1\1, ~8388608/7381125 = 221.5680
* POTE: ~2 = 1\1, ~8388608/7381125 = 221.568031


{{Optimal ET sequence|legend=1| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
{{Optimal ET sequence|legend=1| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
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Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}
Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}


Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5681
Optimal tunings:
* CTE: ~2 = 1\1, ~8388608/7381125 = 221.5681
* POTE: ~2 = 1\1, ~8388608/7381125 = 221.568139


{{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}
{{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}
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: mapping generators: ~2, ~{{monzo| -6 23 -13 }}
: mapping generators: ~2, ~{{monzo| -6 23 -13 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| -6 23 -13 }} = 322.8013
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~{{monzo| -6 23 -13 }} = 322.8013
* [[POTE]]: ~2 = 1\1, ~{{monzo| -6 23 -13 }} = 322.801358


{{Optimal ET sequence|legend=1| 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
{{Optimal ET sequence|legend=1| 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
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: mapping generators: ~2, ~{{monzo| -45 7 15 }}
: mapping generators: ~2, ~{{monzo| -45 7 15 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 46 -7 -15 }} = 91.5310
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~{{monzo| 46 -7 -15 }} = 91.5310
* [[POTE]]: ~2 = 1\1, ~{{monzo| 46 -7 -15 }} = 91.531001


{{Optimal ET sequence|legend=1| 13, 105, 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}
{{Optimal ET sequence|legend=1| 13, 105, 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}
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: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9553
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.9553


{{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}
{{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}
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Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}
Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.955


{{Optimal ET sequence|legend=1| 306, 665, 1636, 2301, 2966 }}
{{Optimal ET sequence|legend=1| 306, 665, 1636, 2301, 2966 }}
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Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}
Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9548
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.9548


{{Optimal ET sequence|legend=1| 306d, 359cd, 665 }}
{{Optimal ET sequence|legend=1| 306d, 359cd, 665 }}
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: mapping generators: ~2, ~6561/4000
: mapping generators: ~2, ~6561/4000


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~8000/6561 = 343.2961
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~8000/6561 = 343.2961
* [[POTE]]: ~2 = 1\1, ~8000/6561 = 343.296098


{{Optimal ET sequence|legend=1| 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}
{{Optimal ET sequence|legend=1| 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}
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: mapping generators: ~2, ~{{monzo| -23 -4 13 }}
: mapping generators: ~2, ~{{monzo| -23 -4 13 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 24 4 -13 }} = 185.7542
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~{{monzo| 24 4 -13 }} = 185.7542
* [[POTE]]: ~2 = 1\1, ~{{monzo| 24 4 -13 }} = 185.754179


{{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}
{{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}
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: mapping generators: ~{{monzo| -67 35 5 }}, ~3
: mapping generators: ~{{monzo| -67 35 5 }}, ~3


[[Optimal tuning]] ([[CTE]]): ~{{monzo| -67 35 5 }} = 1\12, ~3/2 = 701.9552 (or ~32805/32768 = 1.9552)
[[Optimal tuning]]s:
* [[CTE]]: ~{{monzo| -67 35 5 }} = 1\12, ~3/2 = 701.9552 (~32805/32768 = 1.9552)
* [[POTE]]: ~{{monzo| -67 35 5 }} = 1\12, ~3/2 = 701.955162 (~32805/32768 = 1.955162)


{{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}
{{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}
Line 299: Line 331:
Mapping: {{mapping| 12 0 161 338 | 0 1 -7 -16 }}
Mapping: {{mapping| 12 0 161 338 | 0 1 -7 -16 }}


Optimal tuning (CTE): ~30375/28672 = 1\12, ~3/2 = 701.9499 (or ~32805/32768 = 1.9499)
Optimal tunings:
* CTE: ~30375/28672 = 1\12, ~3/2 = 701.9499 (or ~32805/32768 = 1.9499)
* POTE: ~30375/28672 = 1\12, ~3/2 = 701.949608 (or ~32805/32768 = 1.949608)


{{Optimal ET sequence|legend=1| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
{{Optimal ET sequence|legend=1| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
Line 312: Line 346:
Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}


Optimal tuning (CTE): ~30375/28672 = 1\12, ~3/2 = 701.9485 (or ~32805/32768 = 1.9485)
Optimal tunings:
* CTE: ~30375/28672 = 1\12, ~3/2 = 701.9485 (or ~32805/32768 = 1.9485)
* POTE: ~30375/28672 = 1\12, ~3/2 = 701.947988 (or ~32805/32768 = 1.947988)


{{Optimal ET sequence|legend=1| 12, …, 600e, 612, 1236, 1848 }}
{{Optimal ET sequence|legend=1| 12, …, 600e, 612, 1236, 1848 }}
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== Revopentic (2.3.7) ==
== Revopentic (2.3.7) ==
{{Main|Revopentisma}}
{{See also| Revopentisma }}
 
Subgroup: 2.3.7
Subgroup: 2.3.7


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{{Mapping|legend=2| 1 12 5 | 0 -19 -4 }}
{{Mapping|legend=2| 1 12 5 | 0 -19 -4 }}


: mapping generators: ~2 = 1\1, 24576/16807 = 657.792
: mapping generators: ~2 = 1\1, 24576/16807


[[Optimal tuning]] ([[CTE]]): 24576/16807 = 657.792
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~24576/16807 = 657.792


[[Support]]ing [[ET]]s: {{EDOs|135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794}}
[[Support]]ing [[ET]]s: {{EDOs| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794 }}


Badness (Sintel's finder): 0.070
Badness (Sintel's TE logflat): 0.070


=== Revopent ===
=== Revopent ===
Described as the 1848 & 3125 temperament.
Revopent can be described as the 1848 & 3125 temperament.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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Mapping: {{mapping| 1 12 -155 5 | 0 -19 287 -4 }}
Mapping: {{mapping| 1 12 -155 5 | 0 -19 287 -4 }}


Optimal tuning (CTE): ~24576/16807 = 657.792
Optimal tunings:
* CTE: ~24576/16807 = 657.792


{{Optimal ET sequence|legend=1| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
{{Optimal ET sequence|legend=1| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
Line 360: Line 399:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.9578
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1\1, ~3/2 = 701.9578


{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
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