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Catalog of rank-4 temperaments: Difference between revisions

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+CTE tunings. POTE -> CWE (This is one of the pages that didn't have tuning information to start with)
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{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 0 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803
: mapping generators: ~2, ~3, ~5, ~7
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 703.961, ~5/4 = 382.009, ~7/4 = 968.826
* [[CWE]]: ~2 = 1\1, ~3/2 = 704.475, ~5/4 = 383.076, ~7/4 = 969.890


{{Optimal ET sequence|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
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: mapping generators: ~2, ~3, ~11/10, ~7
: mapping generators: ~2, ~3, ~11/10, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.4578, ~11/10 = 157.7466, ~7/4 = 966.9589
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.602, ~11/10 = 157.450, ~7/4 = 968.826
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.985, ~11/10 = 157.610, ~7/4 = 967.819


{{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }}
{{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }}
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: mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.0449, ~5/4 = 389.7641, ~7/4 = 972.1113
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.955, ~5/4 = 388.882, ~7/4 = 970.703
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.587, ~5/4 = 389.393, ~7/4 = 971.520


{{Optimal ET sequence|legend=1| 22, 31, 46, 53, 58, 80, 111 }}
{{Optimal ET sequence|legend=1| 22, 31, 46, 53, 58, 80, 111 }}
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: mapping generators: ~2, ~11/9, ~5, ~7
: mapping generators: ~2, ~11/9, ~5, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~11/9 = 350.572, ~5/4 = 386.314, ~7/4 = 968.826
* [[CWE]]: ~2 = 1\1, ~11/9 = 350.549, ~5/4 = 386.239, ~7/4 = 968.735


{{Optimal ET sequence|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}
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: mapping generators: ~2, ~3, ~5, ~11
: mapping generators: ~2, ~3, ~5, ~11


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.873, ~5/4 = 386.213, ~11/8 = 550.306
* [[POTE]]: ~2 = 1\1, ~3/2 = 702.896, ~5/4 = 386.784, ~11/8 = 551.068


{{Optimal ET sequence|legend=1| 12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f }}
{{Optimal ET sequence|legend=1| 12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f }}
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{{Mapping|legend=1| 1 0 0 0 7 12 |0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }}
{{Mapping|legend=1| 1 0 0 0 7 12 |0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.603, ~5/4 = 385.644, ~7/4 = 967.903


{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }}
{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }}
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: mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.8345, ~5/4 = 387.7585, ~7/4 = 969.8722
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 703.576, ~5/4 = 386.314, ~7/4 = 968.126
* [[CWE]]: ~2 = 1\1, ~3/2 = 703.743, ~5/4 = 387.245, ~7/4 = 969.048


{{Optimal ET sequence|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }}
{{Optimal ET sequence|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }}
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{{Mapping|legend=1| 1 0 0 0 0 | 0 1 0 2 2 | 0 0 1 -1 -1 | 0 0 0 3 4 }}
{{Mapping|legend=1| 1 0 0 0 0 | 0 1 0 2 2 | 0 0 1 -1 -1 | 0 0 0 3 4 }}


: Mapping generators: ~2, ~3, ~5, ~11/7
: mapping generators: ~2, ~3, ~5, ~11/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1＼1, ~3 = 1902.0307, ~5 = 2786.2325, ~11/7 = 783.5074
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.031, ~5/4 = 386.233, ~11/7 = 783.508
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.031, ~5/4 = 386.232, ~11/7 = 783.507


{{Optimal ET sequence|legend=1|12, 46, 58, 72, 118, 121, 130, 190, 202, 239, 248, 311}}
{{Optimal ET sequence|legend=1| 12, 21, 23de, 26, 37, 46, 58, 72, 118, 130, 190, 239, 311, 441, 559, 752e, 870 }}


=== Hensquary ===
=== Hensquary ===
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: Mapping generators: ~2, ~3, ~5, ~11/7
: Mapping generators: ~2, ~3, ~5, ~11/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1＼1, ~3 = 1902.4103, ~5 = 2786.9909, ~11/7 = 783.9209
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.072, ~5/4 = 386.528, ~11/7 = 783.823
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.253, ~5/4 = 386.776, ~11/7 = 783.875


{{Optimal ET sequence|legend=1|9, 12f, 26, 37, 46, 49f, 58, 63, 72, 84, 118f, 121, 130}}
{{Optimal ET sequence|legend=1| 26, 37, 46, 58, 72, 121, 130, 193, 239, 251e, 323e, 369 }}


=== Ekasquary ===
=== Ekasquary ===
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: Mapping generators: ~2, ~3, ~5, ~11/7
: Mapping generators: ~2, ~3, ~5, ~11/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1＼1, ~3 = 1901.9525, ~5 = 2786.1388, ~11/7 = 783.5477
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.952, ~5/4 = 386.139, ~11/7 = 783.188
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.952, ~5/4 = 386.139, ~11/7 = 783.188


{{Optimal ET sequence|legend=1|9, 12, 46f, 49f, 58, 60e, 63, 72, 118, 121, 130, 190, 193, 248, 311, 320, 383, 441}}
{{Optimal ET sequence|legend=1| 46f, 49f, 58, 72, 118, 121, 130, 190, 193, 248, 311, 441, 752e, 1072 }}


== Semicanousmic (14641/14580) ==
== Semicanousmic (14641/14580) ==
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: mapping generators: ~2, ~3, ~18/11, ~7
: mapping generators: ~2, ~3, ~18/11, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2503, ~18/11 = 854.5421, ~7/4 = 968.6866
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.334, ~18/11 = 854.555, ~7/4 = 968.826
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.292, ~18/11 = 854.548, ~7/4 = 968.756


{{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}
{{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}
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Mapping: {{mapping| 1 0 2 0 1 -6 | 0 1 2 0 2 3 | 0 0 -4 0 -1 3 | 0 0 0 1 0 1 }}
Mapping: {{mapping| 1 0 2 0 1 -6 | 0 1 2 0 2 3 | 0 0 -4 0 -1 3 | 0 0 0 1 0 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.4931, ~18/11 = 854.6400, ~7/4 = 969.0099
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 702.469, ~18/11 = 854.644, ~7/4 = 968.959
* CWE: ~2 = 1\1, ~3/2 = 702.483, ~18/11 = 854.642, ~7/4 = 968.989


{{Optimal ET sequence|legend=1| 87, 111, 181, 198, 323, 410 }}
{{Optimal ET sequence|legend=1| 87, 111, 181, 198, 323, 410 }}
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Mapping: {{mapping| 1 0 2 0 1 -6 -4 | 0 1 2 0 2 3 6 | 0 0 -4 0 -1 3 -2 | 0 0 0 1 0 1 0 }}
Mapping: {{mapping| 1 0 2 0 1 -6 -4 | 0 1 2 0 2 3 6 | 0 0 -4 0 -1 3 -2 | 0 0 0 1 0 1 0 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.4099, ~18/11 = 854.6338, ~7/4 = 969.0228
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 702.413, ~18/11 = 854.633, ~7/4 = 969.032
* CWE: ~2 = 1\1, ~3/2 = 702.411, ~18/11 = 854.634, ~7/4 = 969.026


{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }}
{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }}
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Mapping: {{mapping| 1 0 2 0 1 -6 -4 -4 | 0 1 2 0 2 3 6 7 | 0 0 -4 0 -1 3 -2 -4 | 0 0 0 1 0 1 0 0 }}
Mapping: {{mapping| 1 0 2 0 1 -6 -4 -4 | 0 1 2 0 2 3 6 7 | 0 0 -4 0 -1 3 -2 -4 | 0 0 0 1 0 1 0 0 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.3413, ~18/11 = 854.6472, ~7/4 = 968.9734
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 702.368, ~18/11 = 854.639, ~7/4 = 969.075
* CWE: ~2 = 1\1, ~3/2 = 702.351, ~18/11 = 854.644, ~7/4 = 969.010


{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }}
{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }}
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: mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2681, ~5/4 = 386.4785, ~7/4 = 968.9552
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.213, ~5/4 = 386.314, ~7/4 = 968.736
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.244, ~5/4 = 386.406, ~7/4 = 968.859


{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}
{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}
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{{Mapping|legend=1| 1 0 0 0 -8 -13 | 0 1 0 0 9 12 | 0 0 1 0 0 -1 | 0 0 0 1 -1 0 }}
{{Mapping|legend=1| 1 0 0 0 -8 -13 | 0 1 0 0 9 12 | 0 0 1 0 0 -1 | 0 0 0 1 -1 0 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2721, ~5/4 = 386.4790, ~7/4 = 968.9705
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.228, ~5/4 = 386.284, ~7/4 = 968.789
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.254, ~5/4 = 386.401, ~7/4 = 968.898


{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}
{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}
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