Catalog of rank-4 temperaments: Difference between revisions
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{{Mapping|legend=1| 1 0 0 0 -2 | 0 1 0 0 2 | 0 0 1 0 1 | 0 0 0 1 0 }} | {{Mapping|legend=1| 1 0 0 0 -2 | 0 1 0 0 2 | 0 0 1 0 1 | 0 0 0 1 0 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 694.823, ~5/4 = 378.660, ~7/4 = 968.826 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 693.197, ~5/4 = 376.082, ~7/4 = 965.060 | ||
{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 26, 45 }} | {{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 26, 45 }} | ||
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{{Mapping|legend=1| 1 0 0 0 1 | 0 1 0 0 -2 | 0 0 1 0 0 | 0 0 0 1 2 }} | {{Mapping|legend=1| 1 0 0 0 1 | 0 1 0 0 -2 | 0 0 1 0 0 | 0 0 0 1 2 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 700.306, ~5/4 = 386.314, ~7/4 = 974.000 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 700.060, ~5/4 = 385.931, ~7/4 = 973.388 | ||
{{Optimal ET sequence|legend=1| 5, 8d, 9, 12, 17c, 19e, 22, 31, 53, 84e, 96, 127 }} | {{Optimal ET sequence|legend=1| 5, 8d, 9, 12, 17c, 19e, 22, 31, 53, 84e, 96, 127 }} | ||
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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 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 703.961, ~5/4 = 382.009, ~7/4 = 968.826 | ||
* [[CWE]]: ~2 = | * [[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|legend=1| 1 0 1 0 2 | 0 1 1 0 1 | 0 0 -2 0 -1 | 0 0 0 1 0 }} | {{Mapping|legend=1| 1 0 1 0 2 | 0 1 1 0 1 | 0 0 -2 0 -1 | 0 0 0 1 0 }} | ||
: | : Mapping generators: ~2, ~3, ~11/10, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 702.602, ~11/10 = 157.450, ~7/4 = 968.826 | ||
* [[CWE]]: ~2 = | * [[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|legend=1| 1 0 0 0 -4 | 0 1 0 0 0 | 0 0 1 0 2 | 0 0 0 1 1 }} | {{Mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 0 | 0 0 1 0 2 | 0 0 0 1 1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 701.955, ~5/4 = 388.882, ~7/4 = 970.703 | ||
* [[CWE]]: ~2 = | * [[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 }} | ||
| Line 96: | Line 96: | ||
{{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0 }} | {{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0 }} | ||
: | : Mapping generators: ~2, ~11/9, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~11/9 = 350.572, ~5/4 = 386.314, ~7/4 = 968.826 | ||
* [[CWE]]: ~2 = | * [[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 }} | ||
| Line 113: | Line 113: | ||
{{Mapping|legend=1| 1 0 1 0 0 | 0 1 0 0 0 | 0 0 2 0 1 | 0 0 0 1 1 }} | {{Mapping|legend=1| 1 0 1 0 0 | 0 1 0 0 0 | 0 0 2 0 1 | 0 0 0 1 1 }} | ||
: | : Mapping generators: ~2, ~3, ~11/7, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 701.955, ~11/7 = 792.479, ~7/4 = 964.861 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 701.753, ~5/4 = 792.335, ~7/4 = 964.527 | ||
{{Optimal ET sequence|legend=1| 9, 12, 15, 23de, 24, 26, 27e, 38d, 41, 91, 106d }} | {{Optimal ET sequence|legend=1| 9, 12, 15, 23de, 24, 26, 27e, 38d, 41, 91, 106d }} | ||
| Line 130: | Line 130: | ||
{{Mapping|legend=1| 1 0 0 10 0 5 | 0 1 0 -6 0 -3 | 0 0 1 1 0 0 | 0 0 0 0 1 1 }} | {{Mapping|legend=1| 1 0 0 10 0 5 | 0 1 0 -6 0 -3 | 0 0 1 1 0 0 | 0 0 0 0 1 1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~11 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 702.873, ~5/4 = 386.213, ~11/8 = 550.306 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~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 }} | ||
| Line 147: | Line 147: | ||
{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 0 0 2 | 0 0 1 0 -1 | 0 0 0 1 2 }} | {{Mapping|legend=1| 1 0 0 0 -3 | 0 1 0 0 2 | 0 0 1 0 -1 | 0 0 0 1 2 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.620, ~5/4 = 386.673, ~7/4 = 967.775 | |||
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.496, ~5/4 = 386.432, ~7/4 = 967.588 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | * [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~3 = {{monzo| 1/2 2/3 1/6 -1/3 1/6 }}, ~5 = {{monzo| 0 0 1 0 0 }}, ~7 = {{monzo| 1 -2/3 1/3 1/3 1/3 }} | ||
: | |||
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.9/7.11 | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.9/7.11 | ||
| Line 167: | Line 170: | ||
Lattice basis: | Lattice basis: | ||
: 3/2 length = 1.2263, 14/11 length = 1.4629, 21/16 length = 1.4657 | : 3/2 length = 1.2263, 14/11 length = 1.4629, 21/16 length = 1.4657 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.880, ~5/4 = 386.523, ~7/4 = 967.841 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[13-odd-limit]] | * [[13-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 0 }}, ~3 = {{monzo| 5/3 0 1/3 -1/3 -1/3 1/3 }}, ~5 = {{monzo| 1/6 0 5/6 2/3 -5/6 1/3 }}, ~7 = {{monzo| 0 0 0 1 0 0 }} | ||
: | |||
: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/10, 8/7, 16/13 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 11/10, 8/7, 16/13 | ||
* [[15-odd-limit]] | * [[15-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 0 }}, ~3 = {{monzo| 5/4 1/4 1/4 -1/4 -1/4 1/4 }}, ~5 = {{monzo| 5/4 -3/4 5/4 -1/4 -1/4 1/4 }}, ~7 = {{monzo| 17/8 -11/8 5/8 -1/8 3/8 1/8 }} | ||
: | |||
: [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 6/5, 11/9 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 6/5, 11/9 | ||
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{{Mapping|legend=1| 1 0 0 0 -3 1 | 0 1 0 0 2 -3 | 0 0 1 0 -1 2 | 0 0 0 1 2 1 }} | {{Mapping|legend=1| 1 0 0 0 -3 1 | 0 1 0 0 2 -3 | 0 0 1 0 -1 2 | 0 0 0 1 2 1 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.175, ~5/4 = 387.330, ~7/4 = 968.480 | |||
{{Optimal ET sequence|legend=1| 12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf }} | {{Optimal ET sequence|legend=1| 12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf }} | ||
| Line 193: | Line 198: | ||
{{Mapping|legend=1| 1 0 0 0 -3 2 | 0 1 0 0 2 -1 | 0 0 1 0 -1 -1 | 0 0 0 1 2 2 }} | {{Mapping|legend=1| 1 0 0 0 -3 2 | 0 1 0 0 2 -1 | 0 0 1 0 -1 -1 | 0 0 0 1 2 2 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.601, ~5/4 = 387.137, ~7/4 = 966.418 | |||
{{Optimal ET sequence|legend=1| 10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232 }} | {{Optimal ET sequence|legend=1| 10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232 }} | ||
| Line 202: | Line 209: | ||
{{Mapping|legend=1| 1 0 0 0 -3 11 | 0 1 0 0 2 -4 | 0 0 1 0 -1 2 | 0 0 0 1 2 -2 }} | {{Mapping|legend=1| 1 0 0 0 -3 11 | 0 1 0 0 2 -4 | 0 0 1 0 -1 2 | 0 0 0 1 2 -2 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 700.555, ~5/4 = 387.816, ~7/4 = 967.984 | |||
{{Optimal ET sequence|legend=1| 17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }} | {{Optimal ET sequence|legend=1| 17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }} | ||
| Line 211: | Line 220: | ||
{{Mapping|legend=1| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }} | {{Mapping|legend=1| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 700.606, ~5/4 = 387.655, ~7/4 = 967.876 | |||
{{Optimal ET sequence|legend=1| 17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef }} | {{Optimal ET sequence|legend=1| 17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef }} | ||
| Line 221: | Line 232: | ||
{{Mapping|legend=1| 1 0 0 0 -3 -3 | 0 1 0 0 2 2 | 0 0 1 1 1 1 | 0 0 0 2 4 5 }} | {{Mapping|legend=1| 1 0 0 0 -3 -3 | 0 1 0 0 2 2 | 0 0 1 1 1 1 | 0 0 0 2 4 5 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~13/11 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.611, ~5/4 = 386.882, ~13/11 = 290.287 | |||
{{Optimal ET sequence|legend=1| 12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d }} | {{Optimal ET sequence|legend=1| 12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d }} | ||
| Line 234: | Line 247: | ||
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }} | {{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[ | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.363, ~5/4 = 385.439, ~7/4 = 967.547 | |||
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.693, ~5/4 = 385.149, ~7/4 = 967.300 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | * [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~3 = {{monzo| 0 1 0 0 0 }}, ~5 = {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, ~7 = {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }} | ||
: | |||
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.3.7/5.11/5 | : [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.3.7/5.11/5 | ||
| Line 253: | Line 267: | ||
{{Mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }} | {{Mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }} | ||
Lattice basis: | Lattice basis: | ||
: 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247 | : 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.629, ~5/4 = 385.219, ~7/4 = 967.741 | |||
[[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Keenanismic family --> | [[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Keenanismic family --> | ||
* [[13-odd-limit|13-]] and [[15-odd-limit]] | * [[13-odd-limit|13-]] and [[15-odd-limit]]: ~2 = {{val| 1 0 0 0 0 0 }}, ~3 = {{val| 0 1 0 0 0 0 }}, ~5 = {{val| 2/3 4/3 1/3 0 0 -1/3 }}, ~7 = {{val| 19/6 -1/6 -1/6 1/2 -1/2 1/6 }} | ||
: | |||
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.3.11/7.13/5 | : [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.3.11/7.13/5 | ||
| Line 275: | Line 288: | ||
{{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }} | {{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }} | ||
[[ | [[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.358, ~5/4 = 385.674, ~7/4 = 967.452 | ||
{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }} | {{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }} | ||
| Line 287: | Line 300: | ||
{{Mapping|legend=1| 1 0 0 0 7 1 | 0 1 0 0 1 -3 | 0 0 1 0 -1 2 | 0 0 0 1 -1 1 }} | {{Mapping|legend=1| 1 0 0 0 7 1 | 0 1 0 0 1 -3 | 0 0 1 0 -1 2 | 0 0 0 1 -1 1 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.205, ~5/4 = 386.715, ~7/4 = 967.646 | |||
{{Optimal ET sequence|legend=1| 19, 22, 26, 31, 46, 53, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 495bdeefff, 545bddeefff, 598bcdeeefff }} | {{Optimal ET sequence|legend=1| 19, 22, 26, 31, 46, 53, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 495bdeefff, 545bddeefff, 598bcdeeefff }} | ||
| Line 297: | Line 312: | ||
[[Comma list]]: 352/351, 385/384 | [[Comma list]]: 352/351, 385/384 | ||
{{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]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829 | ||
* [[CWE]]: ~2 = | * [[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 }} | ||
| Line 313: | Line 328: | ||
{{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 3 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 -3 }} | {{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 3 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 -3 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.761, ~5/4 = 385.159, ~7/4 = 966.298 | |||
{{Optimal ET sequence|legend=1| 9, 15, 22, 26, 31f, 37, 41, 46, 63, 72, 87, 159 }} | {{Optimal ET sequence|legend=1| 9, 15, 22, 26, 31f, 37, 41, 46, 63, 72, 87, 159 }} | ||
| Line 325: | Line 342: | ||
{{Mapping|legend=1| 1 0 0 0 7 7 | 0 1 0 0 1 1 | 0 0 1 1 -2 -2 | 0 0 0 2 -2 -1 }} | {{Mapping|legend=1| 1 0 0 0 7 7 | 0 1 0 0 1 1 | 0 0 1 1 -2 -2 | 0 0 0 2 -2 -1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~13/11 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.368, ~5/4 = 385.416, ~13/11 = 291.066 | |||
{{Optimal ET sequence|legend=1| 34, 37, 41, 46, 53, 87, 103, 140, 190, 243e, 330e, 520de, 573dee }} | {{Optimal ET sequence|legend=1| 34, 37, 41, 46, 53, 87, 103, 140, 190, 243e, 330e, 520de, 573dee }} | ||
| Line 338: | Line 357: | ||
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 3 | 0 0 1 0 1 | 0 0 0 1 -2 }} | {{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 3 | 0 0 1 0 1 | 0 0 0 1 -2 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 701.6167, ~5/4 = 386.0717, ~7/4 = 969.5334 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 701.6950, ~5/4 = 386.1796, ~7/4 = 969.6366 | ||
{{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }} | {{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }} | ||
| Line 355: | Line 374: | ||
{{Mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 0 3 6 | 0 0 1 0 1 0 | 0 0 0 1 -2 -1 }} | {{Mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 0 3 6 | 0 0 1 0 1 0 | 0 0 0 1 -2 -1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 701.6687, ~5/4 = 386.0441, ~7/4 = 969.5668 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 701.7230, ~5/4 = 386.1818, ~7/4 = 969.6607 | ||
{{Optimal ET sequence|legend=1| 12e, 14cf, 17c, 19, 22f, 31f, 39df, 41, 53, 58, 72, 111, 130, 183, 224, 354, 578, 985d, 1267ddef }} | {{Optimal ET sequence|legend=1| 12e, 14cf, 17c, 19, 22f, 31f, 39df, 41, 53, 58, 72, 111, 130, 183, 224, 354, 578, 985d, 1267ddef }} | ||
| Line 372: | Line 391: | ||
{{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 0 0 3 3 | 0 0 1 1 -1 -1 | 0 0 0 2 -4 -3 }} | {{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 0 0 3 3 | 0 0 1 1 -1 -1 | 0 0 0 2 -4 -3 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~13/11 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.284, ~5/4 = 386.211, ~13/11 = 291.733 | |||
{{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }} | {{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }} | ||
| Line 384: | Line 405: | ||
{{Mapping|legend=1| 1 0 0 0 2 -4 | 0 1 0 0 3 -1 | 0 0 1 0 1 4 | 0 0 0 1 -2 0 }} | {{Mapping|legend=1| 1 0 0 0 2 -4 | 0 1 0 0 3 -1 | 0 0 1 0 1 4 | 0 0 0 1 -2 0 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.702, ~5/4 = 385.631, ~7/4 = 969.467 | |||
{{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }} | {{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }} | ||
| Line 396: | Line 419: | ||
{{Mapping|legend=1| 1 0 0 0 2 -1 | 0 2 0 0 6 3 | 0 0 1 0 1 1 | 0 0 0 1 -2 0 }} | {{Mapping|legend=1| 1 0 0 0 2 -1 | 0 2 0 0 6 3 | 0 0 1 0 1 1 | 0 0 0 1 -2 0 }} | ||
: | : Mapping generators: ~2, ~26/15, ~5, ~7 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~26/15 = 950.906, ~5/4 = 386.474, ~7/4 = 969.892 | |||
{{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }} | {{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }} | ||
| Line 409: | Line 434: | ||
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 -4 | 0 0 1 0 0 | 0 0 0 1 1 }} | {{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 -4 | 0 0 1 0 0 | 0 0 0 1 1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 703.576, ~5/4 = 386.314, ~7/4 = 968.126 | ||
* [[CWE]]: ~2 = | * [[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 }} | ||
| Line 425: | Line 450: | ||
{{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 -4 -7 | 0 0 1 0 0 0 | 0 0 0 1 1 1 }} | {{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 -4 -7 | 0 0 1 0 0 0 | 0 0 0 1 1 1 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 703.786, ~5/4 = 386.314, ~7/4 = 967.665 | |||
{{Optimal ET sequence|legend=1| 12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff }} | {{Optimal ET sequence|legend=1| 12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff }} | ||
| Line 437: | Line 464: | ||
{{Mapping|legend=1| 1 0 0 2 0 1 | 0 1 0 0 0 0 | 0 0 1 1 1 1 | 0 0 0 4 -3 1 }} | {{Mapping|legend=1| 1 0 0 2 0 1 | 0 1 0 0 0 0 | 0 0 1 1 1 1 | 0 0 0 4 -3 1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~13/10 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.955, ~5/4 = 386.699, ~13/10 = 454.558 | |||
{{Optimal ET sequence|legend=1| 16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e }} | {{Optimal ET sequence|legend=1| 16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e }} | ||
| Line 448: | Line 477: | ||
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 1 2 | 0 0 1 0 -1 | 0 0 0 2 1 }} | {{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 1 2 | 0 0 1 0 -1 | 0 0 0 2 1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~55/36 | ||
[[Optimal tuning]]: | |||
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.998, ~5/4 = 386.252, ~55/36 = 733.436 | |||
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.978, ~5/4 = 386.232, ~55/36 = 733.430 | |||
{{Optimal ET sequence|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }} | {{Optimal ET sequence|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }} | ||
| Line 459: | Line 492: | ||
{{Mapping|legend=1| 1 0 0 0 6 | 0 1 0 0 -6 | 0 0 1 0 3 | 0 0 0 1 0 }} | {{Mapping|legend=1| 1 0 0 0 6 | 0 1 0 0 -6 | 0 0 1 0 3 | 0 0 0 1 0 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 701.5449, ~5/4 = 386.7538, ~7/4 = 968.8259 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 701.4729, ~5/4 = 386.5374, ~7/4 = 968.6210 | ||
{{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }} | {{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }} | ||
| Line 479: | Line 512: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 701.5537, ~5/4 = 386.7680, ~7/4 = 968.8144 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 701.4770, ~5/4 = 386.5437, ~7/4 = 968.6150 | ||
{{Optimal ET sequence|legend=1| 53, 58, 72, 111, 130, 183, 190, 243e, 248, 301, 373, 804, 1177be }} | {{Optimal ET sequence|legend=1| 53, 58, 72, 111, 130, 183, 190, 243e, 248, 301, 373, 804, 1177be }} | ||
| Line 493: | Line 526: | ||
{{Mapping|legend=1| 2 0 0 0 3 | 0 1 0 0 -2 | 0 0 1 0 1 | 0 0 0 1 1 }} | {{Mapping|legend=1| 2 0 0 0 3 | 0 1 0 0 -2 | 0 0 1 0 1 | 0 0 0 1 1 }} | ||
: | : Mapping generators: ~99/70, ~3, ~5, ~7 | ||
[[Optimal tuning]]: | |||
* [[CTE]]: ~99/70 = 1＼2, ~3/2 = 701.942, ~5/4 = 386.327, ~7/4 = 968.846 | |||
* [[CWE]]: ~99/70 = 1＼2, ~3/2 = 701.940, ~5/4 = 386.323, ~7/4 = 968.840 | |||
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }} | {{Optimal ET sequence|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }} | ||
| Line 506: | Line 543: | ||
Lattice basis: | Lattice basis: | ||
: 3/2 length = 1.1956, 7/4 length = 1.4506, 14/13 length = 1.8299 | : 3/2 length = 1.1956, 7/4 length = 1.4506, 14/13 length = 1.8299 | ||
[[Optimal tuning]] ([[CTE]]): ~99/70 = 1＼1, ~3/2 = 702.024, ~5/4 = 386.294, ~7/4 = 969.114 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[13-odd-limit|13-]] and [[15-odd-limit]] | * [[13-odd-limit|13-]] and [[15-odd-limit]]: ~99/70 = {{monzo| 1/2 0 0 0 0 0 }}, ~3 = {{monzo| 7/10 4/5 0 -2/5 0 1/5 }}, ~5 = {{monzo| 7/10 -1/5 1 -2/5 0 1/5 }}, ~7 = {{monzo| 7/5 -2/5 0 1/5 0 2/5 }} | ||
: | |||
: [[Eigenmonzo basis|Eigenmonzo (unchanged-intervals) basis]]: 2, 6/5, 16/13, 9/7 | : [[Eigenmonzo basis|Eigenmonzo (unchanged-intervals) basis]]: 2, 6/5, 16/13, 9/7 | ||
| Line 521: | Line 559: | ||
{{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 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]] | * [[CTE]] and [[CWE]]: ~2 = 1＼1, ~3/2 = 702.031, ~5/4 = 386.233, ~11/7 = 783.508 | ||
{{Optimal ET sequence|legend=1| 12, 21, 23de, 26, 37, 46, 58, 72, 118, 130, 190, 239, 311, 441, 559, 752e, 870 }} | {{Optimal ET sequence|legend=1| 12, 21, 23de, 26, 37, 46, 58, 72, 118, 130, 190, 239, 311, 441, 559, 752e, 870 }} | ||
| Line 539: | Line 576: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 702.072, ~5/4 = 386.528, ~11/7 = 783.823 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1＼1, ~3/2 = 702.253, ~5/4 = 386.776, ~11/7 = 783.875 | ||
{{Optimal ET sequence|legend=1| 26, 37, 46, 58, 72, 121, 130, 193, 239, 251e, 323e, 369 }} | {{Optimal ET sequence|legend=1| 26, 37, 46, 58, 72, 121, 130, 193, 239, 251e, 323e, 369 }} | ||
| Line 554: | Line 591: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]] | * [[CTE]] and [[CWE]]: ~2 = 1＼1, ~3/2 = 701.952, ~5/4 = 386.139, ~11/7 = 783.548 | ||
{{Optimal ET sequence|legend=1| 46f, 49f, 58, 72, 118, 121, 130, 190, 193, 248, 311, 441, 752e, 1072 }} | {{Optimal ET sequence|legend=1| 46f, 49f, 58, 72, 118, 121, 130, 190, 193, 248, 311, 441, 752e, 1072 }} | ||
| Line 566: | Line 602: | ||
{{Mapping|legend=1| 1 0 2 0 1 | 0 1 2 0 2 | 0 0 -4 0 -1 | 0 0 0 1 0 }} | {{Mapping|legend=1| 1 0 2 0 1 | 0 1 2 0 2 | 0 0 -4 0 -1 | 0 0 0 1 0 }} | ||
: | : Mapping generators: ~2, ~3, ~18/11, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 702.334, ~18/11 = 854.555, ~7/4 = 968.826 | ||
* [[CWE]]: ~2 = | * [[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 }} | ||
| Line 584: | Line 620: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = | * CTE: ~2 = 1＼1, ~3/2 = 702.469, ~18/11 = 854.644, ~7/4 = 968.959 | ||
* CWE: ~2 = | * CWE: ~2 = 1＼1, ~3/2 = 702.483, ~18/11 = 854.642, ~7/4 = 968.989 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 87, 111, 181, 198, 323, 410 }} | ||
Badness: 17.1 × 10<sup>-6</sup> | Badness: 17.1 × 10<sup>-6</sup> | ||
| Line 599: | Line 635: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = | * CTE: ~2 = 1＼1, ~3/2 = 702.413, ~18/11 = 854.633, ~7/4 = 969.032 | ||
* CWE: ~2 = | * CWE: ~2 = 1＼1, ~3/2 = 702.411, ~18/11 = 854.634, ~7/4 = 969.026 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }} | ||
Badness: 34.0 × 10<sup>-6</sup> | Badness: 34.0 × 10<sup>-6</sup> | ||
| Line 614: | Line 650: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = | * CTE: ~2 = 1＼1, ~3/2 = 702.368, ~18/11 = 854.639, ~7/4 = 969.075 | ||
* CWE: ~2 = | * CWE: ~2 = 1＼1, ~3/2 = 702.351, ~18/11 = 854.644, ~7/4 = 969.010 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }} | ||
Badness: 41.9 × 10<sup>-6</sup> | Badness: 41.9 × 10<sup>-6</sup> | ||
| Line 628: | Line 664: | ||
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 | 0 0 0 1 0 }} | {{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 | 0 0 0 1 0 }} | ||
: | : Mapping generators: ~2, ~3, ~128/99, ~7 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.470, ~128/99 = 442.106, ~7/4 = 968.826 | |||
{{Optimal ET sequence|legend=1| 19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee }} | {{Optimal ET sequence|legend=1| 19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee }} | ||
| Line 641: | Line 679: | ||
{{Mapping|legend=1| 1 0 0 0 -8 | 0 1 0 0 9 | 0 0 1 0 0 | 0 0 0 1 -1 }} | {{Mapping|legend=1| 1 0 0 0 -8 | 0 1 0 0 9 | 0 0 1 0 0 | 0 0 0 1 -1 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 702.213, ~5/4 = 386.314, ~7/4 = 968.736 | ||
* [[CWE]]: ~2 = | * [[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 }} | ||
[[Badness]] | [[Badness]]: 0.120 × 10<sup>-6</sup> | ||
=== Tridecimal symbiotic === | === Tridecimal symbiotic === | ||
| Line 659: | Line 697: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1＼1, ~3/2 = 702.228, ~5/4 = 386.284, ~7/4 = 968.789 | ||
* [[CWE]]: ~2 = | * [[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 }} | ||
[[Badness]] | [[Badness]]: 3.31 × 10<sup>-6</sup> | ||
=== 2.3.5.7.11.13.19 subgroup === | === 2.3.5.7.11.13.19 subgroup === | ||
| Line 674: | Line 712: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = | * CTE: ~2 = 1＼1, ~3/2 = 702.230, ~5/4 = 386.304, ~7/4 = 968.797 | ||
* CWE: ~2 = | * CWE: ~2 = 1＼1, ~3/2 = 702.255, ~5/4 = 386.408, ~7/4 = 968.902 | ||
{{Optimal ET sequence|legend=0| 17ch, 24f, 34dffh, 36ceh, 41, 53, 58h, 94, 111, 152f, 212h, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bfh }} | {{Optimal ET sequence|legend=0| 17ch, 24f, 34dffh, 36ceh, 41, 53, 58h, 94, 111, 152f, 212h, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bfh }} | ||
Badness | Badness: 4.37 × 10<sup>-6</sup> | ||
== Olympic (131072/130977) == | == Olympic (131072/130977) == | ||
| Line 688: | Line 726: | ||
{{Mapping|legend=1| 1 0 0 0 17 | 0 1 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 -2 }} | {{Mapping|legend=1| 1 0 0 0 17 | 0 1 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 -2 }} | ||
: | : Mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.103, ~5/4 = 386.314, ~7/4 = 969.012 | |||
{{Optimal ET sequence|legend=1| 41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee }} | {{Optimal ET sequence|legend=1| 41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee }} | ||
| Line 698: | Line 738: | ||
{{Mapping|legend=1| 1 0 0 0 17 12 | 0 1 0 0 -5 -2 | 0 0 1 0 0 -1 | 0 0 0 1 -2 -1 }} | {{Mapping|legend=1| 1 0 0 0 17 12 | 0 1 0 0 -5 -2 | 0 0 1 0 0 -1 | 0 0 0 1 -2 -1 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.103, ~5/4 = 386.298, ~7/4 = 969.007 | |||
{{Optimal ET sequence|legend=1| 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e }} * | {{Optimal ET sequence|legend=1| 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e }} * | ||
| Line 706: | Line 748: | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: | [[Comma list]]: [[Seascape comma|160083/160000]] | ||
[[Seascape comma|160083/160000]] | |||
{{Mapping|legend=1| 1 0 0 0 4 | 0 2 0 0 -3 | 0 0 1 0 2 | 0 0 0 1 -1 }} | {{Mapping|legend=1| 1 0 0 0 4 | 0 2 0 0 -3 | 0 0 1 0 2 | 0 0 0 1 -1 }} | ||
: | : Mapping generators: ~2, ~400/231, ~5, ~7 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~400/231 = 950.960, ~5/4 = 386.417, ~7/4 = 968.751 | |||
{{Optimal ET sequence|legend=1| 15, 19, 29, 43, 53, 58, 68, 72 }} | |||
== Fifthchromismic (1610510/1594323) == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: [[1610510/1594323]] | |||
{{Mapping|legend=1| 1 0 4 0 -1 | 0 1 3 0 2 | 0 0 -5 0 1 | 0 0 0 1 0 }} | |||
: Mapping generators: ~2, ~3, ~22/9, ~7 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.738, ~11/9 = 344.406, ~7/4 = 968.826 | |||
{{Optimal ET sequence|legend=1| 77, 80, 87, 94 }} | |||
=== Fifthchroma === | |||
{{see also| Fifth-chroma temperaments }} | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 352/351, 951665/944784 | |||
{{Mapping|legend=1| 1 0 4 0 -1 4 | 0 1 3 0 2 -1 | 0 0 -5 0 1 1 | 0 0 0 1 0 0 }} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.776, ~11/9 = 344.410, ~7/4 = 968.826 | |||
{{Optimal ET sequence|legend=1| 77, 80, 87, 94 }} | |||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||