Xenharmonic Wiki

Marvel family: Difference between revisions

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+naming history of hestia
+CTE tunings. POTE -> CWE (This is one of the pages that didn't have tuning information to start with. POTE was only added in 2021 by myself)
Line 30: Line 30:
: Angle (secor, 3/2) = 106.958 degrees
: Angle (secor, 3/2) = 106.958 degrees


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.4075, ~5/4 = 383.6376
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 700.974, ~5/4 = 384.208
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.622, ~5/4 = 383.854


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 93: Line 95:
: Angle (secor, 5/4) = 104.028 degrees
: Angle (secor, 5/4) = 104.028 degrees


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.3887, ~5/4 = 383.5403
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.373, ~5/4 = 383.146
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.605, ~5/4 = 383.454


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 129: Line 133:
Mapping: {{mapping| 1 0 0 -5 12 -4 | 0 1 0 2 -1 -1 | 0 0 1 2 -3 4 }}
Mapping: {{mapping| 1 0 0 -5 12 -4 | 0 1 0 2 -1 -1 | 0 0 1 2 -3 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.7367, ~5/4 = 384.0613
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 700.182, ~5/4 = 384.400
* CWE: ~2 = 1\1, ~3/2 = 699.811, ~5/4 = 384.118


Minimax tuning:  
Minimax tuning:  
Line 135: Line 141:
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.15/11.15/13
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.15/11.15/13


{{Optimal ET sequence|legend=1| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}


Badness: 0.690 × 10<sup>-3</sup>
Badness: 0.690 × 10<sup>-3</sup>
Line 148: Line 154:
Mapping: {{mapping| 1 0 0 -5 12 2 | 0 1 0 2 -1 4 | 0 0 1 2 -3 -2 }}
Mapping: {{mapping| 1 0 0 -5 12 2 | 0 1 0 2 -1 4 | 0 0 1 2 -3 -2 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9779, ~5/4 = 383.1622
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.563, ~5/4 = 383.015
* CWE: ~2 = 1\1, ~3/2 = 701.100, ~5/4 = 383.132


Minimax tuning:  
Minimax tuning:  
Line 154: Line 162:
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13


{{Optimal ET sequence|legend=1| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}


Badness: 0.721 × 10<sup>-3</sup>
Badness: 0.721 × 10<sup>-3</sup>
Line 169: Line 177:
Sval mapping: {{mapping| 1 0 0 -5 12 2 9 | 0 1 0 2 -1 4 -3 | 0 0 1 2 -3 -2 0 }}
Sval mapping: {{mapping| 1 0 0 -5 12 2 9 | 0 1 0 2 -1 4 -3 | 0 0 1 2 -3 -2 0 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4245, ~5/4 = 383.0293
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.424, ~5/4 = 383.029
* CWE: ~2 = 1\1, ~3/2 = 701.200, ~5/4 = 383.114


{{Optimal ET sequence|legend=1| 41, 53, 72, 94, 113, 166 }}
Optimal ET sequence: {{Optimal ET sequence| 41, 53, 72, 94, 113, 166 }}


Badness: 0.773 × 10<sup>-3</sup>
Badness: 0.773 × 10<sup>-3</sup>
Line 182: Line 192:
Mapping: {{mapping| 1 0 0 -5 12 2 18 | 0 1 0 2 -1 4 0 | 0 0 1 2 -3 -2 -6 }}
Mapping: {{mapping| 1 0 0 -5 12 2 18 | 0 1 0 2 -1 4 0 | 0 0 1 2 -3 -2 -6 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.5860, ~5/4 = 382.7331
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.586, ~5/4 = 382.733
* CWE: ~2 = 1\1, ~3/2 = 701.088, ~5/4 = 382.971


{{Optimal ET sequence|legend=1| 41, 53g, 72, 166g, 238cfg }}
Optimal ET sequence: {{Optimal ET sequence| 41, 53g, 72, 166g, 238cfg }}


Badness: 0.869 × 10<sup>-3</sup>
Badness: 0.869 × 10<sup>-3</sup>
Line 195: Line 207:
Mapping: {{mapping| 1 0 0 -5 12 2 18 9 | 0 1 0 2 -1 4 0 -3 | 0 0 1 2 -3 -2 -6 0 }}
Mapping: {{mapping| 1 0 0 -5 12 2 18 9 | 0 1 0 2 -1 4 0 -3 | 0 0 1 2 -3 -2 -6 0 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4435, ~5/4 = 382.7395
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.443, ~5/4 = 382.739
* CWE: ~2 = 1\1, ~3/2 = 701.201, ~5/4 = 382.940


{{Optimal ET sequence|legend=1| 41, 53g, 72, 94, 113, 166g }}
Optimal ET sequence: {{Optimal ET sequence| 41, 53g, 72, 94, 113, 166g }}


Badness: 0.978 × 10<sup>-3</sup>
Badness: 0.978 × 10<sup>-3</sup>
Line 208: Line 222:
Mapping: {{mapping| 1 0 0 -5 12 2 -13 | 0 1 0 2 -1 4 2 | 0 0 1 2 -3 -2 6 }}
Mapping: {{mapping| 1 0 0 -5 12 2 -13 | 0 1 0 2 -1 4 2 | 0 0 1 2 -3 -2 6 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.6270, ~5/4 = 383.3456
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.627, ~5/4 = 383.346
* CWE: ~2 = 1\1, ~3/2 = 701.095, ~5/4 = 383.314


{{Optimal ET sequence|legend=1| 41g, 53, 72, 166g, 238cfg }}
Optimal ET sequence: {{Optimal ET sequence| 41g, 53, 72, 166g, 238cfg }}


Badness: 0.917 × 10<sup>-3</sup>
Badness: 0.917 × 10<sup>-3</sup>
Line 221: Line 237:
Mapping: {{mapping| 1 0 0 -5 12 2 -13 9 | 0 1 0 2 -1 4 2 -3 | 0 0 1 2 -3 -2 6 0 }}
Mapping: {{mapping| 1 0 0 -5 12 2 -13 9 | 0 1 0 2 -1 4 2 -3 | 0 0 1 2 -3 -2 6 0 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4791, ~5/4 = 383.3795
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.479, ~5/4 = 383.379
* CWE: ~2 = 1\1, ~3/2 = 701.211, ~5/4 = 383.305


{{Optimal ET sequence|legend=1| 41g, 53, 72, 94, 125f, 166g }}
Optimal ET sequence: {{Optimal ET sequence| 41g, 53, 72, 94, 125f, 166g }}


Badness: 1.03 × 10<sup>-3</sup>
Badness: 1.03 × 10<sup>-3</sup>
Line 234: Line 252:
Mapping: {{mapping| 1 0 0 -5 12 -29 | 0 1 0 2 -1 6 | 0 0 1 2 -3 10 }}
Mapping: {{mapping| 1 0 0 -5 12 -29 | 0 1 0 2 -1 6 | 0 0 1 2 -3 10 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3937, ~5/4 = 383.5725
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.385, ~5/4 = 383.208
* CWE: ~2 = 1\1, ~3/2 = 700.611, ~5/4 = 383.493


Minimax tuning:  
Minimax tuning:  
Line 240: Line 260:
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13


{{Optimal ET sequence|legend=1| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}
Optimal ET sequence: {{Optimal ET sequence| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}


Badness: 0.862 × 10<sup>-3</sup>
Badness: 0.862 × 10<sup>-3</sup>
Line 251: Line 271:
Mapping: {{mapping| 1 0 0 -5 12 17 | 0 1 0 2 -1 4 | 0 0 1 2 -3 -3 }}
Mapping: {{mapping| 1 0 0 -5 12 17 | 0 1 0 2 -1 4 | 0 0 1 2 -3 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.9156, ~5/4 = 383.2445
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.997, ~5/4 = 383.134
* CWE: ~2 = 1\1, ~3/2 = 701.928, ~5/4 = 383.228


{{Optimal ET sequence|legend=1| 10, 19f, 22, 31, 41, 53, 94 }}
Optimal ET sequence: {{Optimal ET sequence| 10, 19f, 22, 31, 41, 53, 94 }}


Badness: 0.866 × 10<sup>-3</sup>
Badness: 0.866 × 10<sup>-3</sup>
Line 266: Line 288:
Mapping: {{mapping| 1 0 0 -5 12 27 | 0 1 0 2 -1 -3 | 0 0 1 2 -3 -8 }}
Mapping: {{mapping| 1 0 0 -5 12 27 | 0 1 0 2 -1 -3 | 0 0 1 2 -3 -8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.4560, ~5/4 = 382.8177
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.702, ~5/4 = 382.074
* CWE: ~2 = 1\1, ~3/2 = 700.718, ~5/4 = 382.661


Minimax tuning:  
Minimax tuning:  
Line 272: Line 296:
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.3.13/5
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.3.13/5


{{Optimal ET sequence|legend=1| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}
Optimal ET sequence: {{Optimal ET sequence| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}


Badness: 0.920 × 10<sup>-3</sup>
Badness: 0.920 × 10<sup>-3</sup>
Line 285: Line 309:
Mapping: {{mapping| 1 0 0 -5 12 -8 | 0 1 0 2 -1 3 | 0 0 1 2 -3 3 }}
Mapping: {{mapping| 1 0 0 -5 12 -8 | 0 1 0 2 -1 3 | 0 0 1 2 -3 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.2335, ~5/4 = 382.9775
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 700.028, ~5/4 = 382.694
* CWE: ~2 = 1\1, ~3/2 = 699.404, ~5/4 = 382.917


Minimax tuning:  
Minimax tuning:  
Line 291: Line 317:
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.13/11
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.13/11


{{Optimal ET sequence|legend=1| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}
Optimal ET sequence: {{Optimal ET sequence| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}


Badness: 0.745 × 10<sup>-3</sup>
Badness: 0.745 × 10<sup>-3</sup>
Line 306: Line 332:
: mapping generators: ~2, ~26/15, ~5
: mapping generators: ~2, ~26/15, ~5


Optimal tuning (POTE): ~2 = 1\1, ~15/13 = 249.7138, ~5/4 = 383.5816
Optimal tunings:
* CTE: ~2 = 1\1, ~26/15 = 950.961, ~5/4 = 383.088
* CWE: ~2 = 1\1, ~26/15 = 950.426, ~5/4 = 383.479


{{Optimal ET sequence|legend=1| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}
Optimal ET sequence: {{Optimal ET sequence| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}


Badness: 0.9997 × 10<sup>-3</sup>
Badness: 0.9997 × 10<sup>-3</sup>
Line 325: Line 353:
: Angle (16/15, 5/4) = 98.6044 degrees
: Angle (16/15, 5/4) = 98.6044 degrees


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.2593, ~5/4 = 386.5581
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 700.379, ~5/4 = 386.617
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.301, ~5/4 = 386.579


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11/9


{{Optimal ET sequence|legend=1| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}
{{Optimal ET sequence|legend=1| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}
Line 346: Line 376:
Mapping: {{mapping| 1 0 0 -5 -9 -4 | 0 1 0 2 2 -1 | 0 0 1 2 4 4 }}
Mapping: {{mapping| 1 0 0 -5 -9 -4 | 0 1 0 2 2 -1 | 0 0 1 2 4 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.2342, ~5/4 = 385.9594
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 701.179, ~5/4 = 385.888
* CWE: ~2 = 1\1, ~3/2 = 701.214, ~5/4 = 385.934


Minimax tuning:  
Minimax tuning:  
Line 352: Line 384:
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/7
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/7


{{Optimal ET sequence|legend=1| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}


Badness: 0.818 × 10<sup>-3</sup>
Badness: 0.818 × 10<sup>-3</sup>
Line 367: Line 399:
{{Mapping|legend=1| 1 0 0 -5 2 | 0 1 0 2 -2 | 0 0 1 2 2 }}
{{Mapping|legend=1| 1 0 0 -5 2 | 0 1 0 2 -2 | 0 0 1 2 2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.4846, ~5/4 = 381.6033
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 703.418, ~5/4 = 381.331
* [[CWE]]: ~2 = 1\1, ~3/2 = 703.461, ~5/4 = 381.507


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11/9
Line 384: Line 418:
Mapping: {{mapping| 1 0 0 -5 2 7 | 0 1 0 2 -2 -5 | 0 0 1 2 2 2 }}
Mapping: {{mapping| 1 0 0 -5 2 7 | 0 1 0 2 -2 -5 | 0 0 1 2 2 2 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.9984, ~5/4 = 381.5352
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 703.959, ~5/4 = 381.001
* CWE: ~2 = 1\1, ~3/2 = 703.985, ~5/4 = 381.358


Minimax tuning: 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/9
Minimax tuning: 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/9


{{Optimal ET sequence|legend=1| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}


Projection pairs: 7 225/32 11 100/9 13 3200/243
Projection pairs: 7 225/32 11 100/9 13 3200/243
Line 399: Line 435:
{{Mapping|legend=1| 1 0 0 -5 -2 | 0 1 0 2 2 | 0 0 1 2 1 }}
{{Mapping|legend=1| 1 0 0 -5 -2 | 0 1 0 2 2 | 0 0 1 2 1 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 696.1714, ~5/4 = 385.0500
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 695.937, ~5/4 = 384.836
* [[CWE]]: ~2 = 1\1, ~3/2 = 696.059, ~5/4 = 384.947


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7.11
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7.11
Line 416: Line 454:
Mapping: {{mapping| 1 0 0 -5 -2 -8 | 0 1 0 2 2 3 | 0 0 1 2 1 3 }}
Mapping: {{mapping| 1 0 0 -5 -2 -8 | 0 1 0 2 2 3 | 0 0 1 2 1 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.0103, ~5/4 = 384.6785
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.894, ~5/4 = 384.602
* CWE: ~2 = 1\1, ~3/2 = 695.948, ~5/4 = 384.637


Minimax tuning:  
Minimax tuning:  
Line 422: Line 462:
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/9
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/9


{{Optimal ET sequence|legend=1| 9, 10, 12f, 19, 31e, 50e }}
Optimal ET sequence: {{Optimal ET sequence| 9, 10, 12f, 19, 31e, 50e }}


Badness: 0.733 × 10<sup>-3</sup>
Badness: 0.733 × 10<sup>-3</sup>
Line 437: Line 477:
{{Mapping|legend=1| 1 0 0 -5 -3 | 0 1 0 2 7 | 0 0 1 2 -2 }}
{{Mapping|legend=1| 1 0 0 -5 -3 | 0 1 0 2 7 | 0 0 1 2 -2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.8913, ~5/4 = 382.4083
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.322, ~5/4 = 382.976
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.054, ~5/4 = 382.622


{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
Line 450: Line 492:
Mapping: {{mapping| 1 0 0 -5 -3 2 | 0 1 0 2 7 4 | 0 0 1 2 -2 -2 }}
Mapping: {{mapping| 1 0 0 -5 -3 2 | 0 1 0 2 7 4 | 0 0 1 2 -2 -2 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.8913, ~5/4 = 382.4083
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 702.235, ~5/4 = 383.205
* CWE: ~2 = 1\1, ~3/2 = 702.088, ~5/4 = 383.063


{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}


Badness: 1.075 × 10<sup>-3</sup>
Badness: 1.075 × 10<sup>-3</sup>
Line 473: Line 517:
: Angle (secor, 3/2) = 65.933
: Angle (secor, 3/2) = 65.933


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 699.7981, ~5/4 = 383.5114
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 699.995, ~5/4 = 384.330
* [[CWE]]: ~2 = 1\1, ~3/2 = 699.861, ~5/4 = 383.772


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 503: Line 549:
Mapping: {{mapping| 1 0 0 -5 -13 -8 | 0 1 0 2 6 3 | 0 0 1 2 3 3 }}
Mapping: {{mapping| 1 0 0 -5 -13 -8 | 0 1 0 2 6 3 | 0 0 1 2 3 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.4006, ~5/4 = 381.4025
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 700.617, ~5/4 = 382.244
* CWE: ~2 = 1\1, ~3/2 = 700.469, ~5/4 = 381.669


{{Optimal ET sequence|legend=1| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}
Optimal ET sequence: {{Optimal ET sequence| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}


Badness: 0.736 × 10<sup>-3</sup>
Badness: 0.736 × 10<sup>-3</sup>
Line 516: Line 564:
Mapping: {{mapping| 1 0 0 -5 -13 -23 | 0 1 0 2 6 11 | 0 0 1 2 3 4 }}
Mapping: {{mapping| 1 0 0 -5 -13 -23 | 0 1 0 2 6 11 | 0 0 1 2 3 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3407, ~5/4 = 383.2592
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 700.305, ~5/4 = 384.075
* CWE: ~2 = 1\1, ~3/2 = 700.330, ~5/4 = 383.503


{{Optimal ET sequence|legend=1| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}


Badness: 0.900 × 10<sup>-3</sup>
Badness: 0.900 × 10<sup>-3</sup>
Line 529: Line 579:
Mapping: {{mapping| 1 0 0 -5 -13 -4 | 0 1 0 2 6 -1 | 0 0 1 2 3 4 }}
Mapping: {{mapping| 1 0 0 -5 -13 -4 | 0 1 0 2 6 -1 | 0 0 1 2 3 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.4864, ~5/4 = 384.0998
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 699.698, ~5/4 = 384.884
* CWE: ~2 = 1\1, ~3/2 = 699.554, ~5/4 = 384.350


{{Optimal ET sequence|legend=1| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}


Badness: 0.889 × 10<sup>-3</sup>
Badness: 0.889 × 10<sup>-3</sup>
Line 542: Line 594:
Mapping: {{mapping| 1 0 0 -5 -13 21 | 0 1 0 2 6 -8 | 0 0 1 2 3 -2 }}
Mapping: {{mapping| 1 0 0 -5 -13 21 | 0 1 0 2 6 -8 | 0 0 1 2 3 -2 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.5536, ~5/4 = 383.5696
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 698.947, ~5/4 = 385.480
* CWE: ~2 = 1\1, ~3/2 = 699.422, ~5/4 = 383.983


{{Optimal ET sequence|legend=1| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
Optimal ET sequence: {{Optimal ET sequence| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}


Badness: 0.953 × 10<sup>-3</sup>
Badness: 0.953 × 10<sup>-3</sup>
Line 555: Line 609:
Mapping: {{mapping| 1 0 0 -5 -13 21 12 | 0 1 0 2 6 -8 -5 | 0 0 1 2 3 -2 0 }}
Mapping: {{mapping| 1 0 0 -5 -13 21 12 | 0 1 0 2 6 -8 -5 | 0 0 1 2 3 -2 0 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.6262, ~5/4 = 383.4458
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 698.969, ~5/4 = 385.440
* CWE: ~2 = 1\1, ~3/2 = 699.485, ~5/4 = 383.874


{{Optimal ET sequence|legend=1| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
Optimal ET sequence: {{Optimal ET sequence| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}


Badness: 0.772 × 10<sup>-3</sup>
Badness: 0.772 × 10<sup>-3</sup>
Line 570: Line 626:
: mapping generators: ~99/70, ~3, ~5
: mapping generators: ~99/70, ~3, ~5


[[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~3/2 = 700.6242, ~5/4 = 383.2978
[[Optimal tuning]]s:
* [[CTE]]: ~99/70 = 1\2, ~3/2 = 701.132, ~5/4 = 383.926
* [[CWE]]: ~99/70 = 1\2, ~3/2 = 700.816, ~5/4 = 383.535


{{Optimal ET sequence|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
{{Optimal ET sequence|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
Line 587: Line 645:
: mapping generators: ~2, ~400/231, ~5
: mapping generators: ~2, ~400/231, ~5


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~400/231 = 950.1474, ~5/4 = 383.6467
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~400/231 = 950.043, ~5/4 = 384.858
* [[CWE]]: ~2 = 1\1, ~400/231 = 950.121, ~5/4 = 383.953


{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
Line 600: Line 660:
Mapping: {{mapping| 1 0 0 -5 9 -1 | 0 2 0 4 -7 3 | 0 0 1 2 0 1 }}
Mapping: {{mapping| 1 0 0 -5 9 -1 | 0 2 0 4 -7 3 | 0 0 1 2 0 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.2349, ~5/4 = 383.5558
Optimal tunings:
* CTE: ~2 = 1\1, ~26/15 = 950.131, ~5/4 = 385.245
* CWE: ~2 = 1\1, ~26/15 = 950.211, ~5/4 = 383.949


{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
Optimal ET sequence: {{Optimal ET sequence| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}


Badness: 1.062 × 10<sup>-3</sup>
Badness: 1.062 × 10<sup>-3</sup>
Line 615: Line 677:
: mapping generators: ~2, ~3, ~84/55
: mapping generators: ~2, ~3, ~84/55


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.8983, ~84/55 = 739.3812
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.459, ~84/55 = 739.747
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.111, ~84/55 = 739.451


{{Optimal ET sequence|legend=1| 29, 31, 60e, 91e, 94, 125 }}
{{Optimal ET sequence|legend=1| 29, 31, 60e, 91e, 94, 125 }}
Line 630: Line 694:
: mapping generators: ~2, ~6/5, ~11
: mapping generators: ~2, ~6/5, ~11


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 316.7318, ~11/8 = 549.2528
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~6/5 = 316.834, ~11/8 = 551.318
* [[CWE]]: ~2 = 1\1, ~6/5 = 316.771, ~11/8 = 550.034


{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
Line 643: Line 709:
Mapping: {{mapping| 1 0 1 -3 0 0 | 0 6 5 22 0 14 | 0 0 0 0 1 0 }}
Mapping: {{mapping| 1 0 1 -3 0 0 | 0 6 5 22 0 14 | 0 0 0 0 1 0 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.7410, ~11/8 = 548.6028
Optimal tunings:
* CTE: ~2 = 1\1, ~6/5 = 316.886, ~11/8 = 551.318
* CTE: ~2 = 1\1, ~6/5 = 316.794, ~11/8 = 549.590


{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 125f, 197ef, 269cef }}
Optimal ET sequence: {{Optimal ET sequence| 19, 34d, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.916 × 10<sup>-3</sup>
Badness: 0.916 × 10<sup>-3</sup>
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