Miscellaneous 5-limit temperaments: Difference between revisions
Added preimage for periods |
3 significant figures are absolutely enough for badness. More precision offers no extra insight. Also note the specific badness metric being used |
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| Line 22: | Line 22: | ||
{{Optimal ET sequence|legend=1| 8, 9, 17c }} | {{Optimal ET sequence|legend=1| 8, 9, 17c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.200 | ||
== Stump == | == Stump == | ||
| Line 38: | Line 38: | ||
{{Optimal ET sequence|legend=1| 17, 19 }} | {{Optimal ET sequence|legend=1| 17, 19 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.201 | ||
== Dodifo == | == Dodifo == | ||
| Line 54: | Line 54: | ||
{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }} | {{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.213 | ||
== Semidimfourth == | == Semidimfourth == | ||
| Line 70: | Line 70: | ||
{{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }} | {{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.233 | ||
== Mynic == | == Mynic == | ||
| Line 86: | Line 86: | ||
{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }} | {{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.250 | ||
== Progress == | == Progress == | ||
| Line 102: | Line 102: | ||
{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }} | {{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.246 | ||
== Abigail == | == Abigail == | ||
| Line 120: | Line 120: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 0. | * Smith: 0.255 | ||
* Dirichlet: 5. | * Dirichlet: 5.97 | ||
== Supermajor == | == Supermajor == | ||
| Line 139: | Line 139: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 0. | * Smith: 0.264 | ||
* Dirichlet: 6. | * Dirichlet: 6.19 | ||
== Gamera == | == Gamera == | ||
| Line 158: | Line 158: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 0. | * Smith: 0.273 | ||
* Dirichlet: 6.39 | * Dirichlet: 6.39 | ||
| Line 175: | Line 175: | ||
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }} | {{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.284 | ||
== Kangaroo == | == Kangaroo == | ||
| Line 191: | Line 191: | ||
{{Optimal ET sequence|legend=1| 15, 47b, 62b }} | {{Optimal ET sequence|legend=1| 15, 47b, 62b }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.296 | ||
== Tertiaseptal == | == Tertiaseptal == | ||
| Line 207: | Line 207: | ||
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }} | {{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.298 | ||
== Gracecordial == | == Gracecordial == | ||
| Line 223: | Line 223: | ||
{{Optimal ET sequence|legend=1| 12, 113, 125, 137 }} | {{Optimal ET sequence|legend=1| 12, 113, 125, 137 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.307 | ||
== Untriton == | == Untriton == | ||
| Line 239: | Line 239: | ||
{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }} | {{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.307 | ||
== Counterhanson == | == Counterhanson == | ||
| Line 255: | Line 255: | ||
{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }} | {{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.318 | ||
== Nessafof == | == Nessafof == | ||
| Line 273: | Line 273: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 0. | * Smith: 0.333 | ||
* Dirichlet: 7. | * Dirichlet: 7.81 | ||
== Lemba == | == Lemba == | ||
| Line 296: | Line 296: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 0. | * Smith: 0.335 | ||
* Dirichlet: 7.85 | * Dirichlet: 7.85 | ||
| Line 311: | Line 311: | ||
{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }} | {{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.342 | ||
== Delorean == | == Delorean == | ||
| Line 327: | Line 327: | ||
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }} | {{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.356 | ||
== Majvam == | == Majvam == | ||
| Line 343: | Line 343: | ||
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }} | {{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.357 | ||
== Beatles == | == Beatles == | ||
| Line 359: | Line 359: | ||
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }} | {{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.359 | ||
== Magus == | == Magus == | ||
| Line 375: | Line 375: | ||
{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }} | {{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.360 | ||
== Countermeantone == | == Countermeantone == | ||
| Line 389: | Line 389: | ||
{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }} | {{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.373 | ||
== Tritonic == | == Tritonic == | ||
| Line 405: | Line 405: | ||
{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }} | {{Optimal ET sequence|legend=1| 29, 31, 60, 91 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.379 | ||
== Wizard == | == Wizard == | ||
| Line 423: | Line 423: | ||
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }} | {{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.386 | ||
Scales (Scala files): [[wizard22]] | Scales (Scala files): [[wizard22]] | ||
| Line 441: | Line 441: | ||
{{Optimal ET sequence|legend=1| 14, 19 }} | {{Optimal ET sequence|legend=1| 14, 19 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.425 | ||
== Merman == | == Merman == | ||
| Line 457: | Line 457: | ||
{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }} | {{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.454 | ||
== Unsmate == | == Unsmate == | ||
| Line 471: | Line 471: | ||
{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }} | {{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.460 | ||
== Nusecond == | == Nusecond == | ||
| Line 487: | Line 487: | ||
{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }} | {{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.466 | ||
== Sfourth == | == Sfourth == | ||
| Line 503: | Line 503: | ||
{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }} | {{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.505 | ||
== Thuja == | == Thuja == | ||
| Line 519: | Line 519: | ||
{{Optimal ET sequence|legend=1| 15, 43, 58 }} | {{Optimal ET sequence|legend=1| 15, 43, 58 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.511 | ||
== Leapday == | == Leapday == | ||
| Line 535: | Line 535: | ||
{{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }} | {{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.523 | ||
== Vines == | == Vines == | ||
| Line 551: | Line 551: | ||
{{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }} | {{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.542 | ||
== Emka == | == Emka == | ||
| Line 567: | Line 567: | ||
{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }} | {{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.545 | ||
== Misneb == | == Misneb == | ||
| Line 583: | Line 583: | ||
{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }} | {{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.610 | ||
== Semisept == | == Semisept == | ||
| Line 599: | Line 599: | ||
{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }} | {{Optimal ET sequence|legend=1| 18, 31, 80, 111 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.631 | ||
== Mowgli == | == Mowgli == | ||
| Line 615: | Line 615: | ||
{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }} | {{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.654 | ||
== Septimin == | == Septimin == | ||
| Line 631: | Line 631: | ||
{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }} | {{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.671 | ||
== Slurpee == | == Slurpee == | ||
| Line 647: | Line 647: | ||
{{Optimal ET sequence|legend=1| 16, 17c, 33 }} | {{Optimal ET sequence|legend=1| 16, 17c, 33 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.689 | ||
== Pentadecal == | == Pentadecal == | ||
| Line 663: | Line 663: | ||
{{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }} | {{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.692 | ||
== Sentinel == | == Sentinel == | ||
| Line 679: | Line 679: | ||
{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }} | {{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.723 | ||
== Kumonga == | == Kumonga == | ||
| Line 695: | Line 695: | ||
{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }} | {{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.730 | ||
== Mirkat == | == Mirkat == | ||
| Line 713: | Line 713: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 0. | * Smith: 0.752 | ||
* Dirichlet: 17. | * Dirichlet: 17.6 | ||
== Semidimi == | == Semidimi == | ||
| Line 730: | Line 730: | ||
{{Optimal ET sequence|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }} | {{Optimal ET sequence|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.755 | ||
== Slender == | == Slender == | ||
| Line 748: | Line 748: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 0. | * Smith: 0.761 | ||
* Dirichlet: 17. | * Dirichlet: 17.8 | ||
== Quasitemp == | == Quasitemp == | ||
| Line 765: | Line 765: | ||
{{Optimal ET sequence|legend=1| 4, 37, 41 }} | {{Optimal ET sequence|legend=1| 4, 37, 41 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.768 | ||
== Cypress == | == Cypress == | ||
| Line 781: | Line 781: | ||
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }} | {{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.817 | ||
== Chromo == | == Chromo == | ||
| Line 797: | Line 797: | ||
{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }} | {{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.843 | ||
== Tertiosec == | == Tertiosec == | ||
| Line 813: | Line 813: | ||
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }} | {{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.851 | ||
== Fervor == | == Fervor == | ||
| Line 829: | Line 829: | ||
{{Optimal ET sequence|legend=1| 2, 25, 27 }} | {{Optimal ET sequence|legend=1| 2, 25, 27 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.853 | ||
== Bohpier == | == Bohpier == | ||
| Line 845: | Line 845: | ||
{{Optimal ET sequence|legend=1| 8, 41, 131, 172, 213c }} | {{Optimal ET sequence|legend=1| 8, 41, 131, 172, 213c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.861 | ||
== Elvis == | == Elvis == | ||
| Line 861: | Line 861: | ||
{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }} | {{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.884 | ||
== Enneadecacot == | == Enneadecacot == | ||
| Line 875: | Line 875: | ||
{{Optimal ET sequence|legend=1| 65, 292, 357, 422, 487, 1396c }} | {{Optimal ET sequence|legend=1| 65, 292, 357, 422, 487, 1396c }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.892 | ||
== Vinegar == | == Vinegar == | ||
| Line 891: | Line 891: | ||
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b, 84b }} | {{Optimal ET sequence|legend=1| 15, 39c, 54, 69b, 84b }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.903 | ||
== Oolong == | == Oolong == | ||
| Line 907: | Line 907: | ||
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }} | {{Optimal ET sequence|legend=1| 23, 27, 50, 77 }} | ||
[[Badness]]: 0. | [[Badness]] (Smith): 0.943 | ||
== Oncle == | == Oncle == | ||
| Line 923: | Line 923: | ||
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }} | {{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.24 | ||
== Quasiorwell == | == Quasiorwell == | ||
| Line 941: | Line 941: | ||
[[Badness]]: | [[Badness]]: | ||
* Smith: 1. | * Smith: 1.30 | ||
* Dirichlet: 30. | * Dirichlet: 30.6 | ||
== Diesic == | == Diesic == | ||
| Line 958: | Line 958: | ||
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }} | {{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.34 | ||
== Quartemka == | == Quartemka == | ||
| Line 974: | Line 974: | ||
{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }} | {{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.38 | ||
== Genocchi == | == Genocchi == | ||
| Line 988: | Line 988: | ||
{{Optimal ET sequence|legend=1| 6b, 11b, 17c }} | {{Optimal ET sequence|legend=1| 6b, 11b, 17c }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.40 | ||
== Casablanca == | == Casablanca == | ||
| Line 1,004: | Line 1,004: | ||
{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }} | {{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.42 | ||
== Archaeotherium == | == Archaeotherium == | ||
| Line 1,020: | Line 1,020: | ||
{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }} | {{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.43 | ||
== Octacoid == | == Octacoid == | ||
| Line 1,037: | Line 1,037: | ||
{{Optimal ET sequence|legend=1| 13, 14, 27 }} | {{Optimal ET sequence|legend=1| 13, 14, 27 }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.75 | ||
== Quasimoha == | == Quasimoha == | ||
| Line 1,053: | Line 1,053: | ||
{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }} | {{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }} | ||
[[Badness]]: 1. | [[Badness]] (Smith): 1.99 | ||
== Phillips == | == Phillips == | ||
| Line 1,069: | Line 1,069: | ||
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }} | {{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }} | ||
[[Badness]]: 2. | [[Badness]] (Smith): 2.23 | ||
== Triskaidekic == | == Triskaidekic == | ||
| Line 1,085: | Line 1,085: | ||
{{Optimal ET sequence|legend=1| 13, 26, 91c }} | {{Optimal ET sequence|legend=1| 13, 26, 91c }} | ||
[[Badness]]: 2. | [[Badness]] (Smith): 2.24 | ||
== Satin == | == Satin == | ||
| Line 1,101: | Line 1,101: | ||
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }} | {{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }} | ||
[[Badness]]: 2. | [[Badness]] (Smith): 2.85 | ||
== Rarity == | == Rarity == | ||
| Line 1,122: | Line 1,122: | ||
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }} | {{Optimal ET sequence|legend=1| 11, 29, 69, 98c }} | ||
[[Badness]]: 4. | [[Badness]] (Smith): 4.23 | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||