Kleismic family: Difference between revisions
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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* 5-odd-limit diamond monotone and tradeoff: ~6/5 = [315.641, 317.263] | * 5-odd-limit diamond monotone and tradeoff: ~6/5 = [315.641, 317.263] | ||
{{ | {{Optimal ET sequence|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }} | ||
[[Badness]]: 0.013234 | [[Badness]]: 0.013234 | ||
| Line 45: | Line 45: | ||
POTE generator: ~6/5 = 317.0756 | POTE generator: ~6/5 = 317.0756 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 19, 34, 53, 140, 193, 246 }} | ||
Badness: 0.394 | Badness: 0.394 | ||
| Line 69: | Line 69: | ||
* 9-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 320.000] | * 9-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 320.000] | ||
{{ | {{Optimal ET sequence|legend=1| 15, 19, 53d, 72dd, 91dd }} | ||
[[Badness]]: 0.027408 | [[Badness]]: 0.027408 | ||
| Line 87: | Line 87: | ||
* 11-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 320.000] | * 11-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 320.000] | ||
Optimal | {{Optimal ET sequence|legend=1| 4, 15, 19, 34 }} | ||
Badness: 0.027410 | Badness: 0.027410 | ||
| Line 105: | Line 105: | ||
* 13- and 15-odd-limit diamond monotone and tradeoff: ~6/5 = 315.789 | * 13- and 15-odd-limit diamond monotone and tradeoff: ~6/5 = 315.789 | ||
Optimal | {{Optimal ET sequence|legend=1| 4, 15f, 19, 53def, 72def }} | ||
Badness: 0.029749 | Badness: 0.029749 | ||
| Line 125: | Line 125: | ||
* 15-odd-limit diamond monotone and tradeoff: ~6/5 = 315.789 | * 15-odd-limit diamond monotone and tradeoff: ~6/5 = 315.789 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 19, 34, 87ddee }} | ||
Badness: 0.022749 | Badness: 0.022749 | ||
| Line 138: | Line 138: | ||
POTE generator: ~6/5 = 318.595 | POTE generator: ~6/5 = 318.595 | ||
Optimal | {{Optimal ET sequence|legend=1| 4, 15, 19f, 34ff }} | ||
Badness: 0.031633 | Badness: 0.031633 | ||
| Line 151: | Line 151: | ||
POTE generator: ~6/5 = 314.730 | POTE generator: ~6/5 = 314.730 | ||
Optimal | {{Optimal ET sequence|legend=1| 4e, 19, 42bcd, 61bcdd }} | ||
Badness: 0.040056 | Badness: 0.040056 | ||
| Line 164: | Line 164: | ||
POTE generator: ~6/5 = 315.044 | POTE generator: ~6/5 = 315.044 | ||
Optimal | {{Optimal ET sequence|legend=1| 4ef, 19 }} | ||
Badness: 0.029419 | Badness: 0.029419 | ||
| Line 177: | Line 177: | ||
POTE generator: ~6/5 = 317.656 | POTE generator: ~6/5 = 317.656 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 19e, 34e }} | ||
Badness: 0.027648 | Badness: 0.027648 | ||
| Line 190: | Line 190: | ||
POTE generator: ~6/5 = 317.298 | POTE generator: ~6/5 = 317.298 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 19e, 34e, 53dee }} | ||
Badness: 0.021445 | Badness: 0.021445 | ||
| Line 210: | Line 210: | ||
* 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 319.265] | * 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 319.265] | ||
{{ | {{Optimal ET sequence|legend=1| 15, 34d, 49, 132bcd }} | ||
[[Badness]]: 0.094872 | [[Badness]]: 0.094872 | ||
| Line 228: | Line 228: | ||
* 11-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 320.000] | * 11-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 320.000] | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 34d, 49 }} | ||
Badness: 0.036894 | Badness: 0.036894 | ||
| Line 251: | Line 251: | ||
* 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 317.263] | * 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 317.263] | ||
{{ | {{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197, 269c }} | ||
[[Badness]]: 0.021501 | [[Badness]]: 0.021501 | ||
| Line 264: | Line 264: | ||
Optimal tuning (CTE): ~6/5 = 316.8865 | Optimal tuning (CTE): ~6/5 = 316.8865 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 125f, 197f }} | ||
Badness: 0.0118 | Badness: 0.0118 | ||
| Line 282: | Line 282: | ||
* 11-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 316.981] | * 11-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 316.981] | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 34de, 53, 72, 197e, 269ce, 341ce, 610bccee }} | ||
Badness: 0.021849 | Badness: 0.021849 | ||
| Line 300: | Line 300: | ||
* 13- and 15-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 316.981] | * 13- and 15-odd-limit diamond monotone and tradeoff: ~6/5 = [315.789, 316.981] | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 34de, 53, 72, 125f, 197ef, 269cef }} | ||
Badness: 0.016883 | Badness: 0.016883 | ||
| Line 313: | Line 313: | ||
Optimal tuning (POTE): ~6/5 = 317.042 | Optimal tuning (POTE): ~6/5 = 317.042 | ||
Optimal | {{Optimal ET sequence|legend=1| 19e, 34d, 53 }} | ||
Badness: 0.039954 | Badness: 0.039954 | ||
| Line 326: | Line 326: | ||
Optimal tuning (POTE): ~6/5 = 317.036 | Optimal tuning (POTE): ~6/5 = 317.036 | ||
Optimal | {{Optimal ET sequence|legend=1| 19e, 34d, 53 }} | ||
Badness: 0.022555 | Badness: 0.022555 | ||
| Line 339: | Line 339: | ||
Optimal tuning (POTE): ~6/5 = 316.653 | Optimal tuning (POTE): ~6/5 = 316.653 | ||
Optimal | {{Optimal ET sequence|legend=1| 19e, 53e, 72 }} | ||
Badness: 0.030422 | Badness: 0.030422 | ||
| Line 352: | Line 352: | ||
Optimal tuning (POTE): ~6/5 = 316.639 | Optimal tuning (POTE): ~6/5 = 316.639 | ||
Optimal | {{Optimal ET sequence|legend=1| 19e, 53e, 72 }} | ||
Badness: 0.022337 | Badness: 0.022337 | ||
| Line 365: | Line 365: | ||
Optimal tuning (POTE): ~6/5 = 317.083 | Optimal tuning (POTE): ~6/5 = 317.083 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 34d, 53e }} | ||
Badness: 0.044335 | Badness: 0.044335 | ||
| Line 378: | Line 378: | ||
Optimal tuning (POTE): ~6/5 = 317.118 | Optimal tuning (POTE): ~6/5 = 317.118 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 34d, 53e, 87dee }} | ||
Badness: 0.027343 | Badness: 0.027343 | ||
| Line 391: | Line 391: | ||
Optimal tuning (POTE): ~6/5 = 316.721 | Optimal tuning (POTE): ~6/5 = 316.721 | ||
Optimal | {{Optimal ET sequence|legend=1| 34d, 72, 322c, …, 610bcc }} | ||
Badness: 0.029319 | Badness: 0.029319 | ||
| Line 404: | Line 404: | ||
Optimal tuning (POTE): ~6/5 = 316.726 | Optimal tuning (POTE): ~6/5 = 316.726 | ||
Optimal | {{Optimal ET sequence|legend=1| 34d, 72 }} | ||
Badness: 0.021814 | Badness: 0.021814 | ||
| Line 417: | Line 417: | ||
Optimal tuning (POTE): ~6/5 = 316.726 | Optimal tuning (POTE): ~6/5 = 316.726 | ||
Optimal | {{Optimal ET sequence|legend=1| 34d, 38df, 72 }} | ||
Badness: 0.015656 | Badness: 0.015656 | ||
| Line 430: | Line 430: | ||
Optimal tuning (POTE): ~6/5 = 316.726 | Optimal tuning (POTE): ~6/5 = 316.726 | ||
Optimal | {{Optimal ET sequence|legend=1| 34dh, 38df, 72 }} | ||
Badness: 0.015771 | Badness: 0.015771 | ||
| Line 450: | Line 450: | ||
* 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [316.667, 317.263] | * 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [316.667, 317.263] | ||
{{ | {{Optimal ET sequence|legend=1| 19d, 34, 53, 87, 140, 333, 473, 806b }} | ||
[[Badness]]: 0.052129 | [[Badness]]: 0.052129 | ||
| Line 468: | Line 468: | ||
* 11-odd-limit diamond monotone and tradeoff: ~6/5 = [316.981, 317.370] | * 11-odd-limit diamond monotone and tradeoff: ~6/5 = [316.981, 317.370] | ||
Optimal | {{Optimal ET sequence|legend=1| 34, 53, 87, 140, 227, 367e, 507e }} | ||
Badness: 0.039770 | Badness: 0.039770 | ||
| Line 488: | Line 488: | ||
* 15-odd-limit diamond monotone and tradeoff: ~6/5 = [316.981, 317.241] | * 15-odd-limit diamond monotone and tradeoff: ~6/5 = [316.981, 317.241] | ||
Optimal | {{Optimal ET sequence|legend=1| 34, 53, 87, 140, 367e, 507e }} | ||
Badness: 0.020156 | Badness: 0.020156 | ||
| Line 503: | Line 503: | ||
[[POTE generator]]: ~6/5 = 317.314 | [[POTE generator]]: ~6/5 = 317.314 | ||
{{ | {{Optimal ET sequence|legend=1| 34d, 87, 121, 208 }} | ||
[[Badness]]: 0.163519 | [[Badness]]: 0.163519 | ||
| Line 516: | Line 516: | ||
POTE generator: ~6/5 = 317.311 | POTE generator: ~6/5 = 317.311 | ||
Optimal | {{Optimal ET sequence|legend=1| 34d, 53d, 87, 121, 208 }} | ||
Badness: 0.048570 | Badness: 0.048570 | ||
| Line 529: | Line 529: | ||
POTE generator: ~6/5 = 317.311 | POTE generator: ~6/5 = 317.311 | ||
Optimal | {{Optimal ET sequence|legend=1| 34d, 53d, 87, 121, 208 }} | ||
Badness: 0.024371 | Badness: 0.024371 | ||
| Line 544: | Line 544: | ||
[[POTE generator]]: ~35/32 = 158.649 | [[POTE generator]]: ~35/32 = 158.649 | ||
{{ | {{Optimal ET sequence|legend=1| 15, 38, 53, 121 }} | ||
[[Badness]]: 0.052054 | [[Badness]]: 0.052054 | ||
| Line 557: | Line 557: | ||
POTE generator: ~11/10 = 158.677 | POTE generator: ~11/10 = 158.677 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 38, 53, 68, 121e }} | ||
Badness: 0.038023 | Badness: 0.038023 | ||
| Line 570: | Line 570: | ||
Mapping: [{{val| 1 0 1 4 2 0 }}, {{val| 0 12 10 -9 11 28 }}] | Mapping: [{{val| 1 0 1 4 2 0 }}, {{val| 0 12 10 -9 11 28 }}] | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 38f, 53, 121e }} | ||
Badness: 0.026005 | Badness: 0.026005 | ||
| Line 594: | Line 594: | ||
[[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges. | [[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges. | ||
{{ | {{Optimal ET sequence|legend=1| 19, 49, 68, 87, 155 }} | ||
[[Badness]]: 0.047261 | [[Badness]]: 0.047261 | ||
| Line 607: | Line 607: | ||
POTE generator: ~9/7 = 441.355 | POTE generator: ~9/7 = 441.355 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 49e, 68, 87, 329bd, 419bd, 503bd, 590bd }} | ||
Badness: 0.047417 | Badness: 0.047417 | ||
| Line 620: | Line 620: | ||
POTE generator: ~9/7 = 441.363 | POTE generator: ~9/7 = 441.363 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 49ef, 68, 87, 503bdf, 590bdf }} | ||
Badness: 0.026842 | Badness: 0.026842 | ||
| Line 645: | Line 645: | ||
: [[Eigenmonzo]]s (unchanged-intervals): 2, 9/7 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 9/7 | ||
{{ | {{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }} | ||
[[Badness]]: 0.056337 | [[Badness]]: 0.056337 | ||
| Line 665: | Line 665: | ||
: Eigenmonzos (unchanged-intervals): 2, 9/7 | : Eigenmonzos (unchanged-intervals): 2, 9/7 | ||
Optimal | {{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }} | ||
Badness: 0.019333 | Badness: 0.019333 | ||
| Line 680: | Line 680: | ||
POTE generator: ~6/5 = 316.9585 | POTE generator: ~6/5 = 316.9585 | ||
Optimal | {{Optimal ET sequence|legend=1| 72, 87, 159 }} | ||
Badness: 0.015652 | Badness: 0.015652 | ||
| Line 695: | Line 695: | ||
POTE generator: ~6/5 = 316.9082 | POTE generator: ~6/5 = 316.9082 | ||
Optimal | {{Optimal ET sequence|legend=1| 72, 159, 231f }} | ||
Badness: 0.013551 | Badness: 0.013551 | ||
| Line 710: | Line 710: | ||
[[POTE generator]]: ~6/5 = 316.9999 | [[POTE generator]]: ~6/5 = 316.9999 | ||
{{ | {{Optimal ET sequence|legend=1| 68, 72, 140, 212, 776cd, 988ccd, 1200ccd }} | ||
[[Badness]]: 0.039231 | [[Badness]]: 0.039231 | ||
| Line 723: | Line 723: | ||
POTE generator: ~6/5 = 316.9247 | POTE generator: ~6/5 = 316.9247 | ||
Optimal | {{Optimal ET sequence|legend=1| 68, 72, 140, 212, 284, 496ce, 780ccdee }} | ||
Badness: 0.023406 | Badness: 0.023406 | ||
| Line 736: | Line 736: | ||
POTE generator: ~6/5 = 316.9887 | POTE generator: ~6/5 = 316.9887 | ||
Optimal | {{Optimal ET sequence|legend=1| 68, 72, 140, 212 }} | ||
Badness: 0.018731 | Badness: 0.018731 | ||
| Line 749: | Line 749: | ||
POTE generator: ~6/5 = 316.9846 | POTE generator: ~6/5 = 316.9846 | ||
Optimal | {{Optimal ET sequence|legend=1| 68, 72, 140, 212g }} | ||
Badness: 0.012784 | Badness: 0.012784 | ||
| Line 764: | Line 764: | ||
[[POTE generator]]: ~25/21 = 294.303 | [[POTE generator]]: ~25/21 = 294.303 | ||
{{ | {{Optimal ET sequence|legend=1| 49, 53, 314d }} | ||
[[Badness]]: 0.076460 | [[Badness]]: 0.076460 | ||
| Line 777: | Line 777: | ||
POTE generator: ~25/21 = 294.181 | POTE generator: ~25/21 = 294.181 | ||
Optimal | {{Optimal ET sequence|legend=1| 49, 53, 102d, 155d }} | ||
Badness: 0.052805 | Badness: 0.052805 | ||
| Line 790: | Line 790: | ||
POTE generator: ~13/11 = 294.187 | POTE generator: ~13/11 = 294.187 | ||
Optimal | {{Optimal ET sequence|legend=1| 49f, 53, 102df, 155d }} | ||
Badness: 0.031074 | Badness: 0.031074 | ||
| Line 807: | Line 807: | ||
[[POTE generator]]: ~75/56 = 505.705 | [[POTE generator]]: ~75/56 = 505.705 | ||
{{ | {{Optimal ET sequence|legend=1| 19, 121, 140, 579, 719, 859bcd, 999bcd, 1858bbccdd }} | ||
[[Badness]]: 0.063448 | [[Badness]]: 0.063448 | ||
| Line 820: | Line 820: | ||
POTE generator: ~75/56 = 505.684 | POTE generator: ~75/56 = 505.684 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 140, 159, 299 }} | ||
Badness: 0.058902 | Badness: 0.058902 | ||
| Line 833: | Line 833: | ||
POTE generator: ~75/56 = 505.686 | POTE generator: ~75/56 = 505.686 | ||
Optimal | {{Optimal ET sequence|legend=1|19, 140, 159, 299 }} | ||
Badness: 0.030082 | Badness: 0.030082 | ||
| Line 848: | Line 848: | ||
POTE generator: ~75/56 = 505.740 | POTE generator: ~75/56 = 505.740 | ||
Optimal | {{Optimal ET sequence|legend=1|19e, 121, 140, 261, 401, 662bd }} | ||
Badness: 0.061172 | Badness: 0.061172 | ||
| Line 861: | Line 861: | ||
POTE generator: ~75/56 = 505.740 | POTE generator: ~75/56 = 505.740 | ||
Optimal | {{Optimal ET sequence|legend=1| 19e, 121, 140, 261, 401, 662bd }} | ||
Badness: 0.028671 | Badness: 0.028671 | ||
| Line 876: | Line 876: | ||
POTE generator: ~75/56 = 505.769 | POTE generator: ~75/56 = 505.769 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 102d, 121 }} | ||
Badness: 0.075112 | Badness: 0.075112 | ||
| Line 889: | Line 889: | ||
POTE generator: ~75/56 = 505.771 | POTE generator: ~75/56 = 505.771 | ||
Optimal | {{Optimal ET sequence|legend=1| 19, 121 }} | ||
Badness: 0.038317 | Badness: 0.038317 | ||
| Line 906: | Line 906: | ||
[[POTE generator]]: ~56/45 = 379.252 | [[POTE generator]]: ~56/45 = 379.252 | ||
{{ | {{Optimal ET sequence|legend=1| 19, 193, 212, 617c, 829c }} | ||
[[Badness]]: 0.104253 | [[Badness]]: 0.104253 | ||
| Line 919: | Line 919: | ||
POTE generator: ~56/45 = 379.257 | POTE generator: ~56/45 = 379.257 | ||
Optimal | {{Optimal ET sequence|legend=1| 19e, 193, 212, 405, 617c, 1022cce }} | ||
Badness: 0.075624 | Badness: 0.075624 | ||
| Line 932: | Line 932: | ||
POTE generator: ~56/45 = 379.256 | POTE generator: ~56/45 = 379.256 | ||
Optimal | {{Optimal ET sequence|legend=1| 19e, 193, 212, 405f, 617cff }} | ||
Badness: 0.043728 | Badness: 0.043728 | ||
| Line 947: | Line 947: | ||
[[Optimal tuning]] ([[CTE]]): ~36/35 = 52.8562 | [[Optimal tuning]] ([[CTE]]): ~36/35 = 52.8562 | ||
{{ | {{Optimal ET sequence|legend=1| 68, 91, 159, 386d, 545dd }} | ||
[[Badness]]: 0.146 | [[Badness]]: 0.146 | ||
| Line 960: | Line 960: | ||
Optimal tuning (CTE): ~33/32 = 52.8524 | Optimal tuning (CTE): ~33/32 = 52.8524 | ||
Optimal | {{Optimal ET sequence|legend=1| 68, 91, 159, 386d, 545dd }} | ||
Badness: 0.0865 | Badness: 0.0865 | ||
| Line 975: | Line 975: | ||
[[POTE generator]]: ~6/5 = 317.005 | [[POTE generator]]: ~6/5 = 317.005 | ||
{{ | {{Optimal ET sequence|legend=1| 72, 261, 333, 405, 477c, 882c }} | ||
[[Badness]]: 0.193429 | [[Badness]]: 0.193429 | ||
| Line 988: | Line 988: | ||
POTE generator: ~6/5 = 317.010 | POTE generator: ~6/5 = 317.010 | ||
Optimal | {{Optimal ET sequence|legend=1| 72, 261, 333, 405, 882c }} | ||
Badness: 0.051730 | Badness: 0.051730 | ||
| Line 1,001: | Line 1,001: | ||
POTE generator: ~6/5 = 317.086 | POTE generator: ~6/5 = 317.086 | ||
Optimal | {{Optimal ET sequence|legend=1| 72, 261, 333, 738cf, 1071bcff }} | ||
Badness: 0.039072 | Badness: 0.039072 | ||
| Line 1,018: | Line 1,018: | ||
[[POTE generator]]: ~125/98 = 416.603 | [[POTE generator]]: ~125/98 = 416.603 | ||
{{ | {{Optimal ET sequence|legend=1| 49, 72, 193, 265 }} | ||
[[Badness]]: 0.070378 | [[Badness]]: 0.070378 | ||
| Line 1,031: | Line 1,031: | ||
POTE generator: ~14/11 = 416.604 | POTE generator: ~14/11 = 416.604 | ||
Optimal | {{Optimal ET sequence|legend=1| 49, 72, 193, 265 }} | ||
Badness: 0.025515 | Badness: 0.025515 | ||
| Line 1,044: | Line 1,044: | ||
POTE generator: ~14/11 = 416.585 | POTE generator: ~14/11 = 416.585 | ||
Optimal | {{Optimal ET sequence|legend=1| 72, 121, 193 }} | ||
Badness: 0.020040 | Badness: 0.020040 | ||
| Line 1,057: | Line 1,057: | ||
POTE generator: ~14/11 = 416.585 | POTE generator: ~14/11 = 416.585 | ||
Optimal | {{Optimal ET sequence|legend=1| 72, 121, 193 }} | ||
Badness: 0.013028 | Badness: 0.013028 | ||
| Line 1,070: | Line 1,070: | ||
POTE generator: ~14/11 = 416.580 | POTE generator: ~14/11 = 416.580 | ||
Optimal | {{Optimal ET sequence|legend=1| 72, 121, 193 }} | ||
Badness: 0.014748 | Badness: 0.014748 | ||