User:ArrowHead294/Purely consistent EDOs by odd limit: Difference between revisions

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Below is a table of the first 50 EDOs that are [[Minimal consistent EDOs|purely consistent]] (approximate all harmonics with <25% relative error) in the 7-, 15-, 31-, and 63-odd-limits.
Below is a table of the first 50 EDOs that are [[Minimal consistent EDOs|purely consistent]] (approximate all harmonics with <25% relative error) in the 7-, 15-, 31-, and 63-odd-limits.


== Tables ==
{{centre|<div style{{=}}"display: inline-grid; margin-right: 20px;">
{{centre|<div style{{=}}"display: inline-grid; margin-right: 20px;">
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The smallest EDOs purely consistent in the 7-, 15-, 31-, and 63-odd-limits are 10, 87, 311, and 3159811, respectively.
== Results ==
 
Additionally, there are (12) 7-odd-limit purely-consistent EDOs less than 87, (3) 15-odd-limit purely-consistent EDOs less than 311, and (481) 31-odd-limit purely consistent EDOs less than 3159811.
 
<div style="margin-bottom: 1em;">
{{Databox
| 7-odd-limit purely-consistent EDOs less than 87
| {{normal|{{EDOs| 10, 15, 22, 31, 41, 46, 53, 56, 68, 72, 77, 84 }}}}
}}
</div><div style="margin-bottom: 1em;">
{{Databox
| 15-odd-limit purely-consistent EDOs less than 311
| {{normal|{{EDOs| 87, 224, 270 }}}}
}}
</div><div style="margin-bottom: 1em;">
{{Databox
| 31-odd-limit purely consistent EDOs less than 3159811
| {{normal|<span style{{=}}"font-size: 80%;">EDOs not present in the table below are in ''italics''</span><br />{{EDOs| 311, 16808, 20567, 25540, 28342, 31920, 34691, 60392, 65322, 90623, 93664, 116498, 124702, 143958, 148418, 164838, 165226, 165879, 175878, 185793, 195339, 195727, 209851, 210569, 212147, 220633, 241200, 248975, 256119, 263323, 265323, 266901, 285172, 286350, 292376, 298467, 301592, 308712, 318400, 324296, 328645, 330645, 334553, 339998, 344145, 346742, 349643, 351672, 354185, 358987, ''360565, 363466, 370499, 371564, 373677, 377373, 385729, 385912, 389618, 395256, 405050, 406296, 406426, 414965, 431385, 439524, 451051, 459944, 460438, 470372, 477470, 482971, 490175, 490358, 491510, 494589, 530634, 536089, 536443, 536983, 542792, 547442, 550955, 570416, 571134, 579803, 587942, 589737, 590843, 597876, 606545, 607263, 610304, 610776, 612764, 642696, 643349, 646915, 649428, 652630, 666236, 669749, 675269, 684507, 687632, 710208, 729980, 732129, 736360, 739261, 739914, 744899, 746294, 751267, 753168, 763102, 763820, 766861, 771834, 775347, 775530, 785464, 791767, 824588, 829142, 836917, 839818, 849034, 850740, 852075, 855154, 859279, 861279, 866153, 876087, 891199, 896654, 905140, 911520, 920777, 922172, 934600, 937585, 948507, 948724, 951408, 958441, 965315, 965532, 971341, 977560, 986099, 1002907, 1003914, 1007697, 1024505, 1025223, 1030314, 1035157, 1041313, 1042031, 1044761, 1045072, 1051965, 1055543, 1078300, 1090545, 1095937, 1096925, 1099826, 1100479, 1109760, 1110083, 1117287, 1118576, 1122272, 1124385, 1132206, 1132399, 1141410, 1144451, 1146747, 1149207, 1152332, 1161259, 1161977, 1163331, 1173330, 1177679, 1183575, 1183898, 1200383, 1206732, 1220950, 1235074, 1236652, 1238652, 1248586, 1251882, 1265705, 1272803, 1281342, 1298150, 1306164, 1311973, 1326097, 1330723, 1334236, 1336031, 1336749, 1337137, 1349124, 1359058, 1359776, 1363472, 1371247, 1373406, 1385788, 1395722, 1402459, 1403748, 1405326, 1410952, 1412530, 1418879, 1430801, 1432379, 1441583, 1447221, 1456502, 1461044, 1464029, 1476274, 1477852, 1479141, 1501975, 1506905, 1507476, 1508194, 1510114, 1511909, 1521824, 1522542, 1536666, 1539350, 1542475, 1549284, 1553474, 1567297, 1577231, 1581515, 1594757, 1595639, 1598323, 1601448, 1612447, 1615348, 1626270, 1626795, 1660650, 1662269, 1667854, 1680894, 1691893, 1696307, 1697702, 1705229, 1711826, 1712544, 1714510, 1719623, 1726755, 1737149, 1749201, 1756675, 1771517, 1777866, 1785865, 1788325, 1791366, 1800753, 1810687, 1823016, 1824594, 1829312, 1833714, 1836528, 1836839, 1846120, 1853647, 1862540, 1867470, 1872474, 1887704, 1894106, 1895501, 1897231, 1908401, 1912309, 1918335, 1921159, 1953026, 1955322, 1959105, 1973012, 1975913, 1976631, 1984052, 2010604, 2026347, 2027412, 2027636, 2038064, 2044444, 2051887, 2052458, 2066011, 2073109, 2083614, 2086792, 2089917, 2092818, 2092958, 2095859, 2097931, 2109766, 2112279, 2114739, 2116970, 2126090, 2129087, 2132082, 2148890, 2151791, 2161135, 2169674, 2183581, 2186482, 2197404, 2202225, 2203290, 2207338, 2208403, 2222568, 2222751, 2224146, 2235863, 2268836, 2285644, 2287439, 2293658, 2296255, 2299768, 2307242, 2310466, 2313591, 2322655, 2327809, 2331117, 2355228, 2358741, 2372564, 2381821, 2382209, 2384281, 2387794, 2390090, 2396333, 2398629, 2427682, 2442601, 2448969, 2458496, 2461481, 2463951, 2475304, 2479535, 2488074, 2489652, 2504882, 2515127, 2526480, 2534619, 2543158, 2547047, 2556981, 2563855, 2570888, 2581738, 2595250, 2598546, 2599941, 2609328, 2619262, 2622303, 2626006, 2639829, 2640400, 2646426, 2651182, 2654223, 2663952, 2671031, 2676657, 2680900, 2685873, 2687839, 2688774, 2691005, 2702681, 2712926, 2719306, 2722207, 2722925, 2733182, 2739733, 2742774, 2753857, 2756898, 2757616, 2773706, 2774424, 2775819, 2784358, 2784488, 2787936, 2788247, 2793885, 2798181, 2809534, 2810693, 2814989, 2833397, 2839112, 2841541, 2861033, 2861751, 2881600, 2893789, 2895184, 2903723, 2904434, 2924420, 2932776, 2934354, 2940657, 2949196, 2949584, 2963407, 2969045, 2971946, 2972223, 2978249, 2981504, 2982157, 2986571, 2997710, 2999676, 3000394, 3008169, 3014906, 3037222, 3044366, 3046826, 3049339, 3051893, 3056760, 3068949, 3076392, 3083490, 3100298, 3103069, 3114422, 3128115, 3134271, 3134989, 3139285, 3144923, 3148812, 3151797, 3158746'' }}}}
}}
</div>
 
These lists were generated using JavaScript code run in Mozilla Firefox's console. The amount of time it took me to generate these lists is as follows:
These lists were generated using JavaScript code run in Mozilla Firefox's console. The amount of time it took me to generate these lists is as follows:


Line 248: Line 229:


See the {{subpage|appendix|u}} for the code I used to generate these lists.
See the {{subpage|appendix|u}} for the code I used to generate these lists.
== Appendix ==
{{main|{{FULLPAGENAME}}/Appendix}}


[[Category:EDO theory pages]]
[[Category:EDO theory pages]]
[[Category:Tables]]
[[Category:Tables]]

Revision as of 21:05, 31 March 2025

Below is a table of the first 50 EDOs that are purely consistent (approximate all harmonics with <25% relative error) in the 7-, 15-, 31-, and 63-odd-limits.

Tables

First 50 purely consistent EDOs
(25% maximum relative error)
7-odd-limit 15-odd-limit 31-odd-limit 63-odd-limit
10 87 311 3159811
15 224 16808 4393509
22 270 20567 7317929
31 311 25540 8595351
41 364 28342 10143327
46 400 31920 10881306
53 431 34691 16070278
56 494 60392 24700320
68 518 65322 27167203
72 764 90623 27783092
77 795 93664 32452446
84 805 116498 34531581
87 882 124702 39638069
99 925 143958 40326968
108 1012 148418 43237481
109 1376 164838 43272172
125 1506 165226 47518993
130 1665 165879 50203972
140 1802 175878 51781203
161 1870 185793 55331157
162 1889 195339 57807073
171 2029 195727 61698784
186 2096 209851 67708629
193 2159 210569 79746917
202 2190 212147 79863868
212 2320 220633 81853117
214 2373 241200 81926438
217 2383 248975 89927296
224 2414 256119 92431072
239 2460 263323 92867999
243 2501 265323 95660980
248 2590 266901 97834962
255 2631 285172 98134212
270 2684 286350 98798699
280 2730 292376 99646444
301 2771 298467 101833237
311 2814 301592 103428565
323 2877 308712 105324066
332 2901 318400 109559534
333 2908 324296 111221150
342 2954 328645 116368138
354 2995 330645 122984398
357 3084 334553 125090598
364 3171 339998 127311771
369 3178 344145 128730110
373 3202 346742 130221303
385 3224 349643 133768421
395 3265 351672 140849220
400 3395 354185 141033767
410 3448 358987 143662814

Results

These lists were generated using JavaScript code run in Mozilla Firefox's console. The amount of time it took me to generate these lists is as follows:

  • 7-odd-limit: 5ms
  • 15-odd-limit: 62ms
  • 31-odd-limit: 2.891s
  • 63-odd-limit: 2h 53m 26.6s

See the appendix for the code I used to generate these lists.

Appendix

Main page: User:ArrowHead294/Purely consistent EDOs by odd limit/Appendix
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