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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. | The smallest EDOs purely consistent in the 7-, 15-, 31-, and 63-odd-limits are 10, 87, 311, and 3159811, respectively. | ||
{{{{ | 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. | ||
{{Databox | |||
| 7-odd-limit purely-consistent EDOs less than 87 | |||
| {{normal|{{EDOs| 10, 15, 22, 31, 41, 46, 53, 56, 68, 72, 77, 84 }}}} | |||
}}<br /> | |||
{{Databox | |||
| 15-odd-limit purely-consistent EDOs less than 311 | |||
| {{normal|{{EDOs| 87, 224, 270 }}}} | |||
}}<br /> | |||
{{Databox | |||
| 31-odd-limit purely consistent EDOs less than 3159811 | |||
| {{normal|{{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 }}<br /><br /><span style{{=}}"font-size: 85%;">The following EDOs have a pure consistency limit of at least 31 but are not included in the list below:</span><br />{{EDOs| 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 }}}} | |||
}} | |||
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: | ||
Revision as of 00:41, 20 January 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.
The smallest EDOs purely consistent in the 7-, 15-, 31-, and 63-odd-limits are 10, 87, 311, and 3159811, respectively.
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.
31-odd-limit purely consistent EDOs less than 3159811
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
The following EDOs have a pure consistency limit of at least 31 but are not included in the list below:
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
The following EDOs have a pure consistency limit of at least 31 but are not included in the list below:
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
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: 11.9s
- 63-odd-limit: 2h 53m 26.6s