311edo: Difference between revisions
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=== Commas === | === Commas === | ||
Some 41-limit [[comma]]s it tempers out are [[595/594]], [[625/624]], 697/696, 703/702, 714/713, 760/759, [[784/783]], 820/819, [[833/832]], 875/874, 900/899, 925/924, 931/930, 962/961, 969/968, 1000/999, 1015/1014, 1024/1023, [[1025/1024]], 1036/1035, 1045/1044, 1054/1053, 1105/1104, 1148/1147, [[1156/1155]], 1184/1183, 1189/1188, 1190/1189, 1197/1196, 1210/1209, [[1216/1215]], [[1225/1224]], [[1275/1274]], 1288/1287, 1312/1311, 1332/1331, 1353/1352, 1365/1364, 1369/1368, 1444/1443, [[1445/1444]], 1450/1449, 1480/1479, 1496/1495, 1519/1518, 1520/1519, 1540/1539, 1596/1595, 1600/1599, 1625/1624, 1665/1664, 1666/1665, 1681/1680, 1683/1682, 1702/1701, [[1729/1728]], 1768/1767, 1805/1804, 1860/1859, 1886/1885, 1887/1886, 1925/1924, 2002/2001, 2016/2015, 2025/2024, [[2058/2057]], [[2080/2079]], 2091/2090, 2109/2108, 2146/2145, 2176/2175, 2185/2184, 2205/2204, 2233/2232, 2255/2254, 2295/2294, 2296/2295, 2300/2299, [[2401/2400]], [[2431/2430]], [[2432/2431]], 2465/2464, [[2500/2499]], 2542/2541, 2553/2552, 2584/2583, [[2601/2600]], 2625/2624, 2640/2639, 2646/2645, 2665/2664, 2737/2736, 2738/2737, 2755/2754, 2784/2783, 2850/2849, 2926/2925, and 2945/2944. | Some 41-limit [[comma]]s it tempers out are [[595/594]], [[625/624]], 697/696, 703/702, 714/713, 760/759, [[784/783]], 820/819, [[833/832]], 875/874, 900/899, 925/924, 931/930, 962/961, 969/968, 1000/999, 1015/1014, 1024/1023, [[1025/1024]], 1036/1035, 1045/1044, 1054/1053, 1105/1104, 1148/1147, [[1156/1155]], 1184/1183, 1189/1188, 1190/1189, 1197/1196, 1210/1209, [[1216/1215]], [[1225/1224]], [[1275/1274]], 1288/1287, 1312/1311, 1332/1331, 1353/1352, 1365/1364, 1369/1368, 1444/1443, [[1445/1444]], 1450/1449, 1480/1479, 1496/1495, 1519/1518, 1520/1519, 1540/1539, 1596/1595, 1600/1599, 1625/1624, 1665/1664, 1666/1665, 1681/1680, 1683/1682, 1702/1701, [[1729/1728]], 1768/1767, 1805/1804, 1860/1859, 1886/1885, 1887/1886, 1925/1924, 2002/2001, 2016/2015, 2025/2024, [[2058/2057]], [[2080/2079]], 2091/2090, 2109/2108, 2146/2145, 2176/2175, 2185/2184, 2205/2204, 2233/2232, 2255/2254, 2295/2294, 2296/2295, 2300/2299, [[2401/2400]], [[2431/2430]], [[2432/2431]], 2465/2464, [[2500/2499]], 2542/2541, 2553/2552, 2584/2583, [[2601/2600]], 2625/2624, 2640/2639, 2646/2645, 2665/2664, 2737/2736, 2738/2737, 2755/2754, 2784/2783, 2850/2849, 2926/2925, and 2945/2944. | ||
== Scales == | |||
311edo accurately approximates the mode 16 of [[harmonic series]], and the only interval pair not distinct is 14/13 and 15/14. It can also do mode 12 decently. | |||
{| class="wikitable center-all" | |||
|- | |||
! Overtones | |||
! 16 | |||
! 17 | |||
! 18 | |||
! 19 | |||
! 20 | |||
! 21 | |||
! 22 | |||
! 23 | |||
! 24 | |||
|- | |||
! …in cents<br />(octave-reduced) | |||
| 0 | |||
| 104.955 | |||
| 203.910 | |||
| 297.513 | |||
| 386.314 | |||
| 470.781 | |||
| 551.318 | |||
| 628.274 | |||
| 701.955 | |||
|- | |||
! Degrees in 87edo | |||
| 0 | |||
| 27 | |||
| 53 | |||
| 77 | |||
| 100 | |||
| 122 | |||
| 143 | |||
| 163 | |||
| 182 | |||
|- | |||
! … in cents | |||
| 0 | |||
| 104.180 | |||
| 204.502 | |||
| 297.106 | |||
| 385.852 | |||
| 470.740 | |||
| 551.768 | |||
| 628.939 | |||
| 702.251 | |||
|} | |||
{| class="wikitable center-all" | |||
|- | |||
! Overtones | |||
! 25 | |||
! 26 | |||
! 27 | |||
! 28 | |||
! 29 | |||
! 30 | |||
! 31 | |||
! 32 | |||
|- | |||
! …in cents<br />(octave-reduced) | |||
| 773 | |||
| 841 | |||
| 906 | |||
| 969 | |||
| 1030 | |||
| 1088 | |||
| 1145 | |||
| 1200 | |||
|- | |||
! Degrees in 311edo | |||
| 200 | |||
| 218 | |||
| 235 | |||
| 251 | |||
| 267 | |||
| 282 | |||
| 297 | |||
| 311 | |||
|- | |||
! … in cents | |||
| 771.704 | |||
| 841.158 | |||
| 906.752 | |||
| 968.489 | |||
| 1030.23 | |||
| 1088.1 | |||
| 1145.98 | |||
| 1200 | |||
|} | |||
== Detemperaments == | == Detemperaments == | ||