EDOs

I've been looking at EDOs and it seems to me that 12EDO works so well because it contains both a Perfect Fourth (4/3) and a Perfect Fifth (3/2) within 2.0 cents accuracy in all keys. My favorite musical genres are Blues and Rock and this music is usually made using Fourths and Fifths which are the strongest intervals that occur between the tonic and octave. Based on this I suspect that the best EDOs are those that contain a Fourth and Fifth within 6.776 cents (256/255) accuracy. The 6.776 cents threshold is my own best guess at maximum deviation from pure and I do not claim that it should be set in stone.

I looked at all EDOs from 1EDO to 48EDO and below is a complete list of all EDOs (from 1 to 48) which contain a Fourth and Fifth within 6.776 cents accuracy.

With 12EDO there are 4 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 9/8, 4/3, 3/2 and 2/1.

With 31EDO there are 14 good (within +/-6.776 cents accuracy) intervals (see below) an octave or less wide: 8/7, 7/6, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 11/6, 2/1.

12EDO, 4 good
0.0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200

17EDO, 4 good
0.0, 70.5882, 141.176, 211.765, 282.353, 352.941, 423.529, 494.118, 564.706, 635.294, 705.882, 776.471, 847.059, 917.647, 988.235, 1058.82, 1129.41, 1200

24EDO, 6 good
0.0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050, 1100, 1150, 1200

29EDO, 8 good
0.0, 41.3793, 82.7586, 124.138, 165.517, 206.897, 248.276, 289.655, 331.034, 372.414, 413.793, 455.172, 496.552, 537.931, 579.31, 620.69, 662.069, 703.448, 744.828, 786.207, 827.586, 868.966, 910.345, 951.724, 993.103, 1034.48, 1075.86, 1117.24, 1158.62, 1200

31EDO, 14 good
0.0, 38.7097, 77.4194, 116.129, 154.839, 193.548, 232.258, 270.968, 309.677, 348.387, 387.097, 425.806, 464.516, 503.226, 541.935, 580.645, 619.355, 658.065, 696.774, 735.484, 774.194, 812.903, 851.613, 890.323, 929.032, 967.742, 1006.45, 1045.16, 1083.87, 1122.58, 1161.29, 1200

34EDO, 9 good
0.0, 35.2941, 70.5882, 105.882, 141.176, 176.471, 211.765, 247.059, 282.353, 317.647, 352.941, 388.235, 423.529, 458.824, 494.118, 529.412, 564.706, 600, 635.294, 670.588, 705.882, 741.176, 776.471, 811.765, 847.059, 882.353, 917.647, 952.941, 988.235, 1023.53, 1058.82, 1094.12, 1129.41, 1164.71, 1200

36EDO, 10 good
0.0, 33.3333, 66.6667, 100, 133.333, 166.667, 200, 233.333, 266.667, 300, 333.333, 366.667, 400, 433.333, 466.667, 500, 533.333, 566.667, 600, 633.333, 666.667, 700, 733.333, 766.667, 800, 833.333, 866.667, 900, 933.333, 966.667, 1000, 1033.33, 1066.67, 1100, 1133.33, 1166.67, 1200

39EDO, 10 good
0.0, 30.7692, 61.5385, 92.3077, 123.077, 153.846, 184.615, 215.385, 246.154, 276.923, 307.692, 338.462, 369.231, 400, 430.769, 461.538, 492.308, 523.077, 553.846, 584.615, 615.385, 646.154, 676.923, 707.692, 738.462, 769.231, 800, 830.769, 861.538, 892.308, 923.077, 953.846, 984.615, 1015.38, 1046.15, 1076.92, 1107.69, 1138.46, 1169.23, 1200

41EDO, 17 good
0.0, 29.2683, 58.5366, 87.8049, 117.073, 146.341, 175.61, 204.878, 234.146, 263.415, 292.683, 321.951, 351.22, 380.488, 409.756, 439.024, 468.293, 497.561, 526.829, 556.098, 585.366, 614.634, 643.902, 673.171, 702.439, 731.707, 760.976, 790.244, 819.512, 848.78, 878.049, 907.317, 936.585, 965.854, 995.122, 1024.39, 1053.66, 1082.93, 1112.2, 1141.46, 1170.73, 1200
41 = 17 Ratio= 0.414634

43EDO, 8 good
0.0, 27.907, 55.814, 83.7209, 111.628, 139.535, 167.442, 195.349, 223.256, 251.163, 279.07, 306.977, 334.884, 362.791, 390.698, 418.605, 446.512, 474.419, 502.326, 530.233, 558.14, 586.047, 613.953, 641.86, 669.767, 697.674, 725.581, 753.488, 781.395, 809.302, 837.209, 865.116, 893.023, 920.93, 948.837, 976.744, 1004.65, 1032.56, 1060.47, 1088.37, 1116.28, 1144.19, 1172.09, 1200

46EDO, 17 good
0.0, 26.087, 52.1739, 78.2609, 104.348, 130.435, 156.522, 182.609, 208.696, 234.783, 260.87, 286.957, 313.043, 339.13, 365.217, 391.304, 417.391, 443.478, 469.565, 495.652, 521.739, 547.826, 573.913, 600, 626.087, 652.174, 678.261, 704.348, 730.435, 756.522, 782.609, 808.696, 834.783, 860.87, 886.957, 913.043, 939.13, 965.217, 991.304, 1017.39, 1043.48, 1069.57, 1095.65, 1121.74, 1147.83, 1173.91, 1200

48EDO, 9 good
0.0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200

Here is the list of all intervals an octave or less wide that I consider good (in harmony)...
9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.

John.