28edf
Division of the just perfect fifth into 28 equal parts (28EDF) is related to 48 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 25.0698 cents (corresponding to 47.8663 edo). It is related to the regular temperament which tempers out |187 -159 28> in the 5-limit; 6656/6655, 256000/255879, and 38671875/38614472 in the 13-limit (2.3.5.11.13 subgroup), which is supported by 335, 383, 718, 1053, and 1101 EDOs.
Intervals
| ed233\420-5¢ (~101ed4!) | ed31\54 (~49edo!) | ed121/81 (~ed11\19) | ed696¢ | ed32\55 | 48edo=r¢ | ed3/2 | Pyrite | ed708¢ | ed122/81 (~ed13\22) | ed34\57 (~47edo!) | ed37\60+5¢ (~91ed4!) | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (~ed17\29) | (~ed10\17) | ||||||||||||
| 1 | 23.5969-23.7755 | 24.6032 | 24.81485 | 24.8571 | 24.9351 | 25 | 25.0698 | 25.1299 | 25.2091 | 25.2857 | 25.3234 | 25.5639 | 26.4286-26.6071 |
| 2 | 47.1939-47.551 | 49.20635 | 49.6297 | 49.7143 | 49.8701 | 50 | 50.1396 | 50.2597 | 50.41825 | 50.5714 | 50.6475 | 51.1278 | 52.8571-53.2143 |
| 3 | 70.7908-71.3625 | 73.8095 | 74.4446 | 74.5714 | 74.8052 | 75 | 75.2095 | 75.3896 | 75.6274 | 75.8571 | 75.9712 | 76.6917 | 79.2857-79.8574 |
| 4 | 94.3878-95.102 | 98.4127 | 99.2594 | 99.4286 | 99.7403 | 100 | 100.2793 | 100.5194 | 100.8365 | 101.1429 | 101.295 | 102.2556 | 105.7143-106.4286 |
| 5 | 117.9847-118.87755 | 123.0159 | 124.0743 | 124.2857 | 124.6753 | 125 | 125.3491 | 125.6493 | 126.0456 | 126.4286 | 126.6187 | 127.81955 | 132.1429-133.0357 |
| 6 | 141.5816-142.653 | 147.61905 | 148.8891 | 149.1429 | 149.6104 | 150 | 150.4189 | 150.77915 | 151.2547 | 151.7143 | 151.9425 | 153.3835 | 158.5714-159.6429 |
| 7 | 165.1786-166.4286 | 172.2222 | 173.704 | 174 | 174.54545 | 175 | 175.48875 | 175.909 | 176.4639 | 177 | 177.2662 | 178.947 | 185-186.25 |
| 8 | 188.7755-190.2041 | 196.8254 | 198.5188 | 198.8571 | 199.4805 | 200 | 200.5586 | 201.0389 | 201.673 | 202.2857 | 202.5899 | 204.5113 | 211.4286-212.8571 |
| 9 | 212.3724-213.9796 | 221.4286 | 223.3337 | 223.7143 | 224.4156 | 225 | 225.6284 | 226.1687 | 226.8821 | 227.5714 | 227.9137 | 230.0752 | 237.8571-239.4643 |
| 10 | 235.9694-237.7551 | 246.03175 | 248.1485 | 248.5714 | 249.35065 | 250 | 250.6982 | 251.2986 | 252.0912 | 252.8571 | 253.2374 | 255.6391 | 264.2857-266.0714 |
| 11 | 259.5663-261.5306 | 270.6349 | 272.9634 | 273.4286 | 274.2857 | 275 | 275.768 | 276.4284 | 277.3004 | 278.1429 | 278.5612 | 281.203 | 290.7143-292.6786 |
| 12 | 283.1633-285.3061 | 295.2381 | 297.782 | 298.2857 | 299.2208 | 300 | 300.8379 | 301.5583 | 302.5095 | 303.4286 | 303.8849 | 306.7669 | 317.1429-319.2857 |
| 13 | 306.7602-309.0816 | 319.8413 | 322.5931 | 323.1429 | 324.1558 | 325 | 325.9077 | 326.6682 | 327.7186 | 328.7143 | 329.2087 | 332.3308 | 343.5714-345.8929 |
| 14 | 330.3571-332.8571 | 344.4444 | 347.408 | 348 | 349.0909 | 350 | 350.9775 | 351.818 | 352.9277 | 354 | 354.5324 | 357.8947 | 370-372.5 |
| 15 | 353.9541-356.63265 | 369.0476 | 372.2228 | 372.8571 | 374.026 | 375 | 376.0473 | 376.9479 | 378.13685 | 379.2857 | 379.8561 | 383.45865 | 396.4286-399.1071 |
| 16 | 377.551-380.4082 | 393.6508 | 397.03765 | 397.7143 | 398.961 | 400 | 401.1171 | 402.0777 | 403.346 | 404.5714 | 405.1799 | 409.0226 | 422.8571-425.7143 |
| 17 | 401.148-404.1837 | 418.254 | 421.8525 | 422.5714 | 423.8961 | 425 | 426.187 | 427.2076 | 428.5551 | 429.8571 | 430.5036 | 434.5865 | 449.5714-452.3214 |
| 18 | 424.7449-427.9592 | 442.8571 | 446.66735 | 447.4286 | 448.8312 | 450 | 451.2568 | 452.33745 | 453.7642 | 455.1429 | 455.8274 | 460.1504 | 475.7143-478.9286 |
| 19 | 448.3418-451.7347 | 467.460 | 471.4822 | 472.2857 | 473.7662 | 475 | 476.3266 | 477.4673 | 478.97333 | 480.4286 | 481.1511 | 485.7143 | 502.1429-505.5357 |
| 20 | 471.9388-475.5102 | 492.0635 | 496.2971 | 497.1429 | 498.7013 | 500 | 501.3964 | 502.5972 | 504.1825 | 505.7143 | 506.4749 | 511.2781 | 528.5714-532.1429 |
| 21 | 495.5357-499.2857 | 516.6667 | 521.1119 | 522 | 523.6364 | 525 | 526.46625 | 527.727 | 529.3916 | 531 | 531.7986 | 536.8421 | 555-558.75 |
| 22 | 519.13265-523.0612 | 541.2698 | 545.9268 | 546.8571 | 548.5714 | 550 | 551.536 | 552.8569 | 554.6007 | 556.2857 | 557.1223 | 562.406 | 581.4286-585.3571 |
| 23 | 542.7296-546.8367 | 565.873 | 570.7416 | 571.4286 | 573.5065 | 575 | 576.6059 | 577.9867 | 579.8098 | 581.5714 | 582.4461 | 587.9699 | 607.8571-611.9643 |
| 24 | 566.3265-570.6122 | 590.4762 | 595.5565 | 596.5714 | 598.4416 | 600 | 601.6757 | 603.1166 | 605.019 | 606.8571 | 607.7698 | 613.5338 | 634.2857-638.5714 |
| 25 | 589.9235-594.3878 | 615.0794 | 620.3713 | 621.4286 | 623.3766 | 625 | 626.7455 | 628.2465 | 630.2281 | 632.1429 | 633.0936 | 639.0977 | 660.7143-665.1786 |
| 26 | 613.5204-618.1633 | 639.6825 | 645.1862 | 646.2857 | 648.3117 | 650 | 651.8154 | 653.3763 | 655.4372 | 657.4286 | 658.4173 | 664.66165 | 687.1429-691.7857 |
| 27 | 637.1173-641.9388 | 664.2857 | 670.001 | 671.1429 | 673.24765 | 675 | 676.8852 | 678.5062 | 680.6463 | 682.7143 | 683.7411 | 690.2256 | 713.5714-718.3929 |
| 28 | 660.7143-665.7143 | 688.8889 | 694.8158 | 696 | 698.1818 | 700 | 701.955 | 703.636 | 705.85545 | 708 | 709.0648 | 715.7895 | 740-745 |
| 29 | 684.3112-689.4898 | 713.4921 | 719.6307 | 720.8571 | 723.1169 | 725 | 727.0248 | 728.7659 | 731.0646 | 733.2857 | 734.3885 | 741.3534 | 766.4286-771.6071 |
| 30 | 707.9082-713.2653 | 738.0952 | 744.4456 | 745.7143 | 748.05195 | 750 | 752.0946 | 753.89575 | 756.2736 | 758.5714 | 759.7123 | 766.9173 | 792.8571-798.2143 |
| 31 | 731.5051-737.0408 | 762.6984 | 769.2604 | 770.5714 | 772.987 | 775 | 777.1645 | 779.0256 | 781.4828 | 783.8571 | 785.036 | 792.4812 | 819.2857-824.8214 |
| 32 | 755.102-760.8163 | 787.3016 | 794.0753 | 795.4286 | 797.9221 | 800 | 802.2343 | 804.1555 | 806.6919 | 809.1429 | 810.3598 | 818.0451 | 845.7143-851.4286 |
| 33 | 778.699-784.5918 | 811.9048 | 818.89015 | 820.2857 | 822.8571 | 825 | 827.3041 | 829.2853 | 831.9011 | 834.4286 | 835.6835 | 843.609 | 872.1429-876.0357 |
| 34 | 802.2959-808.36735 | 836.5079 | 843.705 | 845.1429 | 847.7922 | 850 | 852.3739 | 854.4152 | 857.1102 | 859.7143 | 961.0073 | 869.1729 | 898.5714-904.6429 |
| 35 | 825.8929-832.1429 | 861.1111 | 868.51985 | 870 | 872.7273 | 875 | 877.44375 | 879.545 | 882.3193 | 885 | 886.331 | 894.7368 | 925-931.25 |
| 36 | 849.4898-855.9184 | 885.7143 | 893.3347 | 894.8571 | 897.6623 | 900 | 902.5136 | 904.6749 | 907.5284 | 910.2857 | 911.6547 | 920.30075 | 951.4286-957.8571 |
| 37 | 873.0867-879.6939 | 910.3175 | 918.1496 | 919.7143 | 922.5974 | 925 | 927.5834 | 929.8048 | 932.3767 | 935.5714 | 936.9785 | 945.8647 | 977.8571-984.4643 |
| 38 | 896.6387-903.4694 | 934.9206 | 942.9644 | 944.5714 | 947.5325 | 950 | 952.6532 | 954.9346 | 957.9467 | 960.8571 | 962.3022 | 971.4286 | 1004.2857-1011.0714 |
| 39 | 920.2806-927.2449 | 959.5238 | 967.7793 | 969.4286 | 972.4675 | 975 | 977.723 | 980.0645 | 983.1558 | 986.1429 | 987.626 | 996.9925 | 1030.7143-1037.6786 |
| 40 | 943.8776-951.0204 | 984.127 | 992.5941 | 994.2857 | 997.4126 | 1000 | 1002.7929 | 1005.1943 | 1008.3649 | 1011.4286 | 1012.9497 | 1022.5564 | 1057.1429-1064.2857 |
| 41 | 967.4745-974.7959 | 1008.7302 | 1017.409 | 1019.1429 | 1022.3377 | 1025 | 1027.8627 | 1030.3242 | 1033.57405 | 1035.7143 | 1038.2735 | 1048.1203 | 1083.5714-1090.8929 |
| 42 | 991.0714-998.5714 | 1033.333 | 1042.2238 | 1044 | 1047.2727 | 1050 | 1052.9325 | 1055.454 | 1058.7832 | 1062 | 1063.5972 | 1073.6842 | 1110-1117.5 |
| 43 | 1014.6684-1022.3469 | 1057.9365 | 1067.0386 | 1068.8571 | 1072.2078 | 1075 | 1078.0023 | 1080.5839 | 1083.9923 | 1087.2857 | 1088.92095 | 1099.2481 | 1136.4286-1144.1071 |
| 44 | 1038.2653-1046.12245 | 1082.5397 | 1091.8535 | 1093.7143 | 1097.1429 | 1100 | 1103.0721 | 1105.7138 | 1109.2014 | 1112.5714 | 1114.2447 | 1124.812 | 1162.8571-1170.7143 |
| 45 | 1061.8622-1069.898 | 1107.1429 | 1116.6684 | 1118.5714 | 1122.0779 | 1125 | 1128.142 | 1130.8436 | 1134.41055 | 1137.8571 | 1139.5684 | 1150.3759 | 1189.2857-1197.3214 |
| 46 | 1085.4592-1093.6735 | 1131.7646 | 1141.4832 | 1143.4286 | 1147.013 | 1150 | 1153.2118 | 1155.9735 | 1159.6297 | 1163.1429 | 1164.8922 | 1175.93985 | 1215.7143-1223.9286 |
| 47 | 1109.0561-1117.449 | 1156.3492 | 1166.2981 | 1168.2857 | 1171.94805 | 1175 | 1178.2816 | 1181.1033 | 1184.8288 | 1188.4286 | 1190.2159 | 1201.5038 | 1242.1429-1250.5357 |
| 48 | 1132.6531-1141.2245 | 1180.9524 | 1191.1129 | 1193.1429 | 1196.8831 | 1200 | 1203.3514 | 1206.2332 | 1210.0379 | 1213.7143 | 1215.5397 | 1227.0677 | 1268.5714-1277.1429 |
| 49 | 1156.25-1165 | 1205.5556 | 1215.9278 | 1218 | 1221.8182 | 1225 | 1228.42125 | 1231.6306 | 1235.247 | 1239 | 1240.8634 | 1252.6316 | 1295-1303.75 |
| 50 | 1179.8469-1188.7755 | 1230.1587 | 1240.74265 | 1242.8571 | 1246.75325 | 1250 | 1253.4911 | 1256.4929 | 1260.4561 | 1264.2857 | 1266.18715 | 1278.1955 | 1321.4286-1330.3571 |
| 51 | 1203.4439-1212.551 | 1254.7619 | 1265.5575 | 1267.7143 | 1271.6883 | 1275 | 1278.5609 | 1281.6228 | 1285.6653 | 1289.5714 | 1291.5109 | 1303.7594 | 1347.8571-1356.9643 |
| 52 | 1227.0408-1236.3265 | 1279.3651 | 1290.37235 | 1292.5714 | 1296.6234 | 1300 | 1303.6307 | 1306.7526 | 1310.8744 | 1314.8571 | 1316.8346 | 1329.3233 | 1374.2857-1383.5714 |
| 53 | 1250.6378-1260.102 | 1303.96825 | 1315.1872 | 1317.4286 | 1321.5584 | 1325 | 1328.7005 | 1331.8825 | 1336.0835 | 1340.1429 | 1342.1584 | 1354.8872 | 1400.7143-1410.1786 |
| 54 | 1227.0408-1236.3265 | 1328.5714 | 1340.0021 | 1342.2857 | 1346.4395 | 1350 | 1353.7704 | 1357.01235 | 1361.2927 | 1365.4286 | 1367.4821 | 1380.4511 | 1427.1429-1436.7857 |
| 55 | 1297.8316-1307.6531 | 1353.1746 | 1364.8169 | 1367.1429 | 1371.4286 | 1375 | 1378.8418 | 1382.1422 | 1386.5018 | 1390.7143 | 1392.8059 | 1406.015 | 1453.5714-1463.3929 |
| 56 | 1321.4286-1331.4286 | 1377.7778 | 1389.6318 | 1392 | 1396.3636 | 1400 | 1403.91 | 1407.2721 | 1411.7109 | 1416 | 1418.1296 | 1431.57895 | 1480-1490 |
