56edf
56EDF is the equal division of the just perfect fifth into 56 parts of 12.5349 cents each, corresponding to 95.7326 edo. It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by 383, 670, 1053, 1436, and 1723 EDOs.
| ed31\54 (~98edo!) | ed121/81 (~ed11\19) | ed3/2 | Pyrite | 95edo | ed122/81 (~ed13\22) | ed34\57 (~94edo!) | ||
|---|---|---|---|---|---|---|---|---|
| (~ed17\29) | (~ed10\17) | |||||||
| 1 | 12.3016 | 12.4074 | 12.5349 | 12.5649 | 12.6046 | 12.6316 | 12.6619 | 12.78195 |
| 2 | 24.6032 | 24.81485 | 25.0698 | 25.1299 | 25.2091 | 25.2632 | 25.3234 | 25.5639 |
| 3 | 36.9048 | 37.2223 | 37.6047 | 376.9479 | 37.8139 | 37.8947 | 37.9856 | 38.3459 |
| 4 | 49.20635 | 49.6297 | 50.1396 | 50.2597 | 50.41825 | 50.5263 | 50.6475 | 51.1278 |
| 5 | 61.5079 | 62.0371 | 62.67455 | 62.82465 | 63.0228 | 63.1579 | 63.3094 | 63.9098 |
| 6 | 73.8095 | 74.4446 | 75.2095 | 75.3896 | 75.6274 | 75.7895 | 75.9712 | 76.6917 |
| 7 | 86.1111 | 86.852 | 87.7444 | 879.545 | 88.2319 | 88.42105 | 88.6331 | 89.4737 |
| 8 | 98.4127 | 99.2594 | 100.2793 | 100.5194 | 100.8365 | 101.0526 | 101.295 | 102.2556 |
| 9 | 110.7143 | 111.6668 | 112.8142 | 113.0844 | 113.44105 | 113.6842 | 113.9568 | 115.0376 |
| 10 | 123.0159 | 124.0743 | 125.3491 | 125.6493 | 126.0456 | 126.3158 | 126.6187 | 127.81955 |
| 11 | 135.3175 | 136.4817 | 137.884 | 138.2142 | 138.6502 | 138.9474 | 139.2806 | 140.6015 |
| 12 | 147.61905 | 148.8891 | 150.4189 | 150.77915 | 151.2547 | 151.57895 | 151.9425 | 153.3835 |
| 13 | 159.9206 | 161.2965 | 162.9538 | 163.3441 | 163.859 | 164.2105 | 164.6043 | 166.1654 |
| 14 | 172.2222 | 173.704 | 175.48875 | 175.909 | 176.4639 | 176.8421 | 177.2662 | 178.947 |
| 15 | 184.5238 | 186.1114 | 188.2366 | 188.4739 | 189.0684 | 189.473 | 189.9281 | 191.7293 |
| 16 | 196.8254 | 198.5188 | 200.5586 | 201.0389 | 201.673 | 202.1053 | 202.5899 | 204.5113 |
| 17 | 209.127 | 210.92625 | 213.0935 | 213.6038 | 214.27755 | 214.7368 | 215.2518 | 217.2932 |
| 18 | 221.4286 | 223.3337 | 225.6284 | 226.1687 | 226.8821 | 227.3684 | 227.9137 | 230.0752 |
| 19 | 233.7302 | 235.7411 | 238.1633 | 238.73365 | 239.4867 | 240 | 240.7556 | 242.8571 |
| 20 | 246.03175 | 248.1485 | 250.6982 | 251.2986 | 252.0912 | 252.6316 | 253.2374 | 255.6391 |
| 21 | 258.3333 | 260.556 | 263.2331 | 263.8635 | 264.6958 | 265.2632 | 265.8993 | 268.42105 |
| 22 | 270.6349 | 272.9634 | 275.768 | 276.4284 | 277.3004 | 277.8947 | 278.5612 | 281.203 |
| 23 | 282.9365 | 285.3708 | 288.30295 | 288.9934 | 289.9049 | 290.5263 | 291.223 | 293.985 |
| 24 | 295.2381 | 297.782 | 300.8379 | 301.5583 | 302.5095 | 303.1579 | 303.8849 | 306.7669 |
| 25 | 307.5397 | 310.1857 | 313.3728 | 314.1232 | 315.114 | 315.7895 | 316.5468 | 319.5489 |
| 26 | 319.8413 | 322.5931 | 325.9077 | 326.6682 | 327.7186 | 328.42105 | 329.2087 | 332.3308 |
| 27 | 332.1429 | 335.0005 | 338.4426 | 339.2531 | 340.3232 | 341.0526 | 341.8705 | 345.1128 |
| 28 | 344.4444 | 347.408 | 350.9775 | 351.818 | 352.9277 | 353.6842 | 354.5324 | 357.8947 |
| 29 | 356.749 | 359.8154 | 363.5214 | 364.38295 | 365.5323 | 366.3158 | 367.1943 | 370.6767 |
| 30 | 369.0476 | 372.2228 | 376.0473 | 376.9479 | 378.13685 | 378.9474 | 379.8561 | 383.45865 |
| 31 | 381.3492 | 384.6302 | 388.5822 | 389.5128 | 390.7414 | 391.57895 | 392.518 | 396.2406 |
| 32 | 393.6508 | 397.03765 | 401.1171 | 402.0777 | 403.346 | 404.2105 | 405.1799 | 409.0226 |
| 33 | 408.9524 | 409.4451 | 413.65205 | 414.6427 | 415.9505 | 416.8421 | 417.8418 | 421.8045 |
| 34 | 418.254 | 421.8525 | 426.187 | 427.2076 | 428.5551 | 429.4736 | 430.5036 | 434.5865 |
| 35 | 430.5556 | 434.2599 | 438.7219 | 439.7725 | 441.1597 | 442.1053 | 443.1655 | 447.3684 |
| 36 | 442.8571 | 446.66735 | 451.2568 | 452.33745 | 453.7642 | 454.7368 | 455.8274 | 460.1504 |
| 37 | 455.1875 | 459.0748 | 463.7917 | 464.9024 | 466.3688 | 467.3684 | 468.4892 | 472.9323 |
| 38 | 467.460 | 471.4822 | 476.3266 | 477.4673 | 478.9733 | 480 | 481.1511 | 485.7143 |
| 39 | 479.7619 | 483.8896 | 488.8615 | 490.0322 | 491.5779 | 492.6316 | 493.913 | 498.4962 |
| 40 | 492.0635 | 496.2971 | 501.3964 | 502.5972 | 504.1825 | 505.2632 | 506.4749 | 511.2781 |
| 41 | 504.3651 | 507.04485 | 513.9313 | 515.1621 | 516.787 | 517.8947 | 519.1367 | 524.06015 |
| 42 | 516.6667 | 521.1119 | 526.46625 | 527.727 | 529.3916 | 530.5263 | 531.7986 | 536.8421 |
| 43 | 528.96825 | 533.5193 | 539.0012 | 540.29195 | 541.99615 | 543.1578 | 544.4605 | 549.6241 |
| 44 | 541.2698 | 545.9268 | 551.536 | 552.8569 | 554.6007 | 555.7895 | 557.1223 | 562.406 |
| 45 | 553.5714 | 558.3341 | 564.071 | 565.4218 | 567.2053 | 568.42105 | 569.7842 | 575.188 |
| 46 | 565.873 | 570.7416 | 576.6059 | 577.9867 | 579.8098 | 581.0526 | 582.4461 | 587.9699 |
| 47 | 578.1746 | 583.149 | 589.1408 | 590.5517 | 592.4144 | 593.6842 | 595.108 | 600.7519 |
| 48 | 590.4762 | 595.5565 | 601.6757 | 603.1166 | 605.019 | 606.3158 | 607.7698 | 613.5338 |
| 49 | 602.7778 | 607.9639 | 614.2106 | 615.6815 | 617.6235 | 618.9474 | 620.4317 | 626.3158 |
| 50 | 615.0794 | 620.3713 | 626.7455 | 628.2465 | 630.2281 | 631.57895 | 633.0936 | 639.0977 |
| 51 | 627.38095 | 632.77875 | 639.28045 | 640.8114 | 642.8326 | 644.2015 | 645.7554 | 651.8797 |
| 52 | 639.6825 | 645.1862 | 651.8154 | 653.3763 | 655.4372 | 656.8421 | 658.4173 | 664.66165 |
| 53 | 651.9841 | 657.5936 | 664.3503 | 665.9412 | 668.0418 | 669.4736 | 671.0792 | 677.4436 |
| 54 | 664.2857 | 670.001 | 676.8852 | 678.5062 | 680.6463 | 682.1053 | 983.7411 | 690.2256 |
| 55 | 676.5873 | 682.40845 | 689.4201 | 691.0711 | 693.2509 | 694.7368 | 696.4029 | 703.0075 |
| 56 | 688.8889 | 694.8158 | 701.955 | 703.636 | 705.85545 | 707.3684 | 709.0648 | 715.7895 |
| 57 | 701.1905 | 707.2233 | 714.4899 | 716.201 | 718.46 | 720 | 721.7267 | 728.5714 |
| 58 | 713.4921 | 719.6307 | 727.0248 | 728.7659 | 731.0646 | 732.6316 | 734.3885 | 741.3534 |
| 59 | 725.79365 | 732.0382 | 739.5597 | 741.3308 | 743.6691 | 745.2632 | 747.0504 | 754.1353 |
| 60 | 738.0952 | 744.4456 | 752.0946 | 753.89575 | 756.2736 | 757.8947 | 759.7123 | 766.9173 |
| 61 | 750.3968 | 756.853 | 764.62955 | 766.4607 | 768.8783 | 770.5263 | 772.3742 | 779.69925 |
| 62 | 762.6984 | 769.2604 | 777.1645 | 779.0256 | 781.4828 | 783.1579 | 785.036 | 792.4812 |
| 63 | 775 | 781.6679 | 789.6994 | 791.5905 | 794.0874 | 795.7895 | 797.6979 | 805.2632 |
| 64 | 787.3016 | 794.0753 | 802.2343 | 804.1555 | 806.6919 | 808.42105 | 810.3598 | 818.0451 |
| 65 | 799.6032 | 806.4827 | 814.7692 | 816.7204 | 819.2965 | 821.0526 | 823.0216 | 830.8271 |
| 66 | 811.9048 | 818.89015 | 827.3041 | 829.2853 | 831.9011 | 833.6842 | 835.6835 | 843.609 |
| 67 | 824.20635 | 831.2976 | 839.839 | 841.85025 | 844.5056 | 846.3158 | 848.3454 | 856.391 |
| 68 | 836.5079 | 843.705 | 852.3739 | 854.4152 | 857.1102 | 858.9473 | 861.0073 | 869.1729 |
| 69 | 848.8095 | 856.1124 | 864.9088 | 866.9801 | 869.71475 | 871.57895 | 873.6691 | 881.9549 |
| 70 | 861.1111 | 868.51985 | 877.44375 | 879.545 | 882.3193 | 884.2105 | 886.331 | 894.7368 |
| 71 | 873.4127 | 880.9273 | 889.9787 | 892.11 | 894.9239 | 896.8421 | 898.9929 | 907.5188 |
| 72 | 885.7143 | 893.3347 | 902.5136 | 904.6749 | 907.5284 | 909.4736 | 911.6547 | 920.30075 |
| 73 | 898.0159 | 905.7421 | 915.0485 | 917.2398 | 920.133 | 922.1053 | 924.3166 | 933.0827 |
| 74 | 910.3175 | 918.1496 | 927.5834 | 929.8048 | 932.3767 | 934.7368 | 936.9785 | 945.8647 |
| 75 | 922.61905 | 930.557 | 940.1183 | 942.3697 | 945.3421 | 947.3684 | 949.6404 | 958.6466 |
| 76 | 934.9206 | 942.9644 | 952.6532 | 954.9346 | 957.9467 | 960 | 962.3022 | 971.4286 |
| 77 | 947.2222 | 955.3718 | 965.1881 | 967.4995 | 970.55125 | 972.6316 | 974.9641 | 984.2105 |
| 78 | 959.5238 | 967.7793 | 977.723 | 980.0645 | 983.1558 | 985.2632 | 987.626 | 996.9925 |
| 79 | 971.8254 | 980.1867 | 990.25795 | 992.6294 | 995.7604 | 997.8947 | 1000.28785 | 1009.7744 |
| 80 | 984.127 | 992.5941 | 1002.7929 | 1005.1943 | 1008.3649 | 1010.5263 | 1012.9497 | 1022.5564 |
| 81 | 996.4286 | 1005.0015 | 1015.3278 | 1017.7593 | 1020.9695 | 1023.1579 | 1025.6116 | 1035.3383 |
| 82 | 1008.7302 | 1017.409 | 1027.8627 | 1030.3242 | 1033.57405 | 1035.57895 | 1038.2735 | 1048.1203 |
| 83 | 1021.03175 | 1029.8164 | 1040.3976 | 1042.8891 | 1046.1786 | 1048.42105 | 1050.9353 | 1060.9023 |
| 84 | 1033.333 | 1042.2238 | 1052.9325 | 1055.454 | 1058.7832 | 1061.0526 | 1063.5972 | 1073.6842 |
| 85 | 1045.6349 | 1054.63125 | 1065.4674 | 1068.019 | 1071.3877 | 1073.6842 | 1076.2591 | 1086.4662 |
| 86 | 1057.9365 | 1067.0386 | 1078.0023 | 1080.5839 | 1083.9923 | 1086.3158 | 1088.92095 | 1099.2481 |
| 87 | 1070.2381 | 1079.4461 | 1090.5372 | 1093.1488 | 1095.5967 | 1098.9474 | 1101.5828 | 1112.0301 |
| 88 | 1082.5397 | 1091.8535 | 1103.0721 | 1105.7138 | 1109.2014 | 1111.57895 | 1114.2447 | 1124.812 |
| 89 | 1094.8413 | 1104.26095 | 1115.6071 | 1118.2787 | 1121.806 | 1124.2105 | 1126.9066 | 1137.594 |
| 90 | 1107.1429 | 1116.6684 | 1128.142 | 1130.8436 | 1137.41055 | 1136.8421 | 1139.5684 | 1150.3759 |
| 91 | 1119.4444 | 1129.0758 | 1140.6769 | 1143.40855 | 1147.0151 | 1149.4737 | 1152.2303 | 1163.1579 |
| 92 | 1131.7646 | 1141.4832 | 1153.2118 | 1155.9735 | 1159.6297 | 1162.1052 | 1164.8922 | 1175.93985 |
| 93 | 1144.0476 | 1153.8907 | 1165.7467 | 1168.5384 | 1172.2242 | 1174.7368 | 1177.55405 | 1187.7218 |
| 94 | 1156.3492 | 1166.2981 | 1178.2816 | 1181.1033 | 1184.8288 | 1187.3684 | 1190.2159 | 1201.5038 |
| 95 | 1168.6508 | 1178.7055 | 1190.8165 | 1193.6683 | 1197.4334 | 1200 | 1202.8778 | 1214.2857 |
| 96 | 1180.9524 | 1191.1129 | 1203.3514 | 1206.2332 | 1210.0379 | 1212.6316 | 1215.5397 | 1227.0677 |
| 97 | 1193.254 | 1203.5204 | 1215.8863 | 1218.7981 | 1222.6425 | 1225.2632 | 1228.2015 | 1239.985 |
| 98 | 1205.5556 | 1215.9278 | 1228.42125 | 1231.6306 | 1235.247 | 1237.8947 | 1240.8634 | 1252.6316 |
| 99 | 1217.8571 | 1228.3352 | 1240.9561 | 1243.328 | 1247.8516 | 1250.5263 | 1253.5253 | 1265.4135 |
| 100 | 1230.1587 | 1240.74265 | 1253.4911 | 1256.4929 | 1260.4561 | 1263.1579 | 1266.18715 | 1278.1955 |
| 101 | 1242.4603 | 1253.1501 | 1266.026 | 1269.0578 | 1273.0607 | 1275.7895 | 1278.849 | 1290.9774 |
| 102 | 1254.7619 | 1265.5575 | 1278.5609 | 1281.6228 | 1286.653 | 1288.42105 | 1291.5109 | 1303.7594 |
| 103 | 1267.0635 | 1277.9649 | 1291.0958 | 12974.1877 | 1298.26985 | 1301.0526 | 1304.1728 | 1316.54135 |
| 104 | 1279.3651 | 1290.37235 | 1303.6307 | 1306.7526 | 1310.8744 | 1313.6842 | 1316.8346 | 1329.3233 |
| 105 | 1291.6667 | 1302.7798 | 1316.1656 | 1319.3176 | 1323.479 | 1326.3158 | 1329.4965 | 1342.1053 |
| 106 | 1303.96825 | 1315.1872 | 1328.7005 | 1331.8825 | 1336.0835 | 1338.9474 | 1342.1584 | 1354.8872 |
| 107 | 1316.2698 | 1327.5946 | 1341.23545 | 1344.4474 | 1348.6881 | 1351.57895 | 1354.82025 | 1367.6692 |
| 108 | 1328.5714 | 1340.0021 | 1353.7704 | 1357.01235 | 1361.2927 | 1364.2105 | 1367.4821 | 1380.4511 |
| 109 | 1340.873 | 1352.4095 | 1366.3053 | 1369.5773 | 1373.8972 | 1376.8421 | 1380.144 | 1393.233 |
| 110 | 1353.1746 | 1364.8169 | 1378.8418 | 1382.1422 | 1386.5018 | 1389.4737 | 1392.8059 | 1406.015 |
| 111 | 1365.4762 | 1377.2243 | 1391.3751 | 1394.7071 | 1399.1063 | 1402.1053 | 1405.4677 | 1418.797 |
| 112 | 1377.7778 | 1389.6318 | 1403.91 | 1407.2721 | 1411.7109 | 1414.7368 | 1418.1296 | 1431.57895 |
Related regular temperaments
7-limit 383&670
Commas: 2401/2400, |91 -80 13 2>
POTE generator: ~|-33 32 -4 -3> = 12.5357
Map: [<1 1 -1 1|, <0 56 318 173|]
EDOs: 383, 670, 1053, 1436, 1723
11-limit 383&670
Commas: 2401/2400, 14348907/14348180, 26214400/26198073
POTE generator: ~13504609503/13421772800 = 12.5359
Map: [<1 1 -1 1 3|, <0 56 318 173 44|]
EDOs: 383, 670, 1053, 1436, 1723