56edf

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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.

ed233\420-5¢ (~101-102edo!) ed31\54 (~98edo!) ed121/81 (~ed11\19) ed696¢ ed3/2 Pyrite 95edo ed708¢ ed122/81 (~ed13\22) ed34\57 (~94edo!) ed37\60+5¢ (~90-91edo!)
(~ed17\29) (~ed10\17)
1 11.7985-11.8878 12.3016 12.4074 12.4286 12.5349 12.5649 12.6046 12.6316 12.6619 12.78195 13.2143-13.2768
2 23.5969-23.7755 24.6032 24.81485 24.8571 25.0698 25.1299 25.2091 25.2632 25.3234 25.5639 26.4286-26.5536
3 35.3954-35.6633 36.9048 37.2223 37.2857 37.6047 376.9479 37.8139 37.8947 37.9856 38.3459 39.6429-39.8304
4 47.1939-47.551 49.20635 49.6297 49.7143 50.1396 50.2597 50.41825 50.5263 50.6475 51.1278 52.8571-53.1071
5 59.99235-59.4388 61.5079 62.0371 62.1429 62.67455 62.82465 63.0228 63.1579 63.3094 63.9098 66.0714-66.3839
6 70.7908-71.3625 73.8095 74.4446 74.5714 75.2095 75.3896 75.6274 75.7895 75.9712 76.6917 79.2857-79.6607
7 82.5893-83.2143 86.1111 86.852 87 87.7444 879.545 88.2319 88.42105 88.6331 89.4737 92.5-92.9375
8 94.3878-95.102 98.4127 99.2594 99.4286 100.2793 100.5194 100.8365 101.0526 101.295 102.2556 105.7143-106.2143
9 106.1862-106.9898 110.7143 111.6668 111.8571 112.8142 113.0844 113.44105 113.6842 113.9568 115.0376 118.9286-119.4911
10 117.9847-118.87755 123.0159 124.0743 124.2857 125.3491 125.6493 126.0456 126.3158 126.6187 127.81955 132.1429-132.7679
11 129.7832-130.7653 135.3175 136.4817 136.7143 137.884 138.2142 138.6502 138.9474 139.2806 140.6015 145.3571-146.0446
12 141.5816-142.653 147.61905 148.8891 149.1429 150.4189 150.77915 151.2547 151.57895 151.9425 153.3835 158.5714-159.3214
13 153.3801-154.5408 159.9206 161.2965 161.5714 162.9538 163.3441 163.859 164.2105 164.6043 166.1654 171.7857-172.5982
14 165.1786-166.4285 172.2222 173.704 174 175.48875 175.909 176.4639 176.8421 177.2662 178.947 185-185.875
15 176.977-178.3163 184.5238 186.1114 186.4286 188.2366 188.4739 189.0684 189.473 189.9281 191.7293 198.2143-199.1518
16 188.7755-190.2041 196.8254 198.5188 198.8571 200.5586 201.0389 201.673 202.1053 202.5899 204.5113 211.4286-212.4286
17 200.574-202.0918 209.127 210.92625 211.2857 213.0935 213.6038 214.27755 214.7368 215.2518 217.2932 224.6429-225.7054
18 212.37245-213.9796 221.4286 223.3337 223.7143 225.6284 226.1687 226.8821 227.3684 227.9137 230.0752 237.8571-238.9791
19 224.1709-225.86735 233.7302 235.7411 236.1429 238.1633 238.73365 239.4867 240 240.7556 242.8571 251.0714-252.2589
20 235.9694-237.7551 246.03175 248.1485 248.5714 250.6982 251.2986 252.0912 252.6316 253.2374 255.6391 264.2857-265.5357
21 247.7674-249.6429 258.3333 260.556 261 263.2331 263.8635 264.6958 265.2632 265.8993 268.42105 277.5-278.8125
22 259.5663-261.5306 270.6349 272.9634 273.4286 275.768 276.4284 277.3004 277.8947 278.5612 281.203 290.7143-292.0693
23 271.3648-273.4184 282.9365 285.3708 285.8571 288.30295 288.9934 289.9049 290.5263 291.223 293.985 303.9286-305.3661
24 283.1633-285.3061 295.2381 297.782 298.2857 300.8379 301.5583 302.5095 303.1579 303.8849 306.7669 317.1429-318.6429
25 294.9617-297.1939 307.5397 310.1857 310.7143 313.3728 314.1232 315.114 315.7895 316.5468 319.5489 330.3571-331.5696
26 306.7602-309.0816 319.8413 322.5931 323.1429 325.9077 326.6682 327.7186 328.42105 329.2087 332.3308 343.5714-345.2664
27 318.5588-320.9694 332.1429 335.0005 335.5714 338.4426 339.2531 340.3232 341.0526 341.8705 345.1128 356.7857-358.5732
28 330.3571-332.8571 344.4444 347.408 348 350.9775 351.818 352.9277 353.6842 354.5324 357.8947 370-372.5
29 342.1556-344.7449 356.749 359.8154 360.4286 363.5214 364.38295 365.5323 366.3158 367.1943 370.6767 383.2143-385.0318
30 353.9541-356.63265 369.0476 372.2228 372.8571 376.0473 376.9479 378.13685 378.9474 379.8561 383.45865 396.4286-398.3036
31 365.75255-368.5204 381.3492 384.6302 385.2857 388.5822 389.5128 390.7414 391.57895 392.518 396.2406 409.6429-411.5804
32 377.551-380.4082 393.6508 397.03765 397.7143 401.1171 402.0777 403.346 404.2105 405.1799 409.0226 422.8571-424.8571
33 389.3495-392.2959 408.9524 409.4451 410.1429 413.65205 414.6427 415.9505 416.8421 417.8418 421.8045 436.0714-438.1339
34 401.148-404.1837 418.254 421.8525 421.5714 426.187 427.2076 428.5551 429.4736 430.5036 434.5865 422.8571-424.8571
35 412.9464-416.0714 430.5556 434.2599 435 438.7219 439.7725 441.1597 442.1053 443.1655 447.3684 462.5-464.1875
36 424.7449-427.9592 442.8571 446.66735 447.4286 451.2568 452.33745 453.7642 454.7368 455.8274 460.1504 475.7143-477.9643
37 436.5434-439.8469 455.1875 459.0748 459.8571 463.7917 464.9024 466.3688 467.3684 468.4892 472.9323 488.9286-491.2411
38 448.3418-451.7347 467.460 471.4822 472.2857 476.3266 477.4673 478.9733 480 481.1511 485.7143 502.1429-504.5179
39 460.1403-463.62245 479.7619 483.8896 484.7143 488.8615 490.0322 491.5779 492.6316 493.913 498.4962 515.3571-517.7946
40 471.9388-475.5102 492.0635 496.2971 497.1429 501.3964 502.5972 504.1825 505.2632 506.4749 511.2781 528.5714-531.0714
41 483.7372-487.398 504.3651 507.04485 508.5714 513.9313 515.1621 516.787 517.8947 519.1367 524.06015 541.7857-544.3482
42 495.5357-499.2857 516.6667 521.1119 522 526.46625 527.727 529.3916 530.5263 531.7986 536.8421 555-557.625
43 507.3342-511.1735 528.96825 533.5193 534.4286 539.0012 540.29195 541.99615 543.1578 544.4605 549.6241 568.2143-570.9018
44 519.13265-523.0612 541.2698 545.9268 546.8571 551.536 552.8569 554.6007 555.7895 557.1223 562.406 581.4286-584.1786
45 530.9311-534.949 553.5714 558.3341 559.2857 564.071 565.4218 567.2053 568.42105 569.7842 575.188 594.6429-597.3254
46 542.7296-546.8367 565.873 570.7416 571.7143 576.6059 577.9867 579.8098 581.0526 582.4461 587.9699 607.8571-610.7321
47 554.5281-558.7245 578.1746 583.149 584.1429 589.1408 590.5517 592.4144 593.6842 595.108 600.7519 620.0714-623.0089
48 566.3265-570.6122 590.4762 595.5565 596.5714 601.6757 603.1166 605.019 606.3158 607.7698 613.5338 634.2857-637.2857
49 578.125-582.5 602.7778 607.9639 609 614.2106 615.6815 617.6235 618.9474 620.4317 626.3158 647.5-650.5625
50 589.9235-594.3878 615.0794 620.3713 621.4286 626.7455 628.2465 630.2281 631.57895 633.0936 639.0977 660.7143-663.8393
51 601.7219-606.2755 627.38095 632.77875 633.8571 639.28045 640.8114 642.8326 644.2015 645.7554 651.8797 673.9286-677.1161
52 613.5204-618.1633 639.6825 645.1862 646.2857 651.8154 653.3763 655.4372 656.8421 658.4173 664.66165 687.1429-690.3929
53 625.3189-630.051 651.9841 657.5936 658.7143 664.3503 665.9412 668.0418 669.4736 671.0792 677.4436 700.3571-703.6696
54 637.11735-641.9388 664.2857 670.001 671.1429 676.8852 678.5062 680.6463 682.1053 983.7411 690.2256 713.5714-716.9264
55 648.9158-653.8265 676.5873 682.40845 683.5714 689.4201 691.0711 693.2509 694.7368 696.4029 703.0075 726.7857-730.2232
56 660.7143-665.7143 688.8889 694.8158 696 701.955 703.636 705.85545 707.3684 709.0648 715.7895 740-745
57 672.5128-677.602 701.1905 707.2233 708.4286 714.4899 716.201 718.46 720 721.7267 728.5714 753.2143-756.7768
58 684.3112-689.4898 713.4921 719.6307 720.8571 727.0248 728.7659 731.0646 732.6316 734.3885 741.3534 766.4286-770.0536
59 696.1097-701.37755 725.79365 732.0382 733.2857 739.5597 741.3308 743.6691 745.2632 747.0504 754.1353 779.6429-783.3304
60 707.9082-713.2653 738.0952 744.4456 745.7143 752.0946 753.89575 756.2736 757.8947 759.7123 766.9173 792.8571-796.6071
61 719.7066-725.1531 750.3968 756.853 758.1429 764.62955 766.4607 768.8783 770.5263 772.3742 779.69925 805.0714-808.8839
62 731.5051-737.0408 762.6984 769.2604 770.5714 777.1645 779.0256 781.4828 783.1579 785.036 792.4812 819.2857-823.1607
63 743.3036-748.9286 775 781.6679 783 789.6994 791.5905 794.0874 795.7895 797.6979 805.2632 832.5-836.4375
64 755.102-760.8163 787.3016 794.0753 795.4286 802.2343 804.1555 806.6919 808.42105 810.3598 818.0451 845.7143-849.7143
65 766.9005-772.704 799.6032 806.4827 807.8571 814.7692 816.7204 819.2965 821.0526 823.0216 830.8271 858.9286-862.9911
66 778.699-784.5918 811.9048 818.89015 820.2857 827.3041 829.2853 831.9011 833.6842 835.6835 843.609 872.1429-876.2679
67 792.49745-796.4796 824.20635 831.2976 832.7143 839.839 841.85025 844.5056 846.3158 848.3454 856.391 885.3571-889.5446
68 802.2959-808.36735 836.5079 843.705 845.1429 852.3739 854.4152 857.1102 858.9473 861.0073 869.1729 898.5714-902.8214
69 814.0944-820.2551 848.8095 856.1124 857.5714 864.9088 866.9801 869.71475 871.57895 873.6691 881.9549 911.7857-916.0982
70 825.8929-832.1429 861.1111 868.51985 870 877.44375 879.545 882.3193 884.2105 886.331 894.7368 925-929.375
71 837.6913-844.9306 873.4127 880.9273 882.4286 889.9787 892.11 894.9239 896.8421 898.9929 907.5188 938.2143-942.6518
72 849.4898-855.9184 885.7143 893.3347 894.8571 902.5136 904.6749 907.5284 909.4736 911.6547 920.30075 951.4286-955.9286
73 861.2882-867.8061 898.0159 905.7421 907.2857 915.0485 917.2398 920.133 922.1053 924.3166 933.0827 964.6429-969.2054
74 873.0867-879.6939 910.3175 918.1496 919.7143 927.5834 929.8048 932.3767 934.7368 936.9785 945.8647 977.8571-982.4821
75 884.8852-891.5816 922.61905 930.557 932.1429 940.1183 942.3697 945.3421 947.3684 949.6404 958.6466 991.0714-995.7589
76 896.6837-903.4694 934.9206 942.9644 944.5714 952.6532 954.9346 957.9467 960 962.3022 971.4286 1004.2857-1009.0357
77 908.4821-915.3571 947.2222 955.3718 957 965.1881 967.4995 970.55125 972.6316 974.9641 984.2105 1017.5-1022.3125
78 920.2806-927.2449 959.5238 967.7793 969.4286 977.723 980.0645 983.1558 985.2632 987.626 996.9925 1030.7143-1035.5893
79 932.0791-939.13265 971.8254 980.1867 981.8571 990.25795 992.6294 995.7604 997.8947 1000.28785 1009.7744 1043.9286-1048.8663
80 943.87755-951.0204 984.127 992.5941 994.2857 1002.7929 1005.1943 1008.3649 1010.5263 1012.9497 1022.5564 1057.1429-1062.1429
81 955.676-962.90812 996.4286 1005.0015 1006.7143 1015.3278 1017.7593 1020.9695 1023.1579 1025.6116 1035.3383 1070.3571-1075.4196
82 967.4745-974.7959 1008.7302 1017.409 1019.1429 1027.8627 1030.3242 1033.57405 1035.57895 1038.2735 1048.1203 1083.5714-1088.6964
83 979.273-986.6837 1021.03175 1029.8164 1031.5714 1040.3976 1042.8891 1046.1786 1048.42105 1050.9353 1060.9023 1096.7857-1101.9732
84 991.0714-998.5714 1033.333 1042.2238 1044 1052.9325 1055.454 1058.7832 1061.0526 1063.5972 1073.6842 1110-1117.5
85 1002.8699-1010.4592 1045.6349 1054.63125 1056.4286 1065.4674 1068.019 1071.3877 1073.6842 1076.2591 1086.4662 1123.2143-1128.5268
86 1014.6684-1022.3469 1057.9365 1067.0386 1068.8571 1078.0023 1080.5839 1083.9923 1086.3158 1088.92095 1099.2481 1136.4286-1141.8036
87 1028.4668-1034.2437 1070.2381 1079.4461 1081.2857 1090.5372 1093.1488 1095.5967 1098.9474 1101.5828 1112.0301 1149.6429-1155.0804
88 1038.2653-1046.12245 1082.5397 1091.8535 1093.7143 1103.0721 1105.7138 1109.2014 1111.57895 1114.2447 1124.812 1162.8571-1167.3571
89 1050.0638-1058.0102 1094.8413 1104.26095 1106.1429 1115.6071 1118.2787 1121.806 1124.2105 1126.9066 1137.594 1175.0714-1180.6339
90 1061.8622-1069.898 1107.1429 1116.6684 1118.5714 1128.142 1130.8436 1137.41055 1136.8421 1139.5684 1150.3759 1189.2857-1194.9107
91 1073.6607-1081.7857 1119.4444 1129.0758 1131 1140.6769 1143.40855 1147.0151 1149.4737 1152.2303 1163.1579 1202.5-1208.1875
92 1085.4592-1093.6735 1131.7646 1141.4832 1143.4286 1153.2118 1155.9735 1159.6297 1162.1052 1164.8922 1175.93985 1215.7143-1221.4643
93 1097.25765-1105.5612 1144.0476 1153.8907 1155.8571 1165.7467 1168.5384 1172.2242 1174.7368 1177.55405 1187.7218 1228.9286-1234.6411
94 1109.0651-1117.449 1156.3492 1166.2981 1168.2857 1178.2816 1181.1033 1184.8288 1187.3684 1190.2159 1201.5038 1242.1429-1248.0179
95 1120.8546-1129.3367 1168.6508 1178.7055 1180.7143 1190.8165 1193.6683 1197.4334 1200 1202.8778 1214.2857 1257.3571-1263.2946
96 1132.6531-1141.2245 1180.9524 1191.1129 1193.1429 1203.3514 1206.2332 1210.0379 1212.6316 1215.5397 1227.0677 1268.5714-1274.5714
97 1144.4515-1153.11225 1193.254 1203.5204 1205.5714 1215.8863 1218.7981 1222.6425 1225.2632 1228.2015 1239.985 1281.7857-1287.8482
98 1156.25-1165 1205.5556 1215.9278 1218 1228.42125 1231.6306 1235.247 1237.8947 1240.8634 1252.6316 1295-1301.125
99 1168.0485-1176.8878 1217.8571 1228.3352 1230.4286 1240.9561 1243.328 1247.8516 1250.5263 1253.5253 1265.4135 1308.2143-1314.4018
100 1179.8469-1188.7755 1230.1587 1240.74265 1242.8571 1253.4911 1256.4929 1260.4561 1263.1579 1266.18715 1278.1955 1321.4286-1327.6786
101 1191.6454-1200.6633 1242.4603 1253.1501 1255.2857 1266.026 1269.0578 1273.0607 1275.7895 1278.849 1290.9774 1334.6429-1340.9554
102 1203.4439-1212.551 1254.7619 1265.5575 1267.7143 1278.5609 1281.6228 1286.653 1288.42105 1291.5109 1303.7594 1347.8571-1354.2321
103 1215.24235-1224.3878 1267.0635 1277.9649 1280.1429 1291.0958 12974.1877 1298.26985 1301.0526 1304.1728 1316.54135 1361.0714-1367.5089
104 1227.0408-1236.3265 1279.3651 1290.37235 1292.5714 1303.6307 1306.7526 1310.8744 1313.6842 1316.8346 1329.3233 1374.2857-1380.7857
105 1238.8393-1248.2143 1291.6667 1302.7798 1305 1316.1656 1319.3176 1323.479 1326.3158 1329.4965 1342.1053 1387.5-1394.0625
106 1250.6378-1260.102 1303.96825 1315.1872 1317.4286 1328.7005 1331.8825 1336.0835 1338.9474 1342.1584 1354.8872 1400.7143-1407.3393
107 1262.4362-1271.9898 1316.2698 1327.5946 1329.8571 1341.23545 1344.4474 1348.6881 1351.57895 1354.82025 1367.6692 1413.9286-1419.6161
108 1274.2347-1283.87755 1328.5714 1340.0021 1342.2857 1353.7704 1357.01235 1361.2927 1364.2105 1367.4821 1380.4511 1427.1429-1433.8929
109 1286.0331-1295.7653 1340.873 1352.4095 1355.7143 1366.3053 1369.5773 1373.8972 1376.8421 1380.144 1393.233 1440.3571-1447.1696
110 1297.8316-1307.6531 1353.1746 1364.8169 1367.1429 1378.8418 1382.1422 1386.5018 1389.4737 1392.8059 1406.015 1453.5714-1460.4464
111 1309.6301-1319.5408 1365.4762 1377.2243 1379.5714 1391.3751 1394.7071 1399.1063 1402.1053 1405.4677 1418.797 1470.7857-1473.7232
112 1321.4286-1331.4286 1377.7778 1389.6318 1392 1403.91 1407.2721 1411.7109 1414.7368 1418.1296 1431.57895 1480-1490


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