28edf: Difference between revisions

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Line 8: Line 8:
! rowspan="2" |ed121/81 (~ed11\19)
! rowspan="2" |ed121/81 (~ed11\19)
! rowspan="2" |ed696¢
! rowspan="2" |ed696¢
! rowspan="2" |ed32\55
! rowspan="2" |[[48edo]]=''r¢''
! rowspan="2" |ed3/2
! rowspan="2" |ed3/2
! colspan="2" |Pyrite
! colspan="2" |Pyrite
Line 23: Line 25:
|24.81485
|24.81485
|24.8571
|24.8571
|24.9351
|''25''
|25.0698
|25.0698
|25.1299
|25.1299
Line 36: Line 40:
|49.6297
|49.6297
|49.7143
|49.7143
|49.8701
|''50''
|50.1396
|50.1396
|50.2597
|50.2597
Line 49: Line 55:
|74.4446
|74.4446
|74.5714
|74.5714
|74.8052
|''75''
|75.2095
|75.2095
|75.3896
|75.3896
Line 62: Line 70:
|99.2594
|99.2594
|99.4286
|99.4286
|99.7403
|''100''
|100.2793
|100.2793
|100.5194
|100.5194
Line 75: Line 85:
|124.0743
|124.0743
|124.2857
|124.2857
|124.6753
|''125''
|125.3491
|125.3491
|125.6493
|125.6493
Line 88: Line 100:
|148.8891
|148.8891
|149.1429
|149.1429
|149.6104
|''150''
|150.4189
|150.4189
|150.77915
|150.77915
Line 101: Line 115:
|173.704
|173.704
|174
|174
|174.54545
|''175''
|175.48875
|175.48875
|175.909
|175.909
Line 114: Line 130:
|198.5188
|198.5188
|198.8571
|198.8571
|199.4805
|''200''
|200.5586
|200.5586
|201.0389
|201.0389
Line 127: Line 145:
|223.3337
|223.3337
|223.7143
|223.7143
|224.4156
|''225''
|225.6284
|225.6284
|226.1687
|226.1687
Line 140: Line 160:
|248.1485
|248.1485
|248.5714
|248.5714
|249.35065
|''250''
|250.6982
|250.6982
|251.2986
|251.2986
Line 153: Line 175:
|272.9634
|272.9634
|273.4286
|273.4286
|274.2857
|''275''
|275.768
|275.768
|276.4284
|276.4284
Line 166: Line 190:
|297.782
|297.782
|298.2857
|298.2857
|299.2208
|''300''
|300.8379
|300.8379
|301.5583
|301.5583
Line 179: Line 205:
|322.5931
|322.5931
|323.1429
|323.1429
|324.1558
|''325''
|325.9077
|325.9077
|326.6682
|326.6682
Line 192: Line 220:
|347.408
|347.408
|348
|348
|349.0909
|''350''
|350.9775
|350.9775
|351.818
|351.818
Line 205: Line 235:
|372.2228
|372.2228
|372.8571
|372.8571
|374.026
|''375''
|376.0473
|376.0473
|376.9479
|376.9479
Line 218: Line 250:
|397.03765
|397.03765
|397.7143
|397.7143
|398.961
|''400''
|401.1171
|401.1171
|402.0777
|402.0777
Line 231: Line 265:
|421.8525
|421.8525
|422.5714
|422.5714
|423.8961
|''425''
|426.187
|426.187
|427.2076
|427.2076
Line 244: Line 280:
|446.66735
|446.66735
|447.4286
|447.4286
|448.8312
|''450''
|451.2568
|451.2568
|452.33745
|452.33745
Line 257: Line 295:
|471.4822
|471.4822
|472.2857
|472.2857
|473.7662
|''475''
|476.3266
|476.3266
|477.4673
|477.4673
Line 270: Line 310:
|496.2971
|496.2971
|497.1429
|497.1429
|498.7013
|''500''
|501.3964
|501.3964
|502.5972
|502.5972
Line 283: Line 325:
|521.1119
|521.1119
|522
|522
|523.6364
|''525''
|526.46625
|526.46625
|527.727
|527.727
Line 296: Line 340:
|545.9268
|545.9268
|546.8571
|546.8571
|548.5714
|''550''
|551.536
|551.536
|552.8569
|552.8569
Line 309: Line 355:
|570.7416
|570.7416
|571.4286
|571.4286
|573.5065
|''575''
|576.6059
|576.6059
|577.9867
|577.9867
Line 322: Line 370:
|595.5565
|595.5565
|596.5714
|596.5714
|598.4416
|''600''
|601.6757
|601.6757
|603.1166
|603.1166
Line 335: Line 385:
|620.3713
|620.3713
|621.4286
|621.4286
|623.3766
|''625''
|626.7455
|626.7455
|628.2465
|628.2465
Line 348: Line 400:
|645.1862
|645.1862
|646.2857
|646.2857
|648.3117
|''650''
|651.8154
|651.8154
|653.3763
|653.3763
Line 361: Line 415:
|670.001
|670.001
|671.1429
|671.1429
|673.24765
|''675''
|676.8852
|676.8852
|678.5062
|678.5062
Line 374: Line 430:
|694.8158
|694.8158
|696
|696
|698.1818
|''700''
|701.955
|701.955
|703.636
|703.636
Line 387: Line 445:
|719.6307
|719.6307
|720.8571
|720.8571
|723.1169
|''725''
|727.0248
|727.0248
|728.7659
|728.7659
Line 400: Line 460:
|744.4456
|744.4456
|745.7143
|745.7143
|748.05195
|''750''
|752.0946
|752.0946
|753.89575
|753.89575
Line 413: Line 475:
|769.2604
|769.2604
|770.5714
|770.5714
|772.987
|''775''
|777.1645
|777.1645
|779.0256
|779.0256
Line 426: Line 490:
|794.0753
|794.0753
|795.4286
|795.4286
|797.9221
|''800''
|802.2343
|802.2343
|804.1555
|804.1555
Line 439: Line 505:
|818.89015
|818.89015
|820.2857
|820.2857
|822.8571
|''825''
|827.3041
|827.3041
|829.2853
|829.2853
Line 452: Line 520:
|843.705
|843.705
|845.1429
|845.1429
|847.7922
|''850''
|852.3739
|852.3739
|854.4152
|854.4152
Line 465: Line 535:
|868.51985
|868.51985
|870
|870
|872.7273
|''875''
|877.44375
|877.44375
|879.545
|879.545
Line 478: Line 550:
|893.3347
|893.3347
|894.8571
|894.8571
|897.6623
|''900''
|902.5136
|902.5136
|904.6749
|904.6749
Line 491: Line 565:
|918.1496
|918.1496
|919.7143
|919.7143
|922.5974
|''925''
|927.5834
|927.5834
|929.8048
|929.8048
Line 504: Line 580:
|942.9644
|942.9644
|944.5714
|944.5714
|947.5325
|''950''
|952.6532
|952.6532
|954.9346
|954.9346
Line 517: Line 595:
|967.7793
|967.7793
|969.4286
|969.4286
|972.4675
|''975''
|977.723
|977.723
|980.0645
|980.0645
Line 530: Line 610:
|992.5941
|992.5941
|994.2857
|994.2857
|997.4126
|''1000''
|1002.7929
|1002.7929
|1005.1943
|1005.1943
Line 543: Line 625:
|1017.409
|1017.409
|1019.1429
|1019.1429
|1022.3377
|''1025''
|1027.8627
|1027.8627
|1030.3242
|1030.3242
Line 556: Line 640:
|1042.2238
|1042.2238
|1044
|1044
|1047.2727
|''1050''
|1052.9325
|1052.9325
|1055.454
|1055.454
Line 569: Line 655:
|1067.0386
|1067.0386
|1068.8571
|1068.8571
|1072.2078
|''1075''
|1078.0023
|1078.0023
|1080.5839
|1080.5839
Line 582: Line 670:
|1091.8535
|1091.8535
|1093.7143
|1093.7143
|1097.1429
|''1100''
|1103.0721
|1103.0721
|1105.7138
|1105.7138
Line 595: Line 685:
|1116.6684
|1116.6684
|1118.5714
|1118.5714
|1122.0779
|''1125''
|1128.142
|1128.142
|1130.8436
|1130.8436
Line 608: Line 700:
|1141.4832
|1141.4832
|1143.4286
|1143.4286
|1147.013
|''1150''
|1153.2118
|1153.2118
|1155.9735
|1155.9735
Line 621: Line 715:
|1166.2981
|1166.2981
|1168.2857
|1168.2857
|1171.94805
|''1175''
|1178.2816
|1178.2816
|1181.1033
|1181.1033
Line 634: Line 730:
|1191.1129
|1191.1129
|1193.1429
|1193.1429
|1196.8831
|''1200''
|1203.3514
|1203.3514
|1206.2332
|1206.2332
Line 647: Line 745:
|1215.9278
|1215.9278
|1218
|1218
|1221.8182
|''1225''
|1228.42125
|1228.42125
|1231.6306
|1231.6306
Line 660: Line 760:
|1240.74265
|1240.74265
|1242.8571
|1242.8571
|1246.75325
|''1250''
|1253.4911
|1253.4911
|1256.4929
|1256.4929
Line 673: Line 775:
|1265.5575
|1265.5575
|1267.7143
|1267.7143
|1271.6883
|''1275''
|1278.5609
|1278.5609
|1281.6228
|1281.6228
Line 686: Line 790:
|1290.37235
|1290.37235
|1292.5714
|1292.5714
|1296.6234
|''1300''
|1303.6307
|1303.6307
|1306.7526
|1306.7526
Line 699: Line 805:
|1315.1872
|1315.1872
|1317.4286
|1317.4286
|1321.5584
|''1325''
|1328.7005
|1328.7005
|1331.8825
|1331.8825
Line 712: Line 820:
|1340.0021
|1340.0021
|1342.2857
|1342.2857
|1346.4395
|''1350''
|1353.7704
|1353.7704
|1357.01235
|1357.01235
Line 725: Line 835:
|1364.8169
|1364.8169
|1367.1429
|1367.1429
|1371.4286
|''1375''
|1378.8418
|1378.8418
|1382.1422
|1382.1422
Line 738: Line 850:
|1389.6318
|1389.6318
|1392
|1392
|1396.3636
|''1400''
|1403.91
|1403.91
|1407.2721
|1407.2721

Revision as of 21:52, 19 August 2019

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
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