28edf: Difference between revisions

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== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
!
! rowspan="2" |
!ed31\54 (~49edo!)
! rowspan="2" |ed31\54 (~49edo!)
!ed121/81
! rowspan="2" |ed121/81 (~ed11\19)
!ed3/2
! rowspan="2" |ed3/2
!Golden (~ed10\17)
! colspan="2" |Pyrite
!ed34\57 (~47edo!)
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57 (~47edo!)
|-
!(~ed17\29)
!(~ed10\17)
|-
|-
|1
|1
Line 14: Line 18:
|24.81485
|24.81485
|25.0698
|25.0698
|25.1299
|25.2091
|25.2091
|25.3234
|25.5639
|25.5639
|-
|-
Line 21: Line 27:
|49.6297
|49.6297
|50.1396
|50.1396
|50.2597
|50.41825
|50.41825
|50.6475
|51.1278
|51.1278
|-
|-
Line 28: Line 36:
|74.4446
|74.4446
|75.2095
|75.2095
|75.3896
|75.6274
|75.6274
|75.9712
|76.6917
|76.6917
|-
|-
Line 35: Line 45:
|99.2594
|99.2594
|100.2793
|100.2793
|100.5194
|100.8365
|100.8365
|101.295
|102.2556
|102.2556
|-
|-
Line 42: Line 54:
|124.0743
|124.0743
|125.3491
|125.3491
|125.6493
|10\26.0456
|10\26.0456
|126.6187
|127.81955
|127.81955
|-
|-
Line 49: Line 63:
|148.8891
|148.8891
|150.4189
|150.4189
|150.77915
|151.2547
|151.2547
|151.9425
|153.3835
|153.3835
|-
|-
Line 56: Line 72:
|173.704
|173.704
|175.48875
|175.48875
|175.909
|176.4639
|176.4639
|177.2662
|178.947
|178.947
|-
|-
Line 63: Line 81:
|198.5188
|198.5188
|200.5586
|200.5586
|201.0389
|201.673
|201.673
|202.5899
|204.5113
|204.5113
|-
|-
Line 70: Line 90:
|223.3337
|223.3337
|225.6284
|225.6284
|226.1687
|226.8821
|226.8821
|227.9137
|230.0752
|230.0752
|-
|-
Line 77: Line 99:
|248.1485
|248.1485
|250.6982
|250.6982
|251.2986
|252.0912
|252.0912
|253.2374
|255.6391
|255.6391
|-
|-
Line 84: Line 108:
|272.9634
|272.9634
|275.768
|275.768
|276.4284
|277.3004
|277.3004
|278.5612
|281.203
|281.203
|-
|-
Line 91: Line 117:
|297.782
|297.782
|300.8379
|300.8379
|301.5583
|302.5095
|302.5095
|303.8849
|306.7669
|306.7669
|-
|-
Line 98: Line 126:
|322.5931
|322.5931
|325.9077
|325.9077
|326.6682
|327.7186
|327.7186
|329.2087
|332.3308
|332.3308
|-
|-
Line 105: Line 135:
|347.408
|347.408
|350.9775
|350.9775
|351.818
|352.9277
|352.9277
|354.5324
|357.8947
|357.8947
|-
|-
Line 112: Line 144:
|372.2228
|372.2228
|376.0473
|376.0473
|376.9479
|378.13685
|378.13685
|279.8561
|383.45865
|383.45865
|-
|-
Line 119: Line 153:
|397.03765
|397.03765
|401.1171
|401.1171
|402.0777
|403.346
|403.346
|405.1799
|409.0226
|409.0226
|-
|-
Line 126: Line 162:
|421.8525
|421.8525
|426.187
|426.187
|427.2076
|428.5551
|428.5551
|430.5036
|434.5865
|434.5865
|-
|-
Line 133: Line 171:
|446.66735
|446.66735
|451.2568
|451.2568
|452.33745
|453.7642
|453.7642
|455.8274
|460.1504
|460.1504
|-
|-
Line 140: Line 180:
|471.4822
|471.4822
|476.3266
|476.3266
|477.4673
|478.97333
|478.97333
|481.1511
|485.7143
|485.7143
|-
|-
Line 147: Line 189:
|496.2971
|496.2971
|501.3964
|501.3964
|502.5972
|504.1825
|504.1825
|506.4749
|511.2781
|511.2781
|-
|-
Line 154: Line 198:
|521.1119
|521.1119
|526.46625
|526.46625
|527.727
|529.3916
|529.3916
|531.7986
|536.8421
|536.8421
|-
|-
Line 161: Line 207:
|545.9268
|545.9268
|551.536
|551.536
|552.8569
|554.6007
|554.6007
|557.1223
|562.406
|562.406
|-
|-
Line 168: Line 216:
|570.7416
|570.7416
|576.6059
|576.6059
|577.9867
|579.8098
|579.8098
|582.4461
|587.9699
|587.9699
|-
|-
Line 175: Line 225:
|595.5565
|595.5565
|601.6757
|601.6757
|603.1166
|605.019
|605.019
|607.7698
|613.5338
|613.5338
|-
|-
Line 182: Line 234:
|620.3713
|620.3713
|626.7455
|626.7455
|628.2465
|630.2281
|630.2281
|633.0936
|639.0977
|639.0977
|-
|-
Line 189: Line 243:
|645.1862
|645.1862
|651.8154
|651.8154
|653.3763
|655.4372
|655.4372
|658.4173
|664.66165
|664.66165
|-
|-
Line 196: Line 252:
|670.001
|670.001
|676.8852
|676.8852
|678.5062
|680.6463
|680.6463
|983.7411
|690.2256
|690.2256
|-
|-
Line 203: Line 261:
|694.8158
|694.8158
|701.955
|701.955
|703.636
|705.85545
|705.85545
|709.0648
|715.7895
|715.7895
|-
|-
Line 210: Line 270:
|719.6307
|719.6307
|727.0248
|727.0248
|728.7659
|731.0646
|731.0646
|734.3885
|741.3534
|741.3534
|-
|-
Line 217: Line 279:
|744.4456
|744.4456
|752.0946
|752.0946
|753.89575
|756.2736
|756.2736
|759.7123
|766.9173
|766.9173
|-
|-
Line 224: Line 288:
|769.2604
|769.2604
|777.1645
|777.1645
|779.0256
|781.4828
|781.4828
|785.036
|792.4812
|792.4812
|-
|-
Line 231: Line 297:
|794.0753
|794.0753
|802.2343
|802.2343
|804.1555
|806.6919
|806.6919
|810.3598
|818.0451
|818.0451
|-
|-
Line 238: Line 306:
|818.89015
|818.89015
|827.3041
|827.3041
|829.2853
|831.9011
|831.9011
|835.6835
|843.609
|843.609
|-
|-
Line 245: Line 315:
|843.705
|843.705
|852.3739
|852.3739
|854.4152
|857.1102
|857.1102
|961.0073
|869.1729
|869.1729
|-
|-
Line 252: Line 324:
|868.51985
|868.51985
|877.44375
|877.44375
|879.545
|882.3193
|882.3193
|886.331
|894.7368
|894.7368
|-
|-
Line 259: Line 333:
|893.3347
|893.3347
|902.5136
|902.5136
|904.6749
|907.5284
|907.5284
|911.6547
|920.30075
|920.30075
|-
|-
Line 266: Line 342:
|918.1496
|918.1496
|927.5834
|927.5834
|929.8048
|932.3767
|932.3767
|936.9785
|945.8647
|945.8647
|-
|-
Line 273: Line 351:
|942.9644
|942.9644
|952.6532
|952.6532
|954.9346
|957.9467
|957.9467
|962.3022
|971.4286
|971.4286
|-
|-
Line 280: Line 360:
|967.7793
|967.7793
|977.723
|977.723
|980.0645
|983.1558
|983.1558
|987.626
|996.9925
|996.9925
|-
|-
Line 287: Line 369:
|992.5941
|992.5941
|1002.7929
|1002.7929
|1005.1943
|1008.3649
|1008.3649
|1012.9497
|1022.5564
|1022.5564
|-
|-
Line 294: Line 378:
|1017.409
|1017.409
|1027.8627
|1027.8627
|1030.3242
|1033.57405
|1033.57405
|1038.2735
|1048.1203
|1048.1203
|-
|-
Line 301: Line 387:
|1042.2238
|1042.2238
|1052.9325
|1052.9325
|1055.454
|1058.7832
|1058.7832
|1063.5972
|1073.6842
|1073.6842
|-
|-
Line 308: Line 396:
|1067.0386
|1067.0386
|1078.0023
|1078.0023
|1080.5839
|1083.9923
|1083.9923
|1088.92095
|1099.2481
|1099.2481
|-
|-
Line 315: Line 405:
|1091.8535
|1091.8535
|1103.0721
|1103.0721
|1105.7138
|1109.2014
|1109.2014
|1114.2447
|1124.812
|1124.812
|-
|-
Line 322: Line 414:
|1116.6684
|1116.6684
|1128.142
|1128.142
|1130.8436
|1137.41055
|1137.41055
|1139.5684
|1150.3759
|1150.3759
|-
|-
Line 329: Line 423:
|1141.4832
|1141.4832
|1153.2118
|1153.2118
|1155.9735
|1159.6297
|1159.6297
|1164.8922
|1175.93985
|1175.93985
|-
|-
Line 336: Line 432:
|1166.2981
|1166.2981
|1178.2816
|1178.2816
|1181.1033
|1184.8288
|1184.8288
|1190.2159
|1201.5038
|1201.5038
|-
|-
Line 343: Line 441:
|1191.1129
|1191.1129
|1203.3514
|1203.3514
|1206.2332
|1210.0379
|1210.0379
|1215.5397
|1227.0677
|1227.0677
|-
|49
|1205.5556
|1215.9278
|1228.42125
|1231.6306
|1235.247
|1240.8634
|1252.6316
|-
|50
|1230.1587
|1240.74265
|1253.4911
|1256.4929
|1260.4561
|1266.18715
|1278.1955
|-
|51
|1254.7619
|1265.5575
|1278.5609
|1281.6228
|128.6653
|1291.5109
|1303.7594
|-
|52
|1279.3651
|1290.37235
|1303.6307
|1306.7526
|1310.8744
|1316.8346
|1329.3233
|-
|53
|1303.96825
|1315.1872
|1328.7005
|1331.8825
|1336.0835
|1342.1584
|1354.8872
|-
|54
|1328.5714
|1340.0021
|1353.7704
|1357.01235
|1361.2927
|1367.4821
|1380.4511
|-
|55
|1353.1746
|1364.8169
|1378.8418
|1382.1422
|1386.5018
|1392.8059
|1406.015
|-
|56
|1377.7778
|1389.6318
|1403.91
|1407.2721
|1411.7109
|1418.1296
|1431.57895
|}
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 23:45, 5 March 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

ed31\54 (~49edo!) ed121/81 (~ed11\19) ed3/2 Pyrite ed122/81 (~ed13\22) ed34\57 (~47edo!)
(~ed17\29) (~ed10\17)
1 24.6032 24.81485 25.0698 25.1299 25.2091 25.3234 25.5639
2 49.20635 49.6297 50.1396 50.2597 50.41825 50.6475 51.1278
3 73.8095 74.4446 75.2095 75.3896 75.6274 75.9712 76.6917
4 98.4127 99.2594 100.2793 100.5194 100.8365 101.295 102.2556
5 123.0159 124.0743 125.3491 125.6493 10\26.0456 126.6187 127.81955
6 147.61905 148.8891 150.4189 150.77915 151.2547 151.9425 153.3835
7 172.2222 173.704 175.48875 175.909 176.4639 177.2662 178.947
8 196.8254 198.5188 200.5586 201.0389 201.673 202.5899 204.5113
9 221.4286 223.3337 225.6284 226.1687 226.8821 227.9137 230.0752
10 246.03175 248.1485 250.6982 251.2986 252.0912 253.2374 255.6391
11 270.6349 272.9634 275.768 276.4284 277.3004 278.5612 281.203
12 295.2381 297.782 300.8379 301.5583 302.5095 303.8849 306.7669
13 319.8413 322.5931 325.9077 326.6682 327.7186 329.2087 332.3308
14 344.4444 347.408 350.9775 351.818 352.9277 354.5324 357.8947
15 369.0476 372.2228 376.0473 376.9479 378.13685 279.8561 383.45865
16 393.6508 397.03765 401.1171 402.0777 403.346 405.1799 409.0226
17 418.254 421.8525 426.187 427.2076 428.5551 430.5036 434.5865
18 442.8571 446.66735 451.2568 452.33745 453.7642 455.8274 460.1504
19 467.460 471.4822 476.3266 477.4673 478.97333 481.1511 485.7143
20 492.0635 496.2971 501.3964 502.5972 504.1825 506.4749 511.2781
21 516.6667 521.1119 526.46625 527.727 529.3916 531.7986 536.8421
22 541.2698 545.9268 551.536 552.8569 554.6007 557.1223 562.406
23 565.873 570.7416 576.6059 577.9867 579.8098 582.4461 587.9699
24 590.4762 595.5565 601.6757 603.1166 605.019 607.7698 613.5338
25 615.0794 620.3713 626.7455 628.2465 630.2281 633.0936 639.0977
26 639.6825 645.1862 651.8154 653.3763 655.4372 658.4173 664.66165
27 664.2857 670.001 676.8852 678.5062 680.6463 983.7411 690.2256
28 688.8889 694.8158 701.955 703.636 705.85545 709.0648 715.7895
29 713.4921 719.6307 727.0248 728.7659 731.0646 734.3885 741.3534
30 738.0952 744.4456 752.0946 753.89575 756.2736 759.7123 766.9173
31 762.6984 769.2604 777.1645 779.0256 781.4828 785.036 792.4812
32 787.3016 794.0753 802.2343 804.1555 806.6919 810.3598 818.0451
33 811.9048 818.89015 827.3041 829.2853 831.9011 835.6835 843.609
34 836.5079 843.705 852.3739 854.4152 857.1102 961.0073 869.1729
35 861.1111 868.51985 877.44375 879.545 882.3193 886.331 894.7368
36 885.7143 893.3347 902.5136 904.6749 907.5284 911.6547 920.30075
37 910.3175 918.1496 927.5834 929.8048 932.3767 936.9785 945.8647
38 934.9206 942.9644 952.6532 954.9346 957.9467 962.3022 971.4286
39 959.5238 967.7793 977.723 980.0645 983.1558 987.626 996.9925
40 984.127 992.5941 1002.7929 1005.1943 1008.3649 1012.9497 1022.5564
41 1008.7302 1017.409 1027.8627 1030.3242 1033.57405 1038.2735 1048.1203
42 1033.333 1042.2238 1052.9325 1055.454 1058.7832 1063.5972 1073.6842
43 1057.9365 1067.0386 1078.0023 1080.5839 1083.9923 1088.92095 1099.2481
44 1082.5397 1091.8535 1103.0721 1105.7138 1109.2014 1114.2447 1124.812
45 1107.1429 1116.6684 1128.142 1130.8436 1137.41055 1139.5684 1150.3759
46 1131.7646 1141.4832 1153.2118 1155.9735 1159.6297 1164.8922 1175.93985
47 1156.3492 1166.2981 1178.2816 1181.1033 1184.8288 1190.2159 1201.5038
48 1180.9524 1191.1129 1203.3514 1206.2332 1210.0379 1215.5397 1227.0677
49 1205.5556 1215.9278 1228.42125 1231.6306 1235.247 1240.8634 1252.6316
50 1230.1587 1240.74265 1253.4911 1256.4929 1260.4561 1266.18715 1278.1955
51 1254.7619 1265.5575 1278.5609 1281.6228 128.6653 1291.5109 1303.7594
52 1279.3651 1290.37235 1303.6307 1306.7526 1310.8744 1316.8346 1329.3233
53 1303.96825 1315.1872 1328.7005 1331.8825 1336.0835 1342.1584 1354.8872
54 1328.5714 1340.0021 1353.7704 1357.01235 1361.2927 1367.4821 1380.4511
55 1353.1746 1364.8169 1378.8418 1382.1422 1386.5018 1392.8059 1406.015
56 1377.7778 1389.6318 1403.91 1407.2721 1411.7109 1418.1296 1431.57895
Retrieved from "https://en.xen.wiki/index.php?title=28edf&oldid=40659"