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'''[[EDF|Division of the just perfect fifth]] into 28 equal parts''' (28EDF) is related to [[48edo|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, [[383edo|383]], 718, [[1053edo|1053]], and 1101 EDOs.
'''[[EDF|Division of the just perfect fifth]] into 28 equal parts''' (28EDF) is related to [[48edo|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, [[383edo|383]], 718, [[1053edo|1053]], and 1101 EDOs.


== Intervals ==
{| class="wikitable"
!
!ed31\54 (~49edo!)
!ed121/81
!ed3/2
!Golden (~ed10\17)
!ed34\57 (~47edo!)
|-
|1
|24.6032
|24.81485
|25.0698
|25.2091
|25.5639
|-
|2
|49.20635
|49.6297
|50.1396
|50.41825
|51.1278
|-
|3
|73.8095
|74.4446
|75.2095
|75.6274
|76.6917
|-
|4
|98.4127
|99.2594
|100.2793
|100.8365
|102.2556
|-
|5
|123.0159
|124.0743
|125.3491
|10\26.0456
|127.81955
|-
|6
|147.61905
|148.8891
|150.4189
|151.2547
|153.3835
|-
|7
|172.2222
|173.704
|175.48875
|176.4639
|178.947
|-
|8
|196.8254
|198.5188
|200.5586
|201.673
|204.5113
|-
|9
|221.4286
|223.3337
|225.6284
|226.8821
|230.0752
|-
|10
|246.03175
|248.1485
|250.6982
|252.0912
|255.6391
|-
|11
|270.6349
|272.9634
|275.768
|277.3004
|281.203
|-
|12
|295.2381
|297.782
|300.8379
|302.5095
|306.7669
|-
|13
|319.8413
|322.5931
|325.9077
|327.7186
|332.3308
|-
|14
|344.4444
|347.408
|350.9775
|352.9277
|357.8947
|-
|15
|369.0476
|372.2228
|376.0473
|378.13685
|383.45865
|-
|16
|393.6508
|397.03765
|401.1171
|403.346
|409.0226
|-
|17
|418.254
|421.8525
|426.187
|428.5551
|434.5865
|-
|18
|442.8571
|446.66735
|451.2568
|453.7642
|460.1504
|-
|19
|467.460
|471.4822
|476.3266
|478.97333
|485.7143
|-
|20
|492.0635
|496.2971
|501.3964
|504.1825
|511.2781
|-
|21
|516.6667
|521.1119
|526.46625
|529.3916
|536.8421
|-
|22
|541.2698
|545.9268
|551.536
|554.6007
|562.406
|-
|23
|565.873
|570.7416
|576.6059
|579.8098
|587.9699
|-
|24
|590.4762
|595.5565
|601.6757
|605.019
|613.5338
|-
|25
|615.0794
|620.3713
|626.7455
|630.2281
|639.0977
|-
|26
|639.6825
|645.1862
|651.8154
|655.4372
|664.66165
|-
|27
|664.2857
|670.001
|676.8852
|680.6463
|690.2256
|-
|28
|688.8889
|694.8158
|701.955
|705.85545
|715.7895
|-
|29
|713.4921
|719.6307
|727.0248
|731.0646
|741.3534
|-
|30
|738.0952
|744.4456
|752.0946
|756.2736
|766.9173
|-
|31
|762.6984
|769.2604
|777.1645
|781.4828
|792.4812
|-
|32
|787.3016
|794.0753
|802.2343
|806.6919
|818.0451
|-
|33
|811.9048
|818.89015
|827.3041
|831.9011
|843.609
|-
|34
|836.5079
|843.705
|852.3739
|857.1102
|869.1729
|-
|35
|861.1111
|868.51985
|877.44375
|882.3193
|894.7368
|-
|36
|885.7143
|893.3347
|902.5136
|907.5284
|920.30075
|-
|37
|910.3175
|918.1496
|927.5834
|932.3767
|945.8647
|-
|38
|934.9206
|942.9644
|952.6532
|957.9467
|971.4286
|-
|39
|959.5238
|967.7793
|977.723
|983.1558
|996.9925
|-
|40
|984.127
|992.5941
|1002.7929
|1008.3649
|1022.5564
|-
|41
|1008.7302
|1017.409
|1027.8627
|1033.57405
|1048.1203
|-
|42
|1033.333
|1042.2238
|1052.9325
|1058.7832
|1073.6842
|-
|43
|1057.9365
|1067.0386
|1078.0023
|1083.9923
|1099.2481
|-
|44
|1082.5397
|1091.8535
|1103.0721
|1109.2014
|1124.812
|-
|45
|1107.1429
|1116.6684
|1128.142
|1137.41055
|1150.3759
|-
|46
|1131.7646
|1141.4832
|1153.2118
|1159.6297
|1175.93985
|-
|47
|1156.3492
|1166.2981
|1178.2816
|1184.8288
|1201.5038
|-
|48
|1180.9524
|1191.1129
|1203.3514
|1210.0379
|1227.0677
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 18:00, 1 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 ed3/2 Golden (~ed10\17) ed34\57 (~47edo!)
1 24.6032 24.81485 25.0698 25.2091 25.5639
2 49.20635 49.6297 50.1396 50.41825 51.1278
3 73.8095 74.4446 75.2095 75.6274 76.6917
4 98.4127 99.2594 100.2793 100.8365 102.2556
5 123.0159 124.0743 125.3491 10\26.0456 127.81955
6 147.61905 148.8891 150.4189 151.2547 153.3835
7 172.2222 173.704 175.48875 176.4639 178.947
8 196.8254 198.5188 200.5586 201.673 204.5113
9 221.4286 223.3337 225.6284 226.8821 230.0752
10 246.03175 248.1485 250.6982 252.0912 255.6391
11 270.6349 272.9634 275.768 277.3004 281.203
12 295.2381 297.782 300.8379 302.5095 306.7669
13 319.8413 322.5931 325.9077 327.7186 332.3308
14 344.4444 347.408 350.9775 352.9277 357.8947
15 369.0476 372.2228 376.0473 378.13685 383.45865
16 393.6508 397.03765 401.1171 403.346 409.0226
17 418.254 421.8525 426.187 428.5551 434.5865
18 442.8571 446.66735 451.2568 453.7642 460.1504
19 467.460 471.4822 476.3266 478.97333 485.7143
20 492.0635 496.2971 501.3964 504.1825 511.2781
21 516.6667 521.1119 526.46625 529.3916 536.8421
22 541.2698 545.9268 551.536 554.6007 562.406
23 565.873 570.7416 576.6059 579.8098 587.9699
24 590.4762 595.5565 601.6757 605.019 613.5338
25 615.0794 620.3713 626.7455 630.2281 639.0977
26 639.6825 645.1862 651.8154 655.4372 664.66165
27 664.2857 670.001 676.8852 680.6463 690.2256
28 688.8889 694.8158 701.955 705.85545 715.7895
29 713.4921 719.6307 727.0248 731.0646 741.3534
30 738.0952 744.4456 752.0946 756.2736 766.9173
31 762.6984 769.2604 777.1645 781.4828 792.4812
32 787.3016 794.0753 802.2343 806.6919 818.0451
33 811.9048 818.89015 827.3041 831.9011 843.609
34 836.5079 843.705 852.3739 857.1102 869.1729
35 861.1111 868.51985 877.44375 882.3193 894.7368
36 885.7143 893.3347 902.5136 907.5284 920.30075
37 910.3175 918.1496 927.5834 932.3767 945.8647
38 934.9206 942.9644 952.6532 957.9467 971.4286
39 959.5238 967.7793 977.723 983.1558 996.9925
40 984.127 992.5941 1002.7929 1008.3649 1022.5564
41 1008.7302 1017.409 1027.8627 1033.57405 1048.1203
42 1033.333 1042.2238 1052.9325 1058.7832 1073.6842
43 1057.9365 1067.0386 1078.0023 1083.9923 1099.2481
44 1082.5397 1091.8535 1103.0721 1109.2014 1124.812
45 1107.1429 1116.6684 1128.142 1137.41055 1150.3759
46 1131.7646 1141.4832 1153.2118 1159.6297 1175.93985
47 1156.3492 1166.2981 1178.2816 1184.8288 1201.5038
48 1180.9524 1191.1129 1203.3514 1210.0379 1227.0677
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