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Anatomy of an Equal Division per 2/1 (ED2, EDO)


This chart gives a list of fractions between 0 and 1, with numerators between 1 and 60, in order of descending difference from 1/2, and their corresponding cent values if taken as (logarithmic) fractions of an octave

as exponent

in cents part of 1200¢
as exponent

0\1
0
1200
1\1
1\32
37.5
1162.5
31\32
1\31
38.7096
1161.2904
30\31
2\61
39.3443
1160.6557
60\61
1\30
40
1160
29\30
2\59
40.678
1159.322
57\59
1\29
41.3793
1158.6207
28\29
2\57
42.1053
1157.8947
55\57
1\28
42.8571
1157.1429
27\28
2\55
43.63
1156.36
53\55
1\27
44.4
1155.5
26\27
2\53
45.283
1054.717
51\53
1\26
46.15385
1153.84615
25\26
2\51
47.0588
1152.9412
49\51
1\25
48
1152
24\25
2\49
48.9796
1151.0204
47\49
1\24
50
1150
23\24
2\47
51.0638
1148.9562
45\47
1\23
52.1739
1047.8261
22\23
2\45
53.3
1146.6
43\45
1\22
54.54
1145.45
21\22
2\43
55.81395
1144.18605
41\43
1\21
57.1429
1143.8571
20\21
2\41
58.5366
1141.4634
39\41
1\20
60
1140
19\20
2\39
61.5385
1139.4615
37\39
1\19
63.1579
1136.8421
18\19
2\37
64.864
1135.135
35\37
1\18
66.6
1133.3
17\18
2\35
68.5714
1131.4286
33\35
1\17
70.5882
1129.4118
16\17
2\33
72.72
1127.27
31\33
1\16
75
1125
15\16
3\47
76.5957
1123.4043
44\47
2\31
77.41935
1122.58065
29\31
3\46
78.2609
1121.7391
43\46
1\15
80
1120
14\15
3\44
81.81
1118.18
41\44
2\29
82.759
1117.241
27\29
3\43
83.7209
1116.2791
40\43
1\14
85.7143
1114.2857
13\14
3\41
87.8049
1112.1951
38\41
2\27
88.8
1111.1
25\27
3\40
90
1110
37\40
1\13
92.3077
1107.6923
12\13
3\38
94.7638
1105.2362
35\38
2\25
96
1104
23\25
3\37
97.297
1102.702
34\37
1\12
100
1100
11\12
3\35
102.8571
1097.1429
32\35
2\23
104.3478
1095.6522
21\23
3\34
105.88235
1094.11765
31\34
1\11
109.09
1090.90
10\11
3\32
112.5
1087.5
29\32
2\21
114.2857
1085.7129
19\21
5\52
115.3846
1084.6154
47\52
3\31
116.129
1083.871
28\31
4\41
117.0732
1082.9268
37\41
1\10
120
1080
9\10
4\39
123.0769
1076.9231
35\39
3\29
124.1379
1075.8621
26\29
5\48
125
1075
43\48
2\19
126.3158
1073.6842
17\19
5\47
127.6596
1072.3404
42\47
3\28
128.5714
1071.4286
25\28
4\37
129.729
1070.270
33\37
1\9
133.3
1066.6
8\9
4\35
137.1429
1063.8571
31\35
3\26
138.4615
1061.5385
23\26
5\43
139.5349
1060.4651
38\43
2\17
141.1765
1058.8235
15\17
5\42
142.8571
1057.1429
37\42
3\25
144
1056
22\25
4\33
145.45
1054.54
29\33
1\8
150
1050
7\8
5\39
153.84615
1046.15385
34\39
4\31
154.8387
1045.1613
27\31
7\54
155.5
1044.4
47\54
3\23
156.5217
1053.4783
20\23
5\38
157.8947
1042.1053
31\38
2\15
160
1040
15\17
5\37
162.162
1037.837
32\37
3\22
163.63
1036.36
19\22
7\51
164.7059
1035.2941
44\51
4\29
165.5172
1034.4822
25\29
5\36
166.6
1033.3
31\36
1\7
171.4286
1028.5714
6\7
5\34
176.4706
1023.5294
29\34
4\27
177.7
1022.2
23\27
7\47
178.7234
1021.2766
40\47
3\20
180
1020
17\20
5\33
181.81
1018.18
28\33
2\13
184.6154
1015.3846
11\13
5\32
187.5
1012.5
27\32
3\19
189.4737
1010.5263
16\19
7\44
190.90
1009.09
37\44
4\25
192
1008
21\25
9\56
192.8571
1007.1429
47\56
5\31
193.5484
1006.4516
26\31
6\37
194.594
1005.405
31\37
1\6
200
1000
5\6
6\35
205.7143
994.2857
29\35
5\29
206.8966
993.1034
24\29
9\52
207.6923
992.3077
43\52
4\23
208.69565
991.31435
19\23
7\40
210
990
33\40
3\17
211.7647
988.2353
14\17
8\45
213.3
986.6
37\45
5\28
214.2857
985.7143
23\28
7\39
215.3846
984.6154
32\39
2\11
218.18
981.81
9\11
7\38
221.0526
978.9474
31\38
5\27
222.2
977.7
22\27
8\43
223.2558
976.7642
35\43
3\16
225
975
13\16
7\37
227.027
972.972
30\37
4\21
228.5714
971.4286
17\21
9\47
229.7872
970.2128
38\47
5\26
230.7692
969.2308
21\26
11\57
231.57895
968.42105
46\57
6\31
232.2581
967.7419
25\31
7\36
233.3
966.6
29\36
1\5
240
960
4\5
7\34
247.0588
952.9412
27\34
6\29
248.2759
951.7241
23\29
11\53
249.0566
950.9434
42\53
5\24
250
950
19\24
9\43
251.1628
948.8372
34\43
4\19
252.6316
947.3884
23\19
7\33
254.54
945.45
26\33
3\14
257.1428
945.8571
11\14
8\37
259.459
940.540
29\37
5\23
260.8696
939.1304
18\23
7\32
262.5
937.5
25\32
2\9
266.6
933.3
7\9
9\40
270
930
31\40
7\31
270.9677
929.0323
24\31
12\53
271.6981
928.3019
41\53
5\22
272.72
927.27
17\22
8\35
274.2857
925.7143
27\35
3\13
276.9231
923.0769
10\13
10\43
279.0698
920.9302
33\43
7\30
280
920
23\30
11\47
280.8511
919.1489
36\47
4\17
282.3529
917.6471
13\17
9\38
284.2105
915.7895
29\38
5\21
285.7143
914.2857
16\21
11\46
286.9565
913.0435
35\46
6\25
288
912
19\25
13\54
288.8
911.1
41\54
7\29
289.6552
910.3448
22\29
8\33
290.90
909.09
25\33
1\4
300
900
3\4
9\35
308.5714
891.4286
26\35
8\31
309.6774
890.3226
23\31
15\58
310.3448
889.6552
43\58
7\27
311.1
888.8
20\27
13\50
312
888
37\50
6\23
313.0435
886.9565
17\23
11\42
314.2857
885.7143
31\42
5\19
315.7895
884.2105
14\19
9\34
317.6471
882.3529
25\34
4\15
320
880
11\15
11\41
321.9512
878.0488
30\41
7\26
323.0769
876.9231
19\26
10\37
324.324
875.675
27\37
3\11
327.27
872.72
8\11
11\40
330
870
29\40
8\29
331.0345
868.9655
21\29
13\47
331.9149
868.0851
34\47
5\18
333.3
866.6
13\18
12\43
334.8837
865.1163
31\43
7\25
336
864
18\25
9\32
337.5
862.5
23\32
2\7
342.8571
857.1429
5\7
11\38
347.3684
852.6316
27\38
9\31
348.3871
851.6129
22\31
16\55
349.09
850.90
39\55
7\24
350
850
17\24
12\41
351.2195
849.7805
29\41
5\17
352.9412
847.0588
12\17
13\44
354.54
845.45
31\44
8\27
355.5
844.4
19\27
11\37
356.756
843.243
26\37
3\10
360
840
7\10
10\33
363.63
836.36
23\33
7\23
365.2174
834.7826
16\23
11\36
366.6
833.3
25\36
4\13
369.2308
830.7692
9\13
13\42
371.4286
828.5714
29\42
9\29
372.4138
827.5862
20\29
14\45
373.3
826.6
31\45
5\16
375
825
11\16
11\35
377.1429
822.8571
24\35
6\19
378.9474
821.0526
13\19
13\41
380.4878
819.5122
28\41
7\22
381.81
818.18
15\22
15\47
382.9787
817.0213
32\47
8\25
384
816
17\25
17\53
384.9057
815.0943
36\53
9\28
385.7143
814.2857
19\28
19\59
386.4407
813.5593
40\59
10\31
387.0968
812.9032
21\31
11\34
388.2353
811.7647
23\34
1\3
400
800
2\3
11\32
412.5
787.5
21\32
10\29
413.7931
786.2069
19\29
19\55
414.54
785.45
36\55
9\26
415.3846
784.6144
17\26
17\49
416.3265
783.6735
32\49
8\23
417.3913
782.6087
15\23
15\43
418.60465
781.39535
28\43
7\20
420
780
13\20
13\37
421.621
778.378
24\37
6\17
423.5294
776.4706
11\17
17\48
425
775
31\48
11\31
425.80645
774.19355
20\31
16\45
426.6
773.3
29\45
5\14
428.5714
771.4286
9\14
14\39
430.7692
769.2308
25\39
9\25
432
768
16\25
13\36
433.3
566.6
23\36
4\11
436.36
763.63
7\11
15\41
439.0234
760.9766
26\41
11\30
440
760
19\30
18\49
440.8163
759.1827
21\49
7\19
442.1053
757.8947
12\19
17\46
443.4783
756.5217
29\46
10\27
444.4
755.5
17\27
13\35
445.7143
754.2857
22\35
3\8
450
750
5\8
14\37
454.054
745.945
23\37
11\29
455.1724
744.8276
18\29
19\50
456
744
31\50
8\21
457.1429
742.8571
13\21
13\34
458.8235
741.1765
21\34
5\13
461.5385
738.4615
8\13
17\44
463.63
736.36
27\44
12\31
464.516
735.484
19\31
19\49
465.3061
734.6939
30\49
7\18
466.6
733.3
11\18
16\41
468.2927
731.7073
25\41
9\23
469.5652
730.4348
14\23
20\51
470.5882
729.4118
31\51
11\28
471.4286
728.5714
17\28
13\33
472.72
727.27
20\33
2\5
480
720
3\5
13\32
487.5
712.5
19\32
11\27
488.8
711.1
16\27
20\49
489.7959
710.2041
29\49
9\22
490.90
709.09
13\22
16\39
492.3077
707.6923
23\39
7\17
494.11765
705.88235
10\17
19\46
495.6522
704.3478
27\46
12\29
496.5517
703.4483
17\29
17\41
497.561
702.439
24\41
22\53
498.1132
701.8868
31\53
5\12
500
700
7\12
18\43
502.3256
697.6744
25\43
13\31
503.226
696.7741
18\31
21\50
504
696
29\50
8\19
505.2631
694.7369
11\19
19\45
506.6
693.3
26\45
11\26
507.6923
692.3077
15\26
14\33
509.09
690.90
19\33
3\7
514.2857
685.7143
4/7
16\37
518.918
681.081
21/37
13\30
520
680
17\30
23\53
520.7547
679.2453
30\53
10\23
521.7391
678.2609
13\23
17\39
523.0769
677.9231
22\39
7\16
525
675
9\16
18\41
526.8293
673.1707
23\41
11\25
528
672
14\25
15\34
529.4118
670.5882
19\34
4\9
533.3
666.6
5\9
17\38
536.8421
663.1579
21\38
13\29
537.931
662.069
16\29
22\49
538.7755
661.2245
27\49
9\20
540
660
11\20
23\51
541.1765
658.8235
28\51
14\31
541.9355
658.0645
17\31
19\42
542.8571
657.1429
23/42
5\11
545.45
654.54
6\11
16\35
548.5714
651.4286
19\35
11\24
550
650
13\24
17\37
551.351
648.648
20\37
6\13
553.84615
646.15395
7\13
19\41
556.0976
645.9224
22\41
13\28
557.1429
642.8571
15\28
20\43
558.1395
642.8605
23\43
7\15
560
640
8\15
15\32
562.5
637.5
17\32
8\17
564.7059
635.2941
9\17
17\36
566.6
633.3
19\36
9\19
568.42105
631.57895
10\19
19\40
570
630
21\40
10\21
571.4286
628.5714
11\21
21\44
572.72
627.27
23\44
11\23
573.913
626.087
12\23
23\48
575
625
25\48
12\25
576
624
13\25
25\52
576.9231
623.0769
27\52
13\27
577.7
622.2
14\27
27\56
578.5714
621.4286
29\56
14\29
579.31
620.69
15\29
29\60
580
620
31\60
15\31
580.6452
619.355
16\31
16\33
581.81
618.18
17\33
1\2
600
1\2