56edf

← 55edf

56edf

57edf →

Prime factorization	23 × 7
Step size	12.5349¢
Octave	96\56edf (1203.35¢) (→12\7edf)
Twelfth	152\56edf (1905.31¢) (→19\7edf)
Consistency limit	2
Distinct consistency limit	2

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.

Related regular temperaments

7-limit 383&670

Commas: 2401/2400, |91 -80 13 2>

POTE generator: ~|-33 32 -4 -3> = 12.5357

Mapping: [<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

Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|]

EDOs: 383, 670, 1053, 1436, 1723

Intervals

56ed3/2
1	12.5349
2	25.0698
3	37.6047
4	50.1396
5	62.67455
6	75.2095
7	87.7444
8	100.2793
9	112.8142
10	125.3491
11	137.884
12	150.4189
13	162.9538
14	175.48875
15	188.2366
16	200.5586
17	213.0935
18	225.6284
19	238.1633
20	250.6982
21	263.2331
22	275.768
23	288.30295
24	300.8379
25	313.3728
26	325.9077
27	338.4426
28	350.9775
29	363.5214
30	376.0473
31	388.5822
32	401.1171
33	413.65205
34	426.187
35	438.7219
36	451.2568
37	463.7917
38	476.3266
39	488.8615
40	501.3964
41	513.9313
42	526.46625
43	539.0012
44	551.536
45	564.071
46	576.6059
47	589.1408
48	601.6757
49	614.2106
50	626.7455
51	639.28045
52	651.8154
53	664.3503
54	676.8852
55	689.4201
56	701.955
57	714.4899
58	727.0248
59	739.5597
60	752.0946
61	764.62955
62	777.1645
63	789.6994
64	802.2343
65	814.7692
66	827.3041
67	839.839
68	852.3739
69	864.9088
70	877.44375
71	889.9787
72	902.5136
73	915.0485
74	927.5834
75	940.1183
76	952.6532
77	965.1881
78	977.723
79	990.25795
80	1002.7929
81	1015.3278
82	1027.8627
83	1040.3976
84	1052.9325
85	1065.4674
86	1078.0023
87	1090.5372
88	1103.0721
89	1115.6071
90	1128.142
91	1140.6769
92	1153.2118
93	1165.7467
94	1178.2816
95	1190.8165
96	1203.3514
97	1215.8863
98	1228.42125
99	1240.9561
100	1253.4911
101	1266.026
102	1278.5609
103	1291.0958
104	1303.6307
105	1316.1656
106	1328.7005
107	1341.23545
108	1353.7704
109	1366.3053
110	1378.8418
111	1391.3751
112	1403.91

Todo: complete table Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically.