56ed7/3

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56ed7/3

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Prime factorization	23 × 7
Step size	26.1941¢
Octave	46\56ed7/3 (1204.93¢) (→23\28ed7/3)
Twelfth	73\56ed7/3 (1912.17¢)
Consistency limit	4
Distinct consistency limit	4

56 equal divisions of 7/3 (abbreviated 56ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 56 equal parts of about 26.2⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/56, or the 56th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	26.2
2	52.4	31/30, 34/33
3	78.6	23/22
4	104.8	33/31
5	131	14/13
6	157.2	34/31
7	183.4
8	209.6
9	235.7	8/7
10	261.9
11	288.1
12	314.3
13	340.5
14	366.7	26/21
15	392.9
16	419.1
17	445.3	22/17
18	471.5	21/16
19	497.7	4/3
20	523.9	19/14, 23/17
21	550.1
22	576.3
23	602.5
24	628.7	33/23
25	654.9	19/13
26	681	34/23
27	707.2
28	733.4	29/19, 32/21
29	759.6	31/20
30	785.8
31	812
32	838.2	13/8
33	864.4	33/20
34	890.6
35	916.8	17/10
36	943
37	969.2	7/4
38	995.4	16/9
39	1021.6
40	1047.8
41	1074	13/7
42	1100.2
43	1126.3
44	1152.5	33/17
45	1178.7
46	1204.9
47	1231.1
48	1257.3	29/14, 31/15
49	1283.5
50	1309.7
51	1335.9	13/6
52	1362.1	11/5
53	1388.3	29/13
54	1414.5	34/15
55	1440.7	23/10
56	1466.9	7/3

Harmonics

Approximation of harmonics in 56ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.9	+10.2	+9.9	-9.7	-11.0	+10.2	-11.4	-5.8	-4.8	-12.6	-6.1
	Relative (%)	+18.8	+39.0	+37.6	-37.2	-42.2	+39.0	-43.5	-22.0	-18.4	-48.3	-23.4
Steps (reduced)		46 (46)	73 (17)	92 (36)	106 (50)	118 (6)	129 (17)	137 (25)	145 (33)	152 (40)	158 (46)	164 (52)

Approximation of harmonics in 56ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+12.5	-11.0	+0.5	-6.5	-6.7	-0.8	+10.3	+0.1	-5.8	-7.7	-6.1
	Relative (%)	+47.6	-42.2	+1.8	-24.7	-25.4	-3.2	+39.5	+0.5	-22.0	-29.5	-23.3
Steps (reduced)		170 (2)	174 (6)	179 (11)	183 (15)	187 (19)	191 (23)	195 (27)	198 (30)	201 (33)	204 (36)	207 (39)