57ed7/3

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57ed7/3

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Prime factorization	3 × 19
Step size	25.7346¢
Octave	47\57ed7/3 (1209.53¢)
Twelfth	74\57ed7/3 (1904.36¢)
Consistency limit	3
Distinct consistency limit	3

57 equal divisions of 7/3 (abbreviated 57ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 57 equal parts of about 25.7 ¢ each. Each step represents a frequency ratio of (7/3)^1/57, or the 57th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	25.7
2	51.5
3	77.2	22/21, 23/22
4	102.9	18/17
5	128.7	14/13
6	154.4	23/21
7	180.1	10/9
8	205.9
9	231.6
10	257.3	22/19
11	283.1	20/17
12	308.8
13	334.5	17/14, 23/19
14	360.3
15	386
16	411.8	19/15
17	437.5	9/7
18	463.2	17/13, 30/23
19	489
20	514.7	31/23
21	540.4	15/11
22	566.2	18/13
23	591.9	31/22
24	617.6	10/7
25	643.4	29/20
26	669.1
27	694.8
28	720.6
29	746.3	20/13
30	772
31	797.8	27/17
32	823.5	29/18
33	849.2	31/19
34	875
35	900.7
36	926.4	29/17
37	952.2	33/19
38	977.9
39	1003.6
40	1029.4
41	1055.1
42	1080.9
43	1106.6	19/10
44	1132.3	27/14
45	1158.1
46	1183.8
47	1209.5
48	1235.3
49	1261	27/13, 29/14, 31/15
50	1286.7	21/10
51	1312.5
52	1338.2	13/6
53	1363.9	11/5
54	1389.7	29/13
55	1415.4
56	1441.1	23/10
57	1466.9	7/3

Harmonics

Approximation of harmonics in 57ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.5	+2.4	-6.7	-7.0	+11.9	+2.4	+2.8	+4.8	+2.5	-8.1	-4.3
	Relative (%)	+37.0	+9.3	-26.0	-27.1	+46.4	+9.3	+11.0	+18.7	+9.9	-31.3	-16.6
Steps (reduced)		47 (47)	74 (17)	93 (36)	108 (51)	121 (7)	131 (17)	140 (26)	148 (34)	155 (41)	161 (47)	167 (53)

Approximation of harmonics in 57ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+11.6	+11.9	-4.6	+12.4	+10.3	-11.4	-2.1	+12.1	+4.8	+1.5	+1.7
	Relative (%)	+44.9	+46.4	-17.8	+48.1	+40.2	-44.3	-8.0	+46.9	+18.7	+5.7	+6.7
Steps (reduced)		173 (2)	178 (7)	182 (11)	187 (16)	191 (20)	194 (23)	198 (27)	202 (31)	205 (34)	208 (37)	211 (40)