57ed5

← 56ed5

57ed5

58ed5 →

Prime factorization	3 × 19
Step size	48.8827¢
Octave	25\57ed5 (1222.07¢)
Twelfth	39\57ed5 (1906.43¢) (→13\19ed5)
Consistency limit	3
Distinct consistency limit	3

57 equal divisions of the 5th harmonic (abbreviated 57ed5) is a nonoctave tuning system that divides the interval of 5/1 into 57 equal parts of about 48.9⁠ ⁠¢ each. Each step represents a frequency ratio of 5^1/57, or the 57th root of 5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	48.9	34/33
2	97.8
3	146.6	25/23
4	195.5	19/17
5	244.4	15/13
6	293.3	13/11
7	342.2
8	391.1
9	439.9
10	488.8
11	537.7	15/11
12	586.6	7/5
13	635.5	13/9
14	684.4
15	733.2	29/19
16	782.1	11/7
17	831	21/13, 34/21
18	879.9	5/3
19	928.8	29/17
20	977.7
21	1026.5
22	1075.4	13/7
23	1124.3
24	1173.2
25	1222.1
26	1271
27	1319.8	15/7
28	1368.7	11/5
29	1417.6	25/11, 34/15
30	1466.5	7/3
31	1515.4
32	1564.2
33	1613.1	33/13
34	1662	34/13
35	1710.9
36	1759.8
37	1808.7
38	1857.5
39	1906.4	3/1
40	1955.3	31/10, 34/11
41	2004.2
42	2053.1
43	2102
44	2150.8
45	2199.7	25/7
46	2248.6	11/3
47	2297.5	34/9
48	2346.4
49	2395.3
50	2444.1
51	2493
52	2541.9	13/3
53	2590.8
54	2639.7	23/5
55	2688.5	33/7
56	2737.4	34/7
57	2786.3	5/1

Harmonics

Approximation of harmonics in 57ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+22.1	+4.5	-4.7	+0.0	-22.3	+4.1	+17.3	+8.9	+22.1	+3.7	-0.3
	Relative (%)	+45.1	+9.1	-9.7	+0.0	-45.7	+8.3	+35.4	+18.3	+45.1	+7.6	-0.6
Steps (reduced)		25 (25)	39 (39)	49 (49)	57 (0)	63 (6)	69 (12)	74 (17)	78 (21)	82 (25)	85 (28)	88 (31)

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