57edt

← 56edt

57edt

58edt →

Prime factorization	3 × 19
Step size	33.3676¢
Octave	36\57edt (1201.23¢) (→12\19edt)
Consistency limit	8
Distinct consistency limit	8

57 divisions of the third harmonic (57edt) is related to 36edo (sixth-tone tuning), but with the 3/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 33.3676 cents. It is consistent to the 9-integer-limit. In comparison, 36edo is only consistent up to the 8-integer-limit.

Lookalikes: 36edo, 93ed6, 101ed7, 21edf

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	33.368
2	66.735	27/26, 28/27
3	100.103	18/17
4	133.471
5	166.838	32/29
6	200.206	9/8
7	233.573	8/7
8	266.941	7/6
9	300.309	19/16, 31/26
10	333.676	17/14, 23/19
11	367.044	21/17, 26/21
12	400.412	24/19, 29/23, 34/27
13	433.779	9/7
14	467.147	17/13, 21/16
15	500.514	4/3
16	533.882
17	567.25	18/13, 32/23
18	600.617	17/12, 24/17
19	633.985	13/9
20	667.353	28/19
21	700.72	3/2
22	734.088	26/17, 29/19
23	767.456	14/9
24	800.823	27/17
25	834.191	21/13, 34/21
26	867.558	28/17
27	900.926	32/19
28	934.294	12/7
29	967.661	7/4
30	1001.029
31	1034.397
32	1067.764	13/7
33	1101.132	17/9
34	1134.499	27/14
35	1167.867
36	1201.235	2/1
37	1234.602
38	1267.97	27/13
39	1301.338	17/8
40	1334.705	13/6
41	1368.073
42	1401.441	9/4
43	1434.808	16/7
44	1468.176	7/3
45	1501.543	19/8, 31/13
46	1534.911	17/7
47	1568.279
48	1601.646
49	1635.014	18/7
50	1668.382	21/8, 34/13
51	1701.749	8/3
52	1735.117
53	1768.484
54	1801.852	17/6
55	1835.22	26/9
56	1868.587
57	1901.955	3/1

Harmonics

Approximation of harmonics in 57edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.2	+0.0	+2.5	+16.6	+1.2	+1.3	+3.7	+0.0	-15.6	-13.7	+2.5
	Relative (%)	+3.7	+0.0	+7.4	+49.7	+3.7	+3.9	+11.1	+0.0	-46.6	-41.2	+7.4
Steps (reduced)		36 (36)	57 (0)	72 (15)	84 (27)	93 (36)	101 (44)	108 (51)	114 (0)	119 (5)	124 (10)	129 (15)

Approximation of harmonics in 57edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	+2.5	+16.6	+4.9	+0.1	+1.2	+7.7	-14.3	+1.3	-12.5	+10.6
	Relative (%)	-7.9	+7.6	+49.7	+14.8	+0.3	+3.7	+23.2	-42.9	+3.9	-37.5	+31.9
Steps (reduced)		133 (19)	137 (23)	141 (27)	144 (30)	147 (33)	150 (36)	153 (39)	155 (41)	158 (44)	160 (46)	163 (49)