57edf

← 56edf

57edf

58edf →

Prime factorization	3 × 19
Step size	12.315 ¢
Octave	97\57edf (1194.56 ¢)
Twelfth	154\57edf (1896.51 ¢)
Consistency limit	3
Distinct consistency limit	3

57EDF is the equal division of the just perfect fifth into 57 parts of 12.3150 cents each, corresponding to 97.4421 edo.

It is related to the regular temperament which tempers out [-32 33 0 -6 -1⟩ and [76 -8 0 -9 -11⟩ in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs.

Related regular temperaments

2.3.7 subgroup 877&5067

Commas: [-428 371 0 -57⟩

POTE generator: ~1605632/1594323 = 12.3149

Mapping: [⟨1 1 -1], ⟨0 57 371]]

EDOs: 877, 4190, 5067, 5944, 6821, 7698, 8575

2.3.7.11 subgroup 877&5067

Commas: [-32 33 0 -6 -1⟩, [76 -8 0 -9 -11⟩

POTE generator: ~1605632/1594323 = 12.3150

Mapping: [⟨1 1 -1 7], ⟨0 57 371 -345]]

EDOs: 877, 3313, 4190, 5067, 5944, 6821, 7698, 11011

2.3.7.11.13 subgroup 877&5067

Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663

POTE generator: ~1605632/1594323 = 12.3150

Mapping: [⟨1 1 -1 7 -10], ⟨0 57 371 -345 1335]]

EDOs: 877, 3313, 4190, 5067, 5944, 9257

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	12.3
2	24.6
3	36.9
4	49.3	34/33
5	61.6	29/28
6	73.9
7	86.2
8	98.5
9	110.8
10	123.2
11	135.5
12	147.8
13	160.1	23/21
14	172.4	21/19
15	184.7	10/9, 29/26
16	197	19/17, 28/25
17	209.4	26/23
18	221.7	25/22, 33/29
19	234
20	246.3
21	258.6	29/25
22	270.9	34/29
23	283.2	33/28
24	295.6
25	307.9	31/26
26	320.2
27	332.5	17/14, 23/19
28	344.8
29	357.1
30	369.5	21/17, 26/21
31	381.8
32	394.1
33	406.4
34	418.7	14/11
35	431
36	443.3	22/17
37	455.7
38	468
39	480.3	29/22, 33/25
40	492.6
41	504.9
42	517.2	27/20, 31/23
43	529.5	19/14, 34/25
44	541.9	26/19
45	554.2	29/21
46	566.5
47	578.8
48	591.1
49	603.4
50	615.8
51	628.1
52	640.4
53	652.7	19/13
54	665	22/15, 25/17
55	677.3	31/21
56	689.6
57	702	3/2

Harmonics

Approximation of harmonics in 57edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.44	-5.44	+1.43	-3.12	+1.43	+5.48	-4.02	+1.43	+3.75	-1.16	-4.02
	Relative (%)	-44.2	-44.2	+11.6	-25.4	+11.6	+44.5	-32.6	+11.6	+30.4	-9.4	-32.6
Steps (reduced)		97 (40)	154 (40)	195 (24)	226 (55)	252 (24)	274 (46)	292 (7)	309 (24)	324 (39)	337 (52)	349 (7)

Approximation of harmonics in 57edf

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.19	+0.04	+3.75	+2.85	-3.59	-4.02	+0.90	-1.70	+0.04	+5.71	+2.64
	Relative (%)	+42.1	+0.3	+30.4	+23.1	-29.1	-32.6	+7.3	-13.8	+0.3	+46.3	+21.4
Steps (reduced)		361 (19)	371 (29)	381 (39)	390 (48)	398 (56)	406 (7)	414 (15)	421 (22)	428 (29)	435 (36)	441 (42)