51edt

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51edt

52edt →

Prime factorization	3 × 17
Step size	37.2932¢
Octave	32\51edt (1193.38¢)
Consistency limit	4
Distinct consistency limit	4

51 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 51edt or 51ed3), is a nonoctave tuning system that divides the interval of 3/1 into 51 equal parts of about 37.3 ¢ each. Each step represents a frequency ratio of 3^1/51, or the 51st root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	37.293
2	74.586
3	111.88	31/29
4	149.173	12/11, 25/23
5	186.466	10/9, 29/26
6	223.759
7	261.053
8	298.346
9	335.639	23/19
10	372.932	26/21
11	410.226	19/15
12	447.519	31/24
13	484.812
14	522.105	23/17, 27/20
15	559.399	18/13, 29/21
16	596.692	31/22
17	633.985	13/9
18	671.278	25/17, 31/21
19	708.571
20	745.865	20/13
21	783.158	11/7
22	820.451	29/18
23	857.744	18/11
24	895.038
25	932.331	12/7
26	969.624	7/4
27	1006.917
28	1044.211	11/6
29	1081.504
30	1118.797	21/11
31	1156.09
32	1193.384
33	1230.677
34	1267.97	27/13
35	1305.263
36	1342.556	13/6
37	1379.85	20/9, 31/14
38	1417.143
39	1454.436
40	1491.729	26/11
41	1529.023	29/12
42	1566.316
43	1603.609
44	1640.902	31/12
45	1678.196	29/11
46	1715.489	27/10
47	1752.782	11/4
48	1790.075	31/11
49	1827.369
50	1864.662
51	1901.955	3/1

Harmonics

Approximation of harmonics in 51edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.6	+0.0	-13.2	+10.7	-6.6	-12.4	+17.4	+0.0	+4.1	-11.8	-13.2
	Relative (%)	-17.7	+0.0	-35.5	+28.6	-17.7	-33.3	+46.8	+0.0	+10.9	-31.6	-35.5
Steps (reduced)		32 (32)	51 (0)	64 (13)	75 (24)	83 (32)	90 (39)	97 (46)	102 (0)	107 (5)	111 (9)	115 (13)

Approximation of harmonics in 51edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	+18.2	+10.7	+10.8	+17.8	-6.6	+11.7	-2.6	-12.4	-18.4	+16.5
	Relative (%)	-7.1	+48.9	+28.6	+29.0	+47.6	-17.7	+31.3	-6.8	-33.3	-49.3	+44.3
Steps (reduced)		119 (17)	123 (21)	126 (24)	129 (27)	132 (30)	134 (32)	137 (35)	139 (37)	141 (39)	143 (41)	146 (44)