51ed7/3

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51ed7/3

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Prime factorization	3 × 17
Step size	28.7622¢
Octave	42\51ed7/3 (1208.01¢) (→14\17ed7/3)
Twelfth	66\51ed7/3 (1898.3¢) (→22\17ed7/3)
Consistency limit	3
Distinct consistency limit	3

51 equal divisions of 7/3 (abbreviated 51ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 51 equal parts of about 28.8⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/51, or the 51st root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	28.8
2	57.5	29/28, 30/29, 31/30
3	86.3
4	115	15/14, 31/29
5	143.8	25/23
6	172.6	21/19, 31/28
7	201.3	28/25
8	230.1
9	258.9	22/19, 29/25
10	287.6	13/11
11	316.4	6/5
12	345.1	11/9, 28/23
13	373.9	26/21, 31/25
14	402.7	29/23
15	431.4	9/7
16	460.2	30/23
17	489
18	517.7	31/23
19	546.5	26/19
20	575.2
21	604	17/12, 27/19
22	632.8	13/9
23	661.5	19/13, 22/15
24	690.3
25	719.1
26	747.8
27	776.6
28	805.3
29	834.1	21/13
30	862.9	23/14, 28/17
31	891.6
32	920.4	17/10, 29/17
33	949.2	19/11, 26/15
34	977.9	30/17
35	1006.7	25/14
36	1035.4	31/17
37	1064.2
38	1093
39	1121.7	21/11, 23/12
40	1150.5
41	1179.2
42	1208
43	1236.8
44	1265.5	25/12, 27/13, 29/14
45	1294.3	19/9
46	1323.1	15/7
47	1351.8
48	1380.6	31/14
49	1409.3
50	1438.1	23/10
51	1466.9	7/3

Harmonics

Approximation of harmonics in 51ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.0	-3.7	-12.7	+3.6	+4.4	-3.7	-4.7	-7.3	+11.6	-9.6	+12.4
	Relative (%)	+27.9	-12.7	-44.3	+12.6	+15.2	-12.7	-16.4	-25.4	+40.4	-33.3	+43.0
Steps (reduced)		42 (42)	66 (15)	83 (32)	97 (46)	108 (6)	117 (15)	125 (23)	132 (30)	139 (37)	144 (42)	150 (48)

Approximation of harmonics in 51ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.2	+4.4	-0.0	+3.3	+13.4	+0.7	-6.6	-9.1	-7.3	-1.6	+7.8
	Relative (%)	-38.8	+15.2	-0.1	+11.4	+46.5	+2.5	-23.0	-31.7	-25.4	-5.4	+27.0
Steps (reduced)		154 (1)	159 (6)	163 (10)	167 (14)	171 (18)	174 (21)	177 (24)	180 (27)	183 (30)	186 (33)	189 (36)