71ed7/3

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71ed7/3

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Prime factorization	71 (prime)
Step size	20.6602¢
Octave	58\71ed7/3 (1198.29¢) (semiconvergent)
Twelfth	92\71ed7/3 (1900.73¢)
Consistency limit	16
Distinct consistency limit	6

71 equal divisions of 7/3 (abbreviated 71ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 71 equal parts of about 20.7 ¢ each. Each step represents a frequency ratio of (7/3)^1/71, or the 71st root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	20.66
2	41.32
3	61.98	27/26, 28/27, 29/28, 30/29
4	82.641	21/20, 22/21
5	103.301	17/16, 35/33
6	123.961	29/27
7	144.621	25/23
8	165.281	11/10
9	185.941	10/9, 29/26
10	206.602	9/8, 35/31
11	227.262	33/29
12	247.922	15/13
13	268.582	7/6
14	289.242	13/11
15	309.902	37/31
16	330.562	23/19, 29/24
17	351.223	27/22
18	371.883	26/21, 31/25, 36/29
19	392.543
20	413.203	33/26
21	433.863	9/7
22	454.523	13/10
23	475.184	25/19, 29/22
24	495.844	4/3
25	516.504	27/20, 31/23, 35/26
26	537.164	15/11
27	557.824	29/21
28	578.484
29	599.144	24/17
30	619.805	10/7
31	640.465	29/20
32	661.125	22/15
33	681.785	37/25
34	702.445	3/2
35	723.105
36	743.766	20/13
37	764.426	14/9
38	785.086	11/7
39	805.746	35/22
40	826.406	29/18, 37/23
41	847.066	31/19
42	867.726	33/20
43	888.387
44	909.047	22/13, 27/16
45	929.707	12/7
46	950.367	26/15
47	971.027	7/4
48	991.687
49	1012.348
50	1033.008	20/11, 29/16
51	1053.668
52	1074.328	13/7
53	1094.988	32/17
54	1115.648
55	1136.308	27/14
56	1156.969	37/19
57	1177.629
58	1198.289	2/1
59	1218.949
60	1239.609
61	1260.269	29/14, 31/15
62	1280.93	21/10
63	1301.59	17/8, 36/17
64	1322.25	15/7
65	1342.91
66	1363.57	11/5
67	1384.23	20/9
68	1404.89	9/4
69	1425.551
70	1446.211	30/13
71	1466.871	7/3

Harmonics

Approximation of harmonics in 71ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.71	-1.22	-3.42	+2.81	-2.93	-1.22	-5.13	-2.44	+1.10	+1.37	-4.64
	Relative (%)	-8.3	-5.9	-16.6	+13.6	-14.2	-5.9	-24.8	-11.8	+5.3	+6.6	-22.5
Steps (reduced)		58 (58)	92 (21)	116 (45)	135 (64)	150 (8)	163 (21)	174 (32)	184 (42)	193 (51)	201 (59)	208 (66)

Approximation of harmonics in 71ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.41	-2.93	+1.59	-6.84	-8.50	-4.15	+5.54	-0.62	-2.44	-0.34	+5.35
	Relative (%)	+6.8	-14.2	+7.7	-33.1	-41.1	-20.1	+26.8	-3.0	-11.8	-1.6	+25.9
Steps (reduced)		215 (2)	221 (8)	227 (14)	232 (19)	237 (24)	242 (29)	247 (34)	251 (38)	255 (42)	259 (46)	263 (50)