86ed7/3

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86ed7/3

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Prime factorization	2 × 43
Step size	17.0566¢
Octave	70\86ed7/3 (1193.96¢) (→35\43ed7/3)
Twelfth	112\86ed7/3 (1910.34¢) (→56\43ed7/3)
Consistency limit	2
Distinct consistency limit	2

86 equal divisions of 7/3 (abbreviated 86ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 86 equal parts of about 17.1 ¢ each. Each step represents a frequency ratio of (7/3)^1/86, or the 86th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.057
2	34.113
3	51.17	34/33, 35/34, 36/35
4	68.227	25/24, 26/25
5	85.283	41/39
6	102.34	35/33
7	119.396	15/14
8	136.453	13/12
9	153.51	12/11
10	170.566
11	187.623	39/35
12	204.68
13	221.736	25/22, 33/29
14	238.793	39/34
15	255.85
16	272.906	34/29, 41/35
17	289.963	13/11
18	307.019	37/31
19	324.076	35/29, 41/34
20	341.133	28/23
21	358.189
22	375.246	36/29, 41/33
23	392.303
24	409.359	19/15
25	426.416
26	443.473
27	460.529	30/23
28	477.586
29	494.643
30	511.699	39/29
31	528.756	19/14
32	545.812
33	562.869
34	579.926
35	596.982	41/29
36	614.039
37	631.096
38	648.152
39	665.209
40	682.266
41	699.322
42	716.379
43	733.435	29/19
44	750.492
45	767.549
46	784.605
47	801.662
48	818.719
49	835.775
50	852.832
51	869.889	38/23
52	886.945
53	904.002
54	921.058
55	938.115
56	955.172	33/19
57	972.228
58	989.285	23/13
59	1006.342	34/19
60	1023.398
61	1040.455	31/17
62	1057.512	35/19
63	1074.568
64	1091.625
65	1108.681	36/19
66	1125.738	23/12
67	1142.795	29/15
68	1159.851
69	1176.908
70	1193.965
71	1211.021
72	1228.078
73	1245.135	37/18, 39/19
74	1262.191	29/14
75	1279.248	23/11
76	1296.305	36/17
77	1313.361
78	1330.418	28/13, 41/19
79	1347.474	37/17
80	1364.531	11/5
81	1381.588
82	1398.644
83	1415.701	34/15
84	1432.758
85	1449.814	30/13
86	1466.871	7/3

Harmonics

Approximation of harmonics in 86ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.04	+8.39	+4.99	-6.08	+2.35	+8.39	-1.05	-0.28	+4.94	-6.55	-3.68
	Relative (%)	-35.4	+49.2	+29.2	-35.7	+13.8	+49.2	-6.2	-1.6	+29.0	-38.4	-21.6
Steps (reduced)		70 (70)	112 (26)	141 (55)	163 (77)	182 (10)	198 (26)	211 (39)	223 (51)	234 (62)	243 (71)	252 (80)

Approximation of harmonics in 86ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.80	+2.35	+2.31	-7.08	+7.36	-6.31	+2.42	-1.10	-0.28	+4.47	-4.26
	Relative (%)	-34.0	+13.8	+13.5	-41.5	+43.1	-37.0	+14.2	-6.4	-1.6	+26.2	-25.0
Steps (reduced)		260 (2)	268 (10)	275 (17)	281 (23)	288 (30)	293 (35)	299 (41)	304 (46)	309 (51)	314 (56)	318 (60)