81ed7/3

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81ed7/3

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Prime factorization	34
Step size	18.1095¢
Octave	66\81ed7/3 (1195.23¢) (→22\27ed7/3)
Twelfth	105\81ed7/3 (1901.5¢) (→35\27ed7/3)
Consistency limit	3
Distinct consistency limit	3

81 equal divisions of 7/3 (abbreviated 81ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 81 equal parts of about 18.1 ¢ each. Each step represents a frequency ratio of (7/3)^1/81, or the 81st root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.11
2	36.219
3	54.329	31/30, 34/33
4	72.438
5	90.548	19/18, 20/19, 39/37
6	108.657	33/31
7	126.767	14/13, 29/27
8	144.876	25/23, 37/34
9	162.986	11/10, 34/31
10	181.095	10/9
11	199.205	37/33
12	217.314	17/15
13	235.424	39/34
14	253.533	22/19
15	271.643
16	289.752	13/11
17	307.862	37/31
18	325.971	35/29
19	344.081
20	362.19	37/30
21	380.3
22	398.409	29/23, 34/27, 39/31
23	416.519	14/11
24	434.628	9/7
25	452.738	13/10
26	470.847
27	488.957
28	507.066
29	525.176	23/17
30	543.286	26/19, 37/27
31	561.395	18/13, 29/21
32	579.505	7/5
33	597.614
34	615.724	10/7
35	633.833	13/9
36	651.943
37	670.052	25/17, 28/19
38	688.162
39	706.271
40	724.381	35/23
41	742.49	23/15
42	760.6	31/20
43	778.709
44	796.819	19/12
45	814.928
46	833.038	21/13, 34/21
47	851.147	18/11
48	869.257	33/20
49	887.366	5/3
50	905.476
51	923.585	29/17
52	941.695	31/18
53	959.804
54	977.914	37/21
55	996.023
56	1014.133
57	1032.242	20/11
58	1050.352	11/6
59	1068.462
60	1086.571
61	1104.681	36/19
62	1122.79
63	1140.9	29/15
64	1159.009	39/20
65	1177.119
66	1195.228
67	1213.338
68	1231.447
69	1249.557	35/17, 37/18
70	1267.666	27/13
71	1285.776	21/10, 40/19
72	1303.885
73	1321.995	15/7
74	1340.104	13/6
75	1358.214
76	1376.323	31/14
77	1394.433
78	1412.542
79	1430.652
80	1448.761	30/13
81	1466.871	7/3

Harmonics

Approximation of harmonics in 81ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.77	-0.46	+8.57	+2.55	-5.23	-0.46	+3.79	-0.91	-2.22	-4.24	+8.11
	Relative (%)	-26.3	-2.5	+47.3	+14.1	-28.9	-2.5	+21.0	-5.0	-12.3	-23.4	+44.8
Steps (reduced)		66 (66)	105 (24)	133 (52)	154 (73)	171 (9)	186 (24)	199 (37)	210 (48)	220 (58)	229 (67)	238 (76)

Approximation of harmonics in 81ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-3.70	-5.23	+2.10	-0.98	+2.72	-5.68	-8.74	-6.99	-0.91	-9.01	+4.58
	Relative (%)	-20.4	-28.9	+11.6	-5.4	+15.0	-31.4	-48.3	-38.6	-5.0	-49.8	+25.3
Steps (reduced)		245 (2)	252 (9)	259 (16)	265 (22)	271 (28)	276 (33)	281 (38)	286 (43)	291 (48)	295 (52)	300 (57)