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	18.1
2	36.2
3	54.3	31/30, 34/33
4	72.4
5	90.5	19/18, 20/19, 39/37
6	108.7	33/31
7	126.8	14/13, 29/27
8	144.9	25/23, 37/34
9	163	11/10, 34/31
10	181.1	10/9
11	199.2	37/33
12	217.3	17/15
13	235.4	39/34
14	253.5	22/19
15	271.6
16	289.8	13/11
17	307.9	37/31
18	326	35/29
19	344.1
20	362.2	37/30
21	380.3
22	398.4	29/23, 34/27, 39/31
23	416.5	14/11
24	434.6	9/7
25	452.7	13/10
26	470.8
27	489
28	507.1
29	525.2	23/17
30	543.3	26/19, 37/27
31	561.4	18/13, 29/21
32	579.5	7/5
33	597.6
34	615.7	10/7
35	633.8	13/9
36	651.9
37	670.1	25/17, 28/19
38	688.2
39	706.3
40	724.4	35/23
41	742.5	23/15
42	760.6	31/20
43	778.7
44	796.8	19/12
45	814.9
46	833	21/13, 34/21
47	851.1	18/11
48	869.3	33/20
49	887.4	5/3
50	905.5
51	923.6	29/17
52	941.7	31/18
53	959.8
54	977.9	37/21
55	996
56	1014.1
57	1032.2	20/11
58	1050.4	11/6
59	1068.5
60	1086.6
61	1104.7	36/19
62	1122.8
63	1140.9	29/15
64	1159	39/20
65	1177.1
66	1195.2
67	1213.3
68	1231.4
69	1249.6	35/17, 37/18
70	1267.7	27/13
71	1285.8	21/10, 40/19
72	1303.9
73	1322	15/7
74	1340.1	13/6
75	1358.2
76	1376.3	31/14
77	1394.4
78	1412.5
79	1430.7
80	1448.8	30/13
81	1466.9	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)