81edt

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← 80edt

81edt

82edt →

Prime factorization	34
Step size	23.4809¢
Octave	51\81edt (1197.53¢) (→17\27edt)
Consistency limit	4
Distinct consistency limit	4

81 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 81edt or 81ed3), is a nonoctave tuning system that divides the interval of 3/1 into 81 equal parts of about 23.5 ¢ each. Each step represents a frequency ratio of 3^1/81, or the 81st root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	23.5
2	47	36/35, 37/36, 38/37, 39/38, 40/39
3	70.4
4	93.9	19/18, 37/35, 39/37
5	117.4	31/29
6	140.9	13/12, 38/35
7	164.4	11/10
8	187.8	29/26, 39/35
9	211.3	26/23, 35/31
10	234.8	39/34
11	258.3	36/31
12	281.8	20/17
13	305.3	31/26, 37/31
14	328.7	23/19, 29/24, 35/29
15	352.2	27/22, 38/31
16	375.7	36/29
17	399.2	29/23, 34/27, 39/31
18	422.7	23/18, 37/29
19	446.1	22/17, 31/24, 35/27
20	469.6	21/16, 38/29
21	493.1
22	516.6	27/20, 31/23, 35/26
23	540.1	15/11, 26/19
24	563.5	18/13
25	587
26	610.5	27/19, 37/26
27	634	13/9
28	657.5	19/13
29	680.9	40/27
30	704.4	3/2
31	727.9	32/21, 35/23
32	751.4	17/11, 37/24
33	774.9	36/23
34	798.4	19/12, 27/17
35	821.8	37/23
36	845.3	31/19
37	868.8	33/20, 38/23
38	892.3
39	915.8	17/10, 39/23
40	939.2	31/18
41	962.7
42	986.2	23/13, 30/17
43	1009.7	34/19
44	1033.2	20/11
45	1056.6	35/19
46	1080.1
47	1103.6	17/9, 36/19
48	1127.1	23/12
49	1150.6	33/17, 35/18
50	1174
51	1197.5	2/1
52	1221
53	1244.5	37/18, 39/19
54	1268	27/13
55	1291.5	19/9, 40/19
56	1314.9
57	1338.4	13/6
58	1361.9	11/5
59	1385.4	20/9
60	1408.9
61	1432.3	16/7
62	1455.8
63	1479.3	40/17
64	1502.8	31/13
65	1526.3	29/12
66	1549.7	22/9
67	1573.2
68	1596.7
69	1620.2
70	1643.7	31/12
71	1667.1	34/13
72	1690.6
73	1714.1	35/13
74	1737.6	30/11
75	1761.1	36/13
76	1784.6
77	1808	37/13
78	1831.5
79	1855	35/12, 38/13
80	1878.5
81	1902	3/1

Harmonics

Approximation of harmonics in 81edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.5	+0.0	-4.9	+7.9	-2.5	-11.1	-7.4	+0.0	+5.4	+4.8	-4.9
	Relative (%)	-10.5	+0.0	-21.1	+33.7	-10.5	-47.1	-31.6	+0.0	+23.2	+20.5	-21.1
Steps (reduced)		51 (51)	81 (0)	102 (21)	119 (38)	132 (51)	143 (62)	153 (72)	162 (0)	170 (8)	177 (15)	183 (21)

Approximation of harmonics in 81edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	+10.0	+7.9	-9.9	+2.6	-2.5	-2.2	+3.0	-11.1	+2.3	-4.2
	Relative (%)	-11.2	+42.4	+33.7	-42.1	+10.9	-10.5	-9.2	+12.7	-47.1	+9.9	-17.8
Steps (reduced)		189 (27)	195 (33)	200 (38)	204 (42)	209 (47)	213 (51)	217 (55)	221 (59)	224 (62)	228 (66)	231 (69)