81edt

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 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	23.481
2	46.962	36/35, 37/36, 38/37, 39/38, 40/39
3	70.443
4	93.924	19/18, 37/35, 39/37
5	117.405	31/29
6	140.886	13/12, 38/35
7	164.366	11/10
8	187.847	29/26, 39/35
9	211.328	26/23, 35/31
10	234.809	39/34
11	258.29	36/31
12	281.771	20/17
13	305.252	31/26, 37/31
14	328.733	23/19, 29/24, 35/29
15	352.214	27/22, 38/31
16	375.695	36/29
17	399.176	29/23, 34/27, 39/31
18	422.657	23/18, 37/29
19	446.138	22/17, 31/24, 35/27
20	469.619	21/16, 38/29
21	493.099
22	516.58	27/20, 31/23, 35/26
23	540.061	15/11, 26/19
24	563.542	18/13
25	587.023
26	610.504	27/19, 37/26
27	633.985	13/9
28	657.466	19/13
29	680.947	40/27
30	704.428	3/2
31	727.909	32/21, 35/23
32	751.39	17/11, 37/24
33	774.871	36/23
34	798.351	19/12, 27/17
35	821.832	37/23
36	845.313	31/19
37	868.794	33/20, 38/23
38	892.275
39	915.756	17/10, 39/23
40	939.237	31/18
41	962.718
42	986.199	23/13, 30/17
43	1009.68	34/19
44	1033.161	20/11
45	1056.642	35/19
46	1080.123
47	1103.604	17/9, 36/19
48	1127.084	23/12
49	1150.565	33/17, 35/18
50	1174.046
51	1197.527	2/1
52	1221.008
53	1244.489	37/18, 39/19
54	1267.97	27/13
55	1291.451	19/9, 40/19
56	1314.932
57	1338.413	13/6
58	1361.894	11/5
59	1385.375	20/9
60	1408.856
61	1432.336	16/7
62	1455.817
63	1479.298	40/17
64	1502.779	31/13
65	1526.26	29/12
66	1549.741	22/9
67	1573.222
68	1596.703
69	1620.184
70	1643.665	31/12
71	1667.146	34/13
72	1690.627
73	1714.108	35/13
74	1737.589	30/11
75	1761.069	36/13
76	1784.55
77	1808.031	37/13
78	1831.512
79	1854.993	35/12, 38/13
80	1878.474
81	1901.955	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)