81edt

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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	Hekts	Approximate ratios
0	0	0	1/1
1	23.5	16
2	47	32.1	36/35, 37/36, 38/37, 39/38, 40/39
3	70.4	48.1
4	93.9	64.2	19/18, 37/35, 39/37
5	117.4	80.2	31/29
6	140.9	96.3	13/12, 38/35
7	164.4	112.3	11/10
8	187.8	128.4	29/26, 39/35
9	211.3	144.4	26/23, 35/31
10	234.8	160.5	39/34
11	258.3	176.5	36/31
12	281.8	192.6	20/17
13	305.3	208.6	31/26, 37/31
14	328.7	224.7	23/19, 29/24, 35/29
15	352.2	240.7	27/22, 38/31
16	375.7	256.8	36/29
17	399.2	272.8	29/23, 34/27, 39/31
18	422.7	288.9	23/18, 37/29
19	446.1	304.9	22/17, 31/24, 35/27
20	469.6	321	21/16, 38/29
21	493.1	337
22	516.6	353.1	27/20, 31/23, 35/26
23	540.1	369.1	15/11, 26/19
24	563.5	385.2	18/13
25	587	401.2
26	610.5	417.3	27/19, 37/26
27	634	433.3	13/9
28	657.5	449.4	19/13
29	680.9	465.4	40/27
30	704.4	481.5	3/2
31	727.9	497.5	32/21, 35/23
32	751.4	513.6	17/11, 37/24
33	774.9	529.6	36/23
34	798.4	545.7	19/12, 27/17
35	821.8	561.7	37/23
36	845.3	577.8	31/19
37	868.8	593.8	33/20, 38/23
38	892.3	609.9
39	915.8	625.9	17/10, 39/23
40	939.2	642	31/18
41	962.7	658
42	986.2	674.1	23/13, 30/17
43	1009.7	690.1	34/19
44	1033.2	706.2	20/11
45	1056.6	722.2	35/19
46	1080.1	738.3
47	1103.6	754.3	17/9, 36/19
48	1127.1	770.4	23/12
49	1150.6	786.4	33/17, 35/18
50	1174	802.5
51	1197.5	818.5	2/1
52	1221	834.6
53	1244.5	850.6	37/18, 39/19
54	1268	866.7	27/13
55	1291.5	882.7	19/9, 40/19
56	1314.9	898.8
57	1338.4	914.8	13/6
58	1361.9	930.9	11/5
59	1385.4	946.9	20/9
60	1408.9	963
61	1432.3	979	16/7
62	1455.8	995.1
63	1479.3	1011.1	40/17
64	1502.8	1027.2	31/13
65	1526.3	1043.2	29/12
66	1549.7	1059.3	22/9
67	1573.2	1075.3
68	1596.7	1091.4
69	1620.2	1107.4
70	1643.7	1123.5	31/12
71	1667.1	1139.5	34/13
72	1690.6	1155.6
73	1714.1	1171.6	35/13
74	1737.6	1187.7	30/11
75	1761.1	1203.7	36/13
76	1784.6	1219.8
77	1808	1235.8	37/13
78	1831.5	1251.9
79	1855	1267.9	35/12, 38/13
80	1878.5	1284
81	1902	1300	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)