80edt

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80edt

81edt →

Prime factorization	24 × 5
Step size	23.7744¢
Octave	50\80edt (1188.72¢) (→5\8edt)
Consistency limit	2
Distinct consistency limit	2

80 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 80edt or 80ed3), is a nonoctave tuning system that divides the interval of 3/1 into 80 equal parts of about 23.8 ¢ each. Each step represents a frequency ratio of 3^1/80, or the 80th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	23.8
2	47.5
3	71.3
4	95.1	19/18, 37/35
5	118.9	15/14
6	142.6	25/23
7	166.4
8	190.2	19/17, 29/26, 39/35
9	214	17/15, 26/23
10	237.7	31/27
11	261.5
12	285.3
13	309.1	37/31
14	332.8	23/19
15	356.6	27/22
16	380.4
17	404.2	29/23
18	427.9
19	451.7	35/27
20	475.5	25/19, 29/22
21	499.3
22	523	23/17
23	546.8	37/27
24	570.6	25/18
25	594.4	31/22
26	618.1
27	641.9
28	665.7	22/15, 25/17
29	689.5
30	713.2
31	737	23/15, 26/17
32	760.8
33	784.6	11/7
34	808.3
35	832.1	21/13
36	855.9
37	879.7
38	903.4
39	927.2	29/17
40	951	26/15
41	974.8
42	998.5
43	1022.3
44	1046.1
45	1069.8	13/7
46	1093.6
47	1117.4	21/11
48	1141.2	29/15
49	1164.9
50	1188.7
51	1212.5
52	1236.3
53	1260	29/14
54	1283.8
55	1307.6
56	1331.4
57	1355.1
58	1378.9	31/14
59	1402.7
60	1426.5
61	1450.2
62	1474
63	1497.8
64	1521.6
65	1545.3	22/9
66	1569.1
67	1592.9
68	1616.7
69	1640.4
70	1664.2
71	1688
72	1711.8	35/13
73	1735.5
74	1759.3
75	1783.1	14/5
76	1806.9
77	1830.6
78	1854.4
79	1878.2
80	1902	3/1

Harmonics

Approximation of harmonics in 80edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.3	+0.0	+1.2	-4.7	-11.3	+7.1	-10.1	+0.0	+7.8	+9.2	+1.2
	Relative (%)	-47.4	+0.0	+5.1	-19.8	-47.4	+30.1	-42.3	+0.0	+32.8	+38.7	+5.1
Steps (reduced)		50 (50)	80 (0)	101 (21)	117 (37)	130 (50)	142 (62)	151 (71)	160 (0)	168 (8)	175 (15)	181 (21)

Approximation of harmonics in 80edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.3	-4.1	-4.7	+2.4	-7.4	-11.3	-9.8	-3.5	+7.1	-2.1	-7.7
	Relative (%)	+22.3	-17.4	-19.8	+10.2	-31.2	-47.4	-41.2	-14.7	+30.1	-8.7	-32.4
Steps (reduced)		187 (27)	192 (32)	197 (37)	202 (42)	206 (46)	210 (50)	214 (54)	218 (58)	222 (62)	225 (65)	228 (68)