80edt

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

← 79edt

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	23.774
2	47.549
3	71.323
4	95.098	19/18, 37/35
5	118.872	15/14
6	142.647	25/23
7	166.421
8	190.196	19/17, 29/26, 39/35
9	213.97	17/15, 26/23
10	237.744	31/27
11	261.519
12	285.293
13	309.068	37/31
14	332.842	23/19
15	356.617	27/22
16	380.391
17	404.165	29/23
18	427.94
19	451.714	35/27
20	475.489	25/19, 29/22
21	499.263
22	523.038	23/17
23	546.812	37/27
24	570.587	25/18
25	594.361	31/22
26	618.135
27	641.91
28	665.684	22/15, 25/17
29	689.459
30	713.233
31	737.008	23/15, 26/17
32	760.782
33	784.556	11/7
34	808.331
35	832.105	21/13
36	855.88
37	879.654
38	903.429
39	927.203	29/17
40	950.978	26/15
41	974.752
42	998.526
43	1022.301
44	1046.075
45	1069.85	13/7
46	1093.624
47	1117.399	21/11
48	1141.173	29/15
49	1164.947
50	1188.722
51	1212.496
52	1236.271
53	1260.045	29/14
54	1283.82
55	1307.594
56	1331.369
57	1355.143
58	1378.917	31/14
59	1402.692
60	1426.466
61	1450.241
62	1474.015
63	1497.79
64	1521.564
65	1545.338	22/9
66	1569.113
67	1592.887
68	1616.662
69	1640.436
70	1664.211
71	1687.985
72	1711.76	35/13
73	1735.534
74	1759.308
75	1783.083	14/5
76	1806.857
77	1830.632
78	1854.406
79	1878.181
80	1901.955	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)