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	3
Distinct consistency limit	3

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	Hekts	Approximate ratios
0	0	0	1/1
1	23.8	16.3
2	47.5	32.5
3	71.3	48.8
4	95.1	65	19/18, 37/35
5	118.9	81.3	15/14
6	142.6	97.5	25/23
7	166.4	113.8
8	190.2	130	19/17, 29/26, 39/35
9	214	146.3	17/15, 26/23
10	237.7	162.5	31/27
11	261.5	178.8
12	285.3	195
13	309.1	211.3	37/31
14	332.8	227.5	23/19
15	356.6	243.8	27/22
16	380.4	260
17	404.2	276.3	29/23
18	427.9	292.5
19	451.7	308.8	35/27
20	475.5	325	25/19, 29/22
21	499.3	341.3
22	523	357.5	23/17
23	546.8	373.8	37/27
24	570.6	390	25/18
25	594.4	406.3	31/22
26	618.1	422.5
27	641.9	438.8
28	665.7	455	22/15, 25/17
29	689.5	471.3
30	713.2	487.5
31	737	503.7	23/15, 26/17
32	760.8	520
33	784.6	536.3	11/7
34	808.3	552.5
35	832.1	568.8	21/13
36	855.9	585
37	879.7	601.3
38	903.4	617.5
39	927.2	633.8	29/17
40	951	650	26/15
41	974.8	666.3
42	998.5	682.5
43	1022.3	698.8
44	1046.1	715
45	1069.8	731.3	13/7
46	1093.6	747.5
47	1117.4	763.8	21/11
48	1141.2	780	29/15
49	1164.9	796.3
50	1188.7	812.5
51	1212.5	828.8
52	1236.3	845
53	1260	861.3	29/14
54	1283.8	877.5
55	1307.6	893.8
56	1331.4	910
57	1355.1	926.3
58	1378.9	942.5	31/14
59	1402.7	958.7
60	1426.5	975
61	1450.2	991.3
62	1474	1007.5
63	1497.8	1023.8
64	1521.6	1040
65	1545.3	1056.3	22/9
66	1569.1	1072.5
67	1592.9	1088.8
68	1616.7	1105
69	1640.4	1121.3
70	1664.2	1137.5
71	1688	1153.8
72	1711.8	1170	35/13
73	1735.5	1186.3
74	1759.3	1202.5
75	1783.1	1218.8	14/5
76	1806.9	1235
77	1830.6	1251.3
78	1854.4	1267.5
79	1878.2	1283.8
80	1902	1300	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)