80ed7/3

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80ed7/3

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Prime factorization	24 × 5
Step size	18.3359¢
Octave	65\80ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth	104\80ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	2
Distinct consistency limit	2

80 equal divisions of 7/3 (abbreviated 80ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 80 equal parts of about 18.3 ¢ each. Each step represents a frequency ratio of (7/3)^1/80, or the 80th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.336
2	36.672
3	55.008	31/30
4	73.344
5	91.679	19/18, 39/37
6	110.015	33/31
7	128.351	14/13
8	146.687	25/23, 37/34
9	165.023	11/10
10	183.359
11	201.695
12	220.031
13	238.367	39/34
14	256.702	29/25, 36/31
15	275.038	34/29
16	293.374
17	311.71
18	330.046	23/19
19	348.382
20	366.718	21/17
21	385.054
22	403.389	29/23
23	421.725	23/18, 37/29
24	440.061
25	458.397	30/23
26	476.733	25/19
27	495.069
28	513.405	39/29
29	531.741	19/14, 34/25
30	550.077
31	568.412	25/18
32	586.748
33	605.084
34	623.42	33/23
35	641.756
36	660.092	19/13
37	678.428	34/23, 37/25
38	696.764
39	715.1
40	733.435	29/19
41	751.771
42	770.107	39/25
43	788.443	30/19
44	806.779
45	825.115	29/18, 37/23
46	843.451
47	861.787	23/14
48	880.123
49	898.458
50	916.794	39/23
51	935.13
52	953.466	33/19
53	971.802
54	990.138	23/13
55	1008.474	34/19
56	1026.81
57	1045.146
58	1063.481
59	1081.817
60	1100.153	17/9
61	1118.489
62	1136.825
63	1155.161	37/19
64	1173.497
65	1191.833
66	1210.168
67	1228.504
68	1246.84	37/18, 39/19
69	1265.176
70	1283.512
71	1301.848
72	1320.184	15/7
73	1338.52	13/6
74	1356.856
75	1375.191	31/14
76	1393.527
77	1411.863
78	1430.199
79	1448.535	30/13
80	1466.871	7/3

Harmonics

Approximation of harmonics in 80ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.17	+4.98	+2.00	+0.74	-3.19	+4.98	-6.17	-8.38	-7.43	-7.41	+6.98
	Relative (%)	-44.5	+27.1	+10.9	+4.0	-17.4	+27.1	-33.6	-45.7	-40.5	-40.4	+38.1
Steps (reduced)		65 (65)	104 (24)	131 (51)	152 (72)	169 (9)	184 (24)	196 (36)	207 (47)	217 (57)	226 (66)	235 (75)

Approximation of harmonics in 80ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-3.24	-3.19	+5.72	+4.00	+9.06	+1.79	-0.14	+2.74	-8.38	+2.76	-0.85
	Relative (%)	-17.7	-17.4	+31.2	+21.8	+49.4	+9.7	-0.7	+15.0	-45.7	+15.1	-4.6
Steps (reduced)		242 (2)	249 (9)	256 (16)	262 (22)	268 (28)	273 (33)	278 (38)	283 (43)	287 (47)	292 (52)	296 (56)