79ed7/3

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79ed7/3

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Prime factorization	79 (prime)
Step size	18.568¢
Octave	65\79ed7/3 (1206.92¢)
Twelfth	102\79ed7/3 (1893.93¢)
Consistency limit	2
Distinct consistency limit	2

79 equal divisions of 7/3 (abbreviated 79ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 79 equal parts of about 18.6 ¢ each. Each step represents a frequency ratio of (7/3)^1/79, or the 79th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	18.568
2	37.136
3	55.704	30/29, 31/30
4	74.272
5	92.84
6	111.408	33/31
7	129.976	14/13
8	148.544	12/11, 37/34
9	167.112	11/10
10	185.68	39/35
11	204.248
12	222.816	33/29
13	241.384
14	259.952	29/25, 36/31
15	278.52	34/29
16	297.088
17	315.656	6/5
18	334.224	17/14
19	352.792
20	371.36	31/25, 36/29
21	389.928
22	408.496
23	427.064	23/18
24	445.632
25	464.2	17/13
26	482.768	33/25, 37/28
27	501.336
28	519.904	31/23
29	538.472
30	557.04
31	575.608
32	594.176
33	612.744	37/26
34	631.312	36/25
35	649.88
36	668.448	25/17, 28/19
37	687.015
38	705.583
39	724.151	35/23
40	742.719	23/15
41	761.287
42	779.855
43	798.423	19/12
44	816.991
45	835.559
46	854.127
47	872.695
48	891.263
49	909.831
50	928.399
51	946.967	19/11
52	965.535
53	984.103	30/17
54	1002.671	25/14
55	1021.239
56	1039.807	31/17
57	1058.375
58	1076.943
59	1095.511
60	1114.079	19/10
61	1132.647	25/13
62	1151.215	33/17, 35/18, 37/19
63	1169.783
64	1188.351
65	1206.919
66	1225.487
67	1244.055
68	1262.623	29/14
69	1281.191
70	1299.759	36/17
71	1318.327	15/7
72	1336.895	13/6
73	1355.463
74	1374.031	31/14
75	1392.599
76	1411.167
77	1429.735
78	1448.303	30/13
79	1466.871	7/3

Harmonics

Approximation of harmonics in 79ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.92	-8.02	-4.73	-1.12	-1.10	-8.02	+2.19	+2.53	+5.80	+7.91	+5.82
	Relative (%)	+37.3	-43.2	-25.5	-6.0	-5.9	-43.2	+11.8	+13.6	+31.3	+42.6	+31.3
Steps (reduced)		65 (65)	102 (23)	129 (50)	150 (71)	167 (9)	181 (23)	194 (36)	205 (47)	215 (57)	224 (66)	232 (74)

Approximation of harmonics in 79ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.78	-1.10	-9.14	+9.11	-3.01	-9.12	+8.68	-5.85	+2.53	-3.74	-6.42
	Relative (%)	-15.0	-5.9	-49.2	+49.1	-16.2	-49.1	+46.8	-31.5	+13.6	-20.1	-34.6
Steps (reduced)		239 (2)	246 (9)	252 (15)	259 (22)	264 (27)	269 (32)	275 (38)	279 (42)	284 (47)	288 (51)	292 (55)