79ed4

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79ed4

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Prime factorization	79 (prime)
Step size	30.3797 ¢
Octave	40\79ed4 (1215.19 ¢)
Twelfth	63\79ed4 (1913.92 ¢)
Consistency limit	1
Distinct consistency limit	1

79 equal divisions of the 4th harmonic (abbreviated 79ed4) is a nonoctave tuning system that divides the interval of 4/1 into 79 equal parts of about 30.4 ¢ each. Each step represents a frequency ratio of 4^1/79, or the 79th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	30.4
2	60.8	28/27
3	91.1	39/37
4	121.5	15/14
5	151.9
6	182.3	10/9
7	212.7	26/23, 35/31
8	243	38/33
9	273.4	34/29
10	303.8	25/21, 31/26, 37/31
11	334.2
12	364.6
13	394.9	39/31
14	425.3
15	455.7
16	486.1
17	516.5	27/20, 31/23, 35/26
18	546.8
19	577.2
20	607.6	37/26
21	638
22	668.4
23	698.7	3/2
24	729.1	29/19, 35/23
25	759.5
26	789.9
27	820.3	37/23
28	850.6	31/19
29	881
30	911.4	39/23
31	941.8
32	972.2
33	1002.5	25/14
34	1032.9
35	1063.3
36	1093.7
37	1124.1
38	1154.4	37/19
39	1184.8
40	1215.2
41	1245.6	39/19
42	1275.9	23/11
43	1306.3
44	1336.7
45	1367.1	11/5
46	1397.5
47	1427.8
48	1458.2
49	1488.6	26/11
50	1519
51	1549.4	22/9
52	1579.7
53	1610.1	38/15
54	1640.5
55	1670.9
56	1701.3
57	1731.6	19/7
58	1762
59	1792.4	31/11
60	1822.8
61	1853.2
62	1883.5
63	1913.9
64	1944.3
65	1974.7
66	2005.1	35/11
67	2035.4
68	2065.8	33/10
69	2096.2
70	2126.6
71	2157
72	2187.3
73	2217.7
74	2248.1	11/3
75	2278.5
76	2308.9	19/5
77	2339.2
78	2369.6
79	2400

Harmonics

Approximation of harmonics in 79ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+15.2	+12.0	+0.0	+8.6	-3.2	+3.3	+15.2	-6.4	-6.6	+10.7	+12.0
	Relative (%)	+50.0	+39.4	+0.0	+28.4	-10.6	+10.9	+50.0	-21.2	-21.6	+35.2	+39.4
Steps (reduced)		40 (40)	63 (63)	79 (0)	92 (13)	102 (23)	111 (32)	119 (40)	125 (46)	131 (52)	137 (58)	142 (63)

Approximation of harmonics in 79ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.1	-11.9	-9.8	+0.0	-13.8	+8.7	+6.3	+8.6	-15.1	-4.5	+9.7
	Relative (%)	-16.7	-39.1	-32.2	+0.0	-45.5	+28.8	+20.7	+28.4	-49.7	-14.8	+31.9
Steps (reduced)		146 (67)	150 (71)	154 (75)	158 (0)	161 (3)	165 (7)	168 (10)	171 (13)	173 (15)	176 (18)	179 (21)