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	30.38
2	60.759	28/27
3	91.139	39/37
4	121.519	15/14
5	151.899
6	182.278	10/9
7	212.658	26/23, 35/31
8	243.038	38/33
9	273.418	34/29
10	303.797	25/21, 31/26, 37/31
11	334.177
12	364.557
13	394.937	39/31
14	425.316
15	455.696
16	486.076
17	516.456	27/20, 31/23, 35/26
18	546.835
19	577.215
20	607.595	37/26
21	637.975
22	668.354
23	698.734	3/2
24	729.114	29/19, 35/23
25	759.494
26	789.873
27	820.253	37/23
28	850.633	31/19
29	881.013
30	911.392	39/23
31	941.772
32	972.152
33	1002.532	25/14
34	1032.911
35	1063.291
36	1093.671
37	1124.051
38	1154.43	37/19
39	1184.81
40	1215.19
41	1245.57	39/19
42	1275.949	23/11
43	1306.329
44	1336.709
45	1367.089	11/5
46	1397.468
47	1427.848
48	1458.228
49	1488.608	26/11
50	1518.987
51	1549.367	22/9
52	1579.747
53	1610.127	38/15
54	1640.506
55	1670.886
56	1701.266
57	1731.646	19/7
58	1762.025
59	1792.405	31/11
60	1822.785
61	1853.165
62	1883.544
63	1913.924
64	1944.304
65	1974.684
66	2005.063	35/11
67	2035.443
68	2065.823	33/10
69	2096.203
70	2126.582
71	2156.962
72	2187.342
73	2217.722
74	2248.101	11/3
75	2278.481
76	2308.861	19/5
77	2339.241
78	2369.62
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)