79ed4

From Xenharmonic Wiki
Jump to navigation Jump to search
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 77ed4 79ed4 81ed4 →
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 41/79, 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)