89ed4

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← 87ed4 89ed4 91ed4 →
Prime factorization 89 (prime)
Step size 26.9663¢ 
Octave 45\89ed4 (1213.48¢)
Twelfth 71\89ed4 (1914.61¢)
Consistency limit 1
Distinct consistency limit 1

89 equal divisions of the 4th harmonic (abbreviated 89ed4) is a nonoctave tuning system that divides the interval of 4/1 into 89 equal parts of about 27 ¢ each. Each step represents a frequency ratio of 41/89, or the 89th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 27
2 53.9 34/33
3 80.9 22/21
4 107.9
5 134.8
6 161.8
7 188.8
8 215.7 17/15
9 242.7 38/33
10 269.7
11 296.6
12 323.6 35/29
13 350.6
14 377.5
15 404.5
16 431.5
17 458.4
18 485.4 41/31
19 512.4
20 539.3 15/11
21 566.3
22 593.3
23 620.2 10/7
24 647.2
25 674.2
26 701.1 3/2
27 728.1 35/23
28 755.1 17/11
29 782 11/7
30 809
31 836 34/21
32 862.9
33 889.9
34 916.9 17/10
35 943.8 19/11
36 970.8
37 997.8
38 1024.7 38/21
39 1051.7
40 1078.7
41 1105.6
42 1132.6
43 1159.6
44 1186.5
45 1213.5
46 1240.4
47 1267.4
48 1294.4
49 1321.3 15/7
50 1348.3 37/17
51 1375.3
52 1402.2 9/4
53 1429.2
54 1456.2
55 1483.1 33/14
56 1510.1
57 1537.1 17/7
58 1564 37/15
59 1591
60 1618
61 1644.9
62 1671.9
63 1698.9
64 1725.8
65 1752.8
66 1779.8
67 1806.7
68 1833.7
69 1860.7
70 1887.6
71 1914.6
72 1941.6
73 1968.5
74 1995.5
75 2022.5
76 2049.4
77 2076.4
78 2103.4 27/8
79 2130.3
80 2157.3
81 2184.3
82 2211.2
83 2238.2
84 2265.2 37/10
85 2292.1
86 2319.1
87 2346.1
88 2373
89 2400

Harmonics

Approximation of harmonics in 89ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +13.5 +12.7 +0.0 -8.8 -0.8 +2.0 +13.5 -1.7 +4.7 +1.5 +12.7
Relative (%) +50.0 +46.9 +0.0 -32.6 -3.1 +7.3 +50.0 -6.2 +17.4 +5.5 +46.9
Steps
(reduced)
45
(45)
71
(71)
89
(0)
103
(14)
115
(26)
125
(36)
134
(45)
141
(52)
148
(59)
154
(65)
160
(71)
Approximation of harmonics in 89ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +8.9 -11.5 +3.9 +0.0 +2.9 +11.8 -0.9 -8.8 -12.4 -12.0 -8.0
Relative (%) +33.0 -42.7 +14.3 +0.0 +10.8 +43.8 -3.3 -32.6 -45.8 -44.5 -29.9
Steps
(reduced)
165
(76)
169
(80)
174
(85)
178
(0)
182
(4)
186
(8)
189
(11)
192
(14)
195
(17)
198
(20)
201
(23)