45ed5/2

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← 44ed5/245ed5/246ed5/2 →
Prime factorization 32 × 5
Step size 35.2514¢ 
Octave 34\45ed5/2 (1198.55¢)
Twelfth 54\45ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit 6
Distinct consistency limit 6

45 equal divisions of 5/2 (abbreviated 45ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 45 equal parts of about 35.3 ¢ each. Each step represents a frequency ratio of (5/2)1/45, or the 45th root of 5/2.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 35.251
2 70.503 24/23, 25/24, 26/25, 27/26
3 105.754 16/15, 17/16
4 141.006 13/12, 25/23
5 176.257 10/9, 21/19, 31/28
6 211.508 17/15, 26/23
7 246.76 15/13, 23/20
8 282.011 20/17, 27/23
9 317.263 6/5
10 352.514 11/9, 27/22
11 387.766 5/4
12 423.017 14/11, 23/18
13 458.268 13/10, 17/13, 30/23
14 493.52 4/3
15 528.771 19/14, 23/17
16 564.023 18/13, 25/18
17 599.274 17/12, 24/17, 31/22
18 634.525 13/9, 23/16
19 669.777 25/17, 28/19, 31/21
20 705.028 3/2
21 740.28 20/13, 23/15, 26/17
22 775.531 25/16
23 810.783 8/5
24 846.034 13/8, 31/19
25 881.285 5/3
26 916.537 17/10, 22/13
27 951.788 19/11, 26/15
28 987.04 23/13, 30/17
29 1022.291 9/5
30 1057.542 24/13
31 1092.794 15/8
32 1128.045 23/12, 25/13
33 1163.297
34 1198.548 2/1
35 1233.8
36 1269.051 25/12, 27/13
37 1304.302 17/8
38 1339.554 13/6
39 1374.805 31/14
40 1410.057 9/4
41 1445.308 23/10, 30/13
42 1480.559
43 1515.811 12/5
44 1551.062 22/9, 27/11
45 1586.314 5/2

Harmonics

Approximation of harmonics in 45ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -1.5 +1.6 -2.9 -1.5 +0.2 +15.3 -4.4 +3.2 -2.9 +8.3 -1.3
Relative (%) -4.1 +4.6 -8.2 -4.1 +0.5 +43.4 -12.4 +9.2 -8.2 +23.7 -3.6
Steps
(reduced)
34
(34)
54
(9)
68
(23)
79
(34)
88
(43)
96
(6)
102
(12)
108
(18)
113
(23)
118
(28)
122
(32)
Approximation of harmonics in 45ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +1.2 +13.9 +0.2 -5.8 -5.0 +1.8 +13.9 -4.4 +16.9 +6.9 +0.4
Relative (%) +3.3 +39.3 +0.5 -16.5 -14.2 +5.1 +39.6 -12.4 +48.0 +19.6 +1.3
Steps
(reduced)
126
(36)
130
(40)
133
(43)
136
(1)
139
(4)
142
(7)
145
(10)
147
(12)
150
(15)
152
(17)
154
(19)