45ed11/5

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← 44ed11/5 45ed11/5 46ed11/5 →
Prime factorization 32 × 5
Step size 30.3334¢ 
Octave 40\45ed11/5 (1213.34¢) (→8\9ed11/5)
Twelfth 63\45ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit 3
Distinct consistency limit 3

45 equal divisions of 11/5 (abbreviated 45ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 45 equal parts of about 30.3 ¢ each. Each step represents a frequency ratio of (11/5)1/45, or the 45th root of 11/5.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 30.333
2 60.667 28/27
3 91
4 121.334 15/14, 31/29
5 151.667 23/21
6 182.001 10/9
7 212.334 17/15, 26/23
8 242.667
9 273.001
10 303.334 25/21, 31/26
11 333.668 17/14, 23/19
12 364.001 21/17, 26/21
13 394.335
14 424.668
15 455.001
16 485.335
17 515.668 27/20, 31/23
18 546.002 26/19
19 576.335 7/5
20 606.669
21 637.002
22 667.335 22/15, 25/17
23 697.669 3/2
24 728.002 29/19
25 758.336 17/11
26 788.669 11/7
27 819.003
28 849.336 31/19
29 879.669 5/3
30 910.003
31 940.336 19/11
32 970.67
33 1001.003 25/14
34 1031.337
35 1061.67
36 1092.003
37 1122.337 21/11
38 1152.67
39 1183.004
40 1213.337
41 1243.671
42 1274.004 23/11
43 1304.337
44 1334.671
45 1365.004 11/5

Harmonics

Approximation of harmonics in 45ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +13.3 +9.1 -3.7 +4.4 -7.9 -1.8 +9.7 -12.2 -12.6 +4.4 +5.4
Relative (%) +44.0 +29.8 -12.1 +14.4 -26.2 -6.0 +31.9 -40.3 -41.7 +14.4 +17.8
Steps
(reduced)
40
(40)
63
(18)
79
(34)
92
(2)
102
(12)
111
(21)
119
(29)
125
(35)
131
(41)
137
(2)
142
(7)
Approximation of harmonics in 45ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -11.8 +11.5 +13.4 -7.3 +9.1 +1.1 -1.5 +0.7 +7.2 -12.6 +1.4
Relative (%) -39.1 +38.0 +44.2 -24.1 +29.9 +3.6 -4.9 +2.3 +23.9 -41.7 +4.6
Steps
(reduced)
146
(11)
151
(16)
155
(20)
158
(23)
162
(27)
165
(30)
168
(33)
171
(36)
174
(39)
176
(41)
179
(44)