36ed5/2

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← 35ed5/2 36ed5/2 37ed5/2 →
Prime factorization 22 × 32
Step size 44.0643¢ 
Octave 27\36ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth 43\36ed5/2 (1894.76¢)
(semiconvergent)
Consistency limit 7
Distinct consistency limit 3
Special properties

36 equal divisions of 5/2 (abbreviated 36ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 36 equal parts of about 44.1⁠ ⁠¢ each. Each step represents a frequency ratio of (5/2)1/36, or the 36th root of 5/2.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 44.1
2 88.1 21/20, 22/21
3 132.2 27/25
4 176.3 10/9
5 220.3 17/15, 25/22, 26/23
6 264.4 7/6, 29/25
7 308.4 6/5, 25/21
8 352.5 11/9, 27/22
9 396.6 29/23
10 440.6 9/7, 22/17
11 484.7 29/22
12 528.8 23/17
13 572.8 25/18
14 616.9 10/7
15 661 19/13, 22/15, 25/17
16 705 3/2
17 749.1 17/11
18 793.2 27/17
19 837.2
20 881.3 5/3
21 925.3 12/7, 17/10, 29/17
22 969.4 7/4
23 1013.5 9/5
24 1057.5
25 1101.6 17/9
26 1145.7 29/15
27 1189.7
28 1233.8
29 1277.9 21/10, 23/11, 25/12
30 1321.9 15/7
31 1366 11/5
32 1410.1 9/4
33 1454.1
34 1498.2
35 1542.2 17/7, 22/9
36 1586.3 5/2

Harmonics

Approximation of harmonics in 36ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -10.3 -7.2 -20.5 -10.3 -17.5 -19.9 +13.3 -14.4 -20.5 -9.3 +16.3
Relative (%) -23.3 -16.3 -46.6 -23.3 -39.6 -45.3 +30.1 -32.6 -46.6 -21.1 +37.1
Steps
(reduced)
27
(27)
43
(7)
54
(18)
63
(27)
70
(34)
76
(4)
82
(10)
86
(14)
90
(18)
94
(22)
98
(26)
Approximation of harmonics in 36ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +10.0 +13.9 -17.5 +3.0 -13.8 +19.4 +13.9 +13.3 +16.9 -19.5 -8.4
Relative (%) +22.6 +31.4 -39.6 +6.8 -31.4 +44.1 +31.6 +30.1 +38.4 -44.3 -19.0
Steps
(reduced)
101
(29)
104
(32)
106
(34)
109
(1)
111
(3)
114
(6)
116
(8)
118
(10)
120
(12)
121
(13)
123
(15)