36ed5/4

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← 35ed5/436ed5/437ed5/4 →
Prime factorization 22 × 32
Step size 10.7309¢ 
Octave 112\36ed5/4 (1201.86¢) (→28\9ed5/4)
Twelfth 177\36ed5/4 (1899.38¢) (→59\12ed5/4)
Consistency limit 3
Distinct consistency limit 3
Special properties

36 equal divisions of 5/4 (abbreviated 36ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 36 equal parts of about 10.7 ¢ each. Each step represents a frequency ratio of (5/4)1/36, or the 36th root of 5/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 10.731
2 21.462
3 32.193
4 42.924
5 53.655 29/28
6 64.386 26/25
7 75.117 23/22, 24/23, 25/24
8 85.847 22/21
9 96.578 18/17, 19/18, 20/19
10 107.309
11 118.04 15/14, 16/15
12 128.771 14/13, 29/27
13 139.502 13/12
14 150.233 12/11, 25/23
15 160.964 11/10, 23/21
16 171.695 21/19
17 182.426 29/26
18 193.157 19/17, 28/25
19 203.888
20 214.619 17/15, 26/23
21 225.35 25/22
22 236.081 8/7, 23/20
23 246.812 15/13
24 257.542 22/19
25 268.273 7/6
26 279.004
27 289.735 13/11, 19/16
28 300.466
29 311.197 6/5
30 321.928 29/24
31 332.659 17/14, 23/19
32 343.39 28/23
33 354.121 11/9
34 364.852 16/13, 21/17
35 375.583 26/21
36 386.314 5/4

Harmonics

Approximation of harmonics in 36ed5/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.86 -2.58 +3.73 +3.73 -0.71 +0.69 -5.14 -5.16 -5.14 +1.55 +1.15
Relative (%) +17.4 -24.0 +34.8 +34.8 -6.7 +6.4 -47.9 -48.1 -47.9 +14.5 +10.7
Steps
(reduced)
112
(4)
177
(33)
224
(8)
260
(8)
289
(1)
314
(26)
335
(11)
354
(30)
371
(11)
387
(27)
401
(5)
Approximation of harmonics in 36ed5/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +2.08 +2.55 +1.15 -3.27 -0.92 -3.29 -0.32 -3.27 -1.89 +3.42 +1.58
Relative (%) +19.4 +23.8 +10.7 -30.5 -8.5 -30.7 -3.0 -30.5 -17.6 +31.9 +14.7
Steps
(reduced)
414
(18)
426
(30)
437
(5)
447
(15)
457
(25)
466
(34)
475
(7)
483
(15)
491
(23)
499
(31)
506
(2)