36ed5/2
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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
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← 35ed5/2 | 36ed5/2 | 37ed5/2 → |
(semiconvergent)
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
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) |
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) |