36ed5/4
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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
 |
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| ← 35ed5/4 | 36ed5/4 | 37ed5/4 → |
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 | 10.7 | |
| 2 | 21.5 | |
| 3 | 32.2 | |
| 4 | 42.9 | |
| 5 | 53.7 | 29/28 |
| 6 | 64.4 | 26/25 |
| 7 | 75.1 | 23/22, 24/23, 25/24 |
| 8 | 85.8 | 22/21 |
| 9 | 96.6 | 18/17, 19/18, 20/19 |
| 10 | 107.3 | |
| 11 | 118 | 15/14, 16/15 |
| 12 | 128.8 | 14/13, 29/27 |
| 13 | 139.5 | 13/12 |
| 14 | 150.2 | 12/11, 25/23 |
| 15 | 161 | 11/10, 23/21 |
| 16 | 171.7 | 21/19 |
| 17 | 182.4 | 29/26 |
| 18 | 193.2 | 19/17, 28/25 |
| 19 | 203.9 | |
| 20 | 214.6 | 17/15, 26/23 |
| 21 | 225.3 | 25/22 |
| 22 | 236.1 | 8/7, 23/20 |
| 23 | 246.8 | 15/13 |
| 24 | 257.5 | 22/19 |
| 25 | 268.3 | 7/6 |
| 26 | 279 | |
| 27 | 289.7 | 13/11, 19/16 |
| 28 | 300.5 | |
| 29 | 311.2 | 6/5 |
| 30 | 321.9 | 29/24 |
| 31 | 332.7 | 17/14, 23/19 |
| 32 | 343.4 | 28/23 |
| 33 | 354.1 | 11/9 |
| 34 | 364.9 | 16/13, 21/17 |
| 35 | 375.6 | 26/21 |
| 36 | 386.3 | 5/4 |
Harmonics
| 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) | |
| 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) | |