36ed7/3
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Prime factorization
22 × 32
Step size
40.7464¢
Octave
29\36ed7/3 (1181.65¢)
Twelfth
47\36ed7/3 (1915.08¢)
Consistency limit
2
Distinct consistency limit
2
Special properties
 |
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| ← 35ed7/3 | 36ed7/3 | 37ed7/3 → |
36 equal divisions of 7/3 (abbreviated 36ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 36 equal parts of about 40.7 ¢ each. Each step represents a frequency ratio of (7/3)1/36, or the 36th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 40.746 | |
| 2 | 81.493 | 23/22 |
| 3 | 122.239 | 14/13, 15/14 |
| 4 | 162.986 | |
| 5 | 203.732 | 28/25 |
| 6 | 244.478 | 15/13 |
| 7 | 285.225 | 13/11 |
| 8 | 325.971 | 23/19 |
| 9 | 366.718 | |
| 10 | 407.464 | 19/15, 29/23 |
| 11 | 448.211 | 22/17 |
| 12 | 488.957 | |
| 13 | 529.703 | 15/11, 19/14, 23/17 |
| 14 | 570.45 | 18/13 |
| 15 | 611.196 | |
| 16 | 651.943 | 19/13 |
| 17 | 692.689 | |
| 18 | 733.435 | 23/15, 26/17, 29/19 |
| 19 | 774.182 | |
| 20 | 814.928 | |
| 21 | 855.675 | 18/11, 23/14 |
| 22 | 896.421 | |
| 23 | 937.168 | |
| 24 | 977.914 | |
| 25 | 1018.66 | |
| 26 | 1059.407 | |
| 27 | 1100.153 | |
| 28 | 1140.9 | 29/15 |
| 29 | 1181.646 | |
| 30 | 1222.392 | |
| 31 | 1263.139 | 25/12, 29/14 |
| 32 | 1303.885 | |
| 33 | 1344.632 | 13/6 |
| 34 | 1385.378 | 29/13 |
| 35 | 1426.124 | |
| 36 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.4 | +13.1 | +4.0 | -15.6 | -5.2 | +13.1 | -14.3 | -14.5 | +6.8 | +4.8 | +17.2 |
| Relative (%) | -45.0 | +32.2 | +9.9 | -38.2 | -12.8 | +32.2 | -35.1 | -35.6 | +16.8 | +11.8 | +42.1 | |
| Steps (reduced) |
29 (29) |
47 (11) |
59 (23) |
68 (32) |
76 (4) |
83 (11) |
88 (16) |
93 (21) |
98 (26) |
102 (30) |
106 (34) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.8 | -5.2 | -2.4 | +8.1 | -15.4 | +7.9 | -4.2 | -11.5 | -14.5 | -13.5 | -9.0 |
| Relative (%) | +2.0 | -12.8 | -6.0 | +19.8 | -37.8 | +19.4 | -10.3 | -28.3 | -35.6 | -33.2 | -22.1 | |
| Steps (reduced) |
109 (1) |
112 (4) |
115 (7) |
118 (10) |
120 (12) |
123 (15) |
125 (17) |
127 (19) |
129 (21) |
131 (23) |
133 (25) | |