72ed7/3
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Prime factorization
23 × 32
Step size
20.3732¢
Octave
59\72ed7/3 (1202.02¢)
Twelfth
93\72ed7/3 (1894.71¢) (→31\24ed7/3)
Consistency limit
3
Distinct consistency limit
3
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| ← 71ed7/3 | 72ed7/3 | 73ed7/3 → |
72 equal divisions of 7/3 (abbreviated 72ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 72 equal parts of about 20.4 ¢ each. Each step represents a frequency ratio of (7/3)1/72, or the 72nd root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 20.4 | |
| 2 | 40.7 | |
| 3 | 61.1 | 29/28, 30/29 |
| 4 | 81.5 | |
| 5 | 101.9 | 17/16, 35/33 |
| 6 | 122.2 | 15/14 |
| 7 | 142.6 | 38/35 |
| 8 | 163 | 11/10, 34/31 |
| 9 | 183.4 | |
| 10 | 203.7 | |
| 11 | 224.1 | 25/22, 33/29 |
| 12 | 244.5 | 15/13, 38/33 |
| 13 | 264.9 | 7/6 |
| 14 | 285.2 | 33/28 |
| 15 | 305.6 | 31/26, 37/31 |
| 16 | 326 | 29/24, 35/29 |
| 17 | 346.3 | |
| 18 | 366.7 | 37/30 |
| 19 | 387.1 | 5/4 |
| 20 | 407.5 | 19/15, 24/19 |
| 21 | 427.8 | 23/18, 32/25 |
| 22 | 448.2 | 22/17 |
| 23 | 468.6 | 38/29 |
| 24 | 489 | |
| 25 | 509.3 | |
| 26 | 529.7 | 19/14, 34/25 |
| 27 | 550.1 | 11/8 |
| 28 | 570.4 | |
| 29 | 590.8 | 31/22 |
| 30 | 611.2 | 37/26 |
| 31 | 631.6 | |
| 32 | 651.9 | 16/11, 35/24 |
| 33 | 672.3 | 28/19 |
| 34 | 692.7 | |
| 35 | 713.1 | |
| 36 | 733.4 | 26/17, 29/19 |
| 37 | 753.8 | 17/11 |
| 38 | 774.2 | 25/16, 36/23 |
| 39 | 794.6 | 19/12 |
| 40 | 814.9 | 8/5 |
| 41 | 835.3 | |
| 42 | 855.7 | |
| 43 | 876 | |
| 44 | 896.4 | 37/22 |
| 45 | 916.8 | 17/10 |
| 46 | 937.2 | |
| 47 | 957.5 | 33/19 |
| 48 | 977.9 | |
| 49 | 998.3 | |
| 50 | 1018.7 | |
| 51 | 1039 | 31/17 |
| 52 | 1059.4 | 24/13, 35/19 |
| 53 | 1079.8 | 28/15 |
| 54 | 1100.2 | |
| 55 | 1120.5 | |
| 56 | 1140.9 | 29/15 |
| 57 | 1161.3 | |
| 58 | 1181.6 | |
| 59 | 1202 | 2/1 |
| 60 | 1222.4 | |
| 61 | 1242.8 | |
| 62 | 1263.1 | 29/14 |
| 63 | 1283.5 | |
| 64 | 1303.9 | 17/8 |
| 65 | 1324.3 | |
| 66 | 1344.6 | 37/17 |
| 67 | 1365 | 11/5 |
| 68 | 1385.4 | |
| 69 | 1405.8 | |
| 70 | 1426.1 | |
| 71 | 1446.5 | 30/13 |
| 72 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.02 | -7.25 | +4.04 | +4.82 | -5.23 | -7.25 | +6.06 | +5.88 | +6.83 | +4.82 | -3.21 |
| Relative (%) | +9.9 | -35.6 | +19.8 | +23.6 | -25.7 | -35.6 | +29.7 | +28.9 | +33.5 | +23.6 | -15.7 | |
| Steps (reduced) |
59 (59) |
93 (21) |
118 (46) |
137 (65) |
152 (8) |
165 (21) |
177 (33) |
187 (43) |
196 (52) |
204 (60) |
211 (67) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.83 | -5.23 | -2.43 | +8.08 | +4.99 | +7.90 | -4.21 | +8.85 | +5.88 | +6.84 | -9.00 |
| Relative (%) | +4.1 | -25.7 | -11.9 | +39.6 | +24.5 | +38.8 | -20.7 | +43.5 | +28.9 | +33.6 | -44.2 | |
| Steps (reduced) |
218 (2) |
224 (8) |
230 (14) |
236 (20) |
241 (25) |
246 (30) |
250 (34) |
255 (39) |
259 (43) |
263 (47) |
266 (50) | |