75ed7/3
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Prime factorization
3 × 52
Step size
19.5583¢
Octave
61\75ed7/3 (1193.06¢)
Twelfth
97\75ed7/3 (1897.15¢)
Consistency limit
3
Distinct consistency limit
3
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| ← 74ed7/3 | 75ed7/3 | 76ed7/3 → |
75 equal divisions of 7/3 (abbreviated 75ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 75 equal parts of about 19.6 ¢ each. Each step represents a frequency ratio of (7/3)1/75, or the 75th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 19.6 | |
| 2 | 39.1 | |
| 3 | 58.7 | |
| 4 | 78.2 | 22/21 |
| 5 | 97.8 | |
| 6 | 117.3 | 15/14, 31/29 |
| 7 | 136.9 | |
| 8 | 156.5 | 34/31 |
| 9 | 176 | |
| 10 | 195.6 | 19/17, 28/25 |
| 11 | 215.1 | |
| 12 | 234.7 | |
| 13 | 254.3 | |
| 14 | 273.8 | 34/29 |
| 15 | 293.4 | |
| 16 | 312.9 | 6/5 |
| 17 | 332.5 | 23/19 |
| 18 | 352 | 27/22, 38/31 |
| 19 | 371.6 | 26/21 |
| 20 | 391.2 | |
| 21 | 410.7 | 33/26 |
| 22 | 430.3 | |
| 23 | 449.8 | 35/27 |
| 24 | 469.4 | 38/29 |
| 25 | 489 | |
| 26 | 508.5 | |
| 27 | 528.1 | |
| 28 | 547.6 | |
| 29 | 567.2 | 25/18 |
| 30 | 586.7 | |
| 31 | 606.3 | |
| 32 | 625.9 | |
| 33 | 645.4 | |
| 34 | 665 | 22/15 |
| 35 | 684.5 | |
| 36 | 704.1 | 3/2 |
| 37 | 723.7 | |
| 38 | 743.2 | |
| 39 | 762.8 | 14/9 |
| 40 | 782.3 | 11/7 |
| 41 | 801.9 | 35/22 |
| 42 | 821.4 | 37/23 |
| 43 | 841 | |
| 44 | 860.6 | |
| 45 | 880.1 | |
| 46 | 899.7 | |
| 47 | 919.2 | |
| 48 | 938.8 | |
| 49 | 958.4 | |
| 50 | 977.9 | |
| 51 | 997.5 | |
| 52 | 1017 | 9/5 |
| 53 | 1036.6 | |
| 54 | 1056.1 | |
| 55 | 1075.7 | |
| 56 | 1095.3 | |
| 57 | 1114.8 | |
| 58 | 1134.4 | 27/14 |
| 59 | 1153.9 | 35/18, 37/19 |
| 60 | 1173.5 | |
| 61 | 1193.1 | |
| 62 | 1212.6 | |
| 63 | 1232.2 | |
| 64 | 1251.7 | |
| 65 | 1271.3 | 25/12 |
| 66 | 1290.8 | |
| 67 | 1310.4 | |
| 68 | 1330 | |
| 69 | 1349.5 | 37/17 |
| 70 | 1369.1 | |
| 71 | 1388.6 | 29/13 |
| 72 | 1408.2 | |
| 73 | 1427.8 | |
| 74 | 1447.3 | |
| 75 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.94 | -4.80 | +5.67 | -9.04 | +7.81 | -4.80 | -1.28 | -9.60 | +3.58 | -4.96 | +0.87 |
| Relative (%) | -35.5 | -24.6 | +29.0 | -46.2 | +39.9 | -24.6 | -6.5 | -49.1 | +18.3 | -25.4 | +4.4 | |
| Steps (reduced) |
61 (61) |
97 (22) |
123 (48) |
142 (67) |
159 (9) |
172 (22) |
184 (34) |
194 (44) |
204 (54) |
212 (62) |
220 (70) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.80 | +7.81 | +5.72 | -8.22 | +4.17 | +3.01 | +7.20 | -3.37 | -9.60 | +7.65 | +8.93 |
| Relative (%) | -4.1 | +39.9 | +29.2 | -42.0 | +21.3 | +15.4 | +36.8 | -17.2 | -49.1 | +39.1 | +45.6 | |
| Steps (reduced) |
227 (2) |
234 (9) |
240 (15) |
245 (20) |
251 (26) |
256 (31) |
261 (36) |
265 (40) |
269 (44) |
274 (49) |
278 (53) | |