74ed7/3
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Prime factorization
2 × 37
Step size
19.8226¢
Octave
61\74ed7/3 (1209.18¢)
Twelfth
96\74ed7/3 (1902.97¢) (→48\37ed7/3)
Consistency limit
3
Distinct consistency limit
3
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| ← 73ed7/3 | 74ed7/3 | 75ed7/3 → |
74 equal divisions of 7/3 (abbreviated 74ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 74 equal parts of about 19.8 ¢ each. Each step represents a frequency ratio of (7/3)1/74, or the 74th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 19.8 | |
| 2 | 39.6 | |
| 3 | 59.5 | |
| 4 | 79.3 | 22/21, 23/22 |
| 5 | 99.1 | |
| 6 | 118.9 | 15/14, 31/29 |
| 7 | 138.8 | |
| 8 | 158.6 | 23/21, 34/31 |
| 9 | 178.4 | |
| 10 | 198.2 | 28/25, 37/33 |
| 11 | 218 | |
| 12 | 237.9 | 31/27 |
| 13 | 257.7 | |
| 14 | 277.5 | 27/23, 34/29 |
| 15 | 297.3 | |
| 16 | 317.2 | 6/5 |
| 17 | 337 | |
| 18 | 356.8 | 27/22 |
| 19 | 376.6 | |
| 20 | 396.5 | 34/27 |
| 21 | 416.3 | |
| 22 | 436.1 | 9/7 |
| 23 | 455.9 | |
| 24 | 475.7 | 29/22 |
| 25 | 495.6 | |
| 26 | 515.4 | 31/23, 35/26 |
| 27 | 535.2 | |
| 28 | 555 | |
| 29 | 574.9 | |
| 30 | 594.7 | 31/22, 38/27 |
| 31 | 614.5 | |
| 32 | 634.3 | 13/9, 36/25 |
| 33 | 654.1 | 19/13 |
| 34 | 674 | 31/21, 34/23 |
| 35 | 693.8 | |
| 36 | 713.6 | |
| 37 | 733.4 | 29/19 |
| 38 | 753.3 | 17/11 |
| 39 | 773.1 | |
| 40 | 792.9 | |
| 41 | 812.7 | |
| 42 | 832.5 | 21/13, 34/21 |
| 43 | 852.4 | |
| 44 | 872.2 | 38/23 |
| 45 | 892 | |
| 46 | 911.8 | 22/13 |
| 47 | 931.7 | |
| 48 | 951.5 | 26/15 |
| 49 | 971.3 | |
| 50 | 991.1 | 23/13 |
| 51 | 1011 | 34/19 |
| 52 | 1030.8 | |
| 53 | 1050.6 | |
| 54 | 1070.4 | 13/7 |
| 55 | 1090.2 | |
| 56 | 1110.1 | |
| 57 | 1129.9 | |
| 58 | 1149.7 | 33/17, 35/18 |
| 59 | 1169.5 | |
| 60 | 1189.4 | |
| 61 | 1209.2 | |
| 62 | 1229 | |
| 63 | 1248.8 | |
| 64 | 1268.6 | 25/12, 27/13 |
| 65 | 1288.5 | |
| 66 | 1308.3 | |
| 67 | 1328.1 | |
| 68 | 1347.9 | 37/17 |
| 69 | 1367.8 | |
| 70 | 1387.6 | 29/13 |
| 71 | 1407.4 | |
| 72 | 1427.2 | |
| 73 | 1447 | |
| 74 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.18 | +1.01 | -1.47 | +8.67 | -9.63 | +1.01 | +7.71 | +2.03 | -1.98 | -8.40 | -0.46 |
| Relative (%) | +46.3 | +5.1 | -7.4 | +43.7 | -48.6 | +5.1 | +38.9 | +10.2 | -10.0 | -42.4 | -2.3 | |
| Steps (reduced) |
61 (61) |
96 (22) |
121 (47) |
141 (67) |
156 (8) |
170 (22) |
182 (34) |
192 (44) |
201 (53) |
209 (61) |
217 (69) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.27 | -9.63 | +9.68 | -2.94 | -8.78 | -8.62 | -3.11 | +7.20 | +2.03 | +0.78 | +3.11 |
| Relative (%) | -1.4 | -48.6 | +48.8 | -14.8 | -44.3 | -43.5 | -15.7 | +36.3 | +10.2 | +3.9 | +15.7 | |
| Steps (reduced) |
224 (2) |
230 (8) |
237 (15) |
242 (20) |
247 (25) |
252 (30) |
257 (35) |
262 (40) |
266 (44) |
270 (48) |
274 (52) | |