61ed7/3
Jump to navigation
Jump to search
Prime factorization
61 (prime)
Step size
24.0471¢
Octave
50\61ed7/3 (1202.35¢)
Twelfth
79\61ed7/3 (1899.72¢)
Consistency limit
10
Distinct consistency limit
9
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 60ed7/3 | 61ed7/3 | 62ed7/3 → |
61 equal divisions of 7/3 (abbreviated 61ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 61 equal parts of about 24 ¢ each. Each step represents a frequency ratio of (7/3)1/61, or the 61st root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 24.047 | |
| 2 | 48.094 | 34/33, 35/34 |
| 3 | 72.141 | 24/23, 25/24, 26/25 |
| 4 | 96.188 | 18/17, 19/18 |
| 5 | 120.235 | 15/14, 29/27 |
| 6 | 144.282 | 25/23 |
| 7 | 168.329 | 11/10 |
| 8 | 192.377 | 19/17, 28/25 |
| 9 | 216.424 | 17/15, 26/23 |
| 10 | 240.471 | 23/20, 31/27 |
| 11 | 264.518 | 7/6 |
| 12 | 288.565 | 13/11, 33/28 |
| 13 | 312.612 | 6/5 |
| 14 | 336.659 | 17/14, 28/23 |
| 15 | 360.706 | 16/13 |
| 16 | 384.753 | 5/4 |
| 17 | 408.8 | 19/15, 24/19, 33/26 |
| 18 | 432.847 | 9/7 |
| 19 | 456.894 | 13/10, 30/23 |
| 20 | 480.941 | 33/25 |
| 21 | 504.988 | |
| 22 | 529.035 | 19/14, 34/25 |
| 23 | 553.082 | 11/8 |
| 24 | 577.13 | |
| 25 | 601.177 | 17/12, 24/17 |
| 26 | 625.224 | 23/16, 33/23 |
| 27 | 649.271 | 16/11, 35/24 |
| 28 | 673.318 | 28/19, 31/21, 34/23 |
| 29 | 697.365 | |
| 30 | 721.412 | |
| 31 | 745.459 | 20/13 |
| 32 | 769.506 | 25/16 |
| 33 | 793.553 | 19/12, 30/19 |
| 34 | 817.6 | 8/5 |
| 35 | 841.647 | 13/8 |
| 36 | 865.694 | 28/17, 33/20 |
| 37 | 889.741 | |
| 38 | 913.788 | 22/13 |
| 39 | 937.835 | 31/18 |
| 40 | 961.883 | |
| 41 | 985.93 | 23/13, 30/17 |
| 42 | 1009.977 | 34/19 |
| 43 | 1034.024 | 20/11 |
| 44 | 1058.071 | 24/13, 35/19 |
| 45 | 1082.118 | 28/15 |
| 46 | 1106.165 | |
| 47 | 1130.212 | 23/12, 25/13 |
| 48 | 1154.259 | 35/18 |
| 49 | 1178.306 | |
| 50 | 1202.353 | 2/1 |
| 51 | 1226.4 | |
| 52 | 1250.447 | 33/16, 35/17 |
| 53 | 1274.494 | 23/11, 25/12 |
| 54 | 1298.541 | |
| 55 | 1322.589 | 15/7 |
| 56 | 1346.636 | 24/11 |
| 57 | 1370.683 | |
| 58 | 1394.73 | |
| 59 | 1418.777 | 25/11, 34/15 |
| 60 | 1442.824 | 23/10 |
| 61 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.4 | -2.2 | +4.7 | +3.1 | +0.1 | -2.2 | +7.1 | -4.5 | +5.5 | +8.8 | +2.5 |
| Relative (%) | +9.8 | -9.3 | +19.6 | +13.1 | +0.5 | -9.3 | +29.4 | -18.6 | +22.9 | +36.7 | +10.3 | |
| Steps (reduced) |
50 (50) |
79 (18) |
100 (39) |
116 (55) |
129 (7) |
140 (18) |
150 (28) |
158 (36) |
166 (44) |
173 (51) |
179 (57) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.2 | +0.1 | +0.9 | +9.4 | +0.6 | -2.1 | +0.5 | +7.9 | -4.5 | +11.2 | +6.4 |
| Relative (%) | +34.0 | +0.5 | +3.8 | +39.1 | +2.7 | -8.8 | +1.9 | +32.7 | -18.6 | +46.5 | +26.5 | |
| Steps (reduced) |
185 (2) |
190 (7) |
195 (12) |
200 (17) |
204 (21) |
208 (25) |
212 (29) |
216 (33) |
219 (36) |
223 (40) |
226 (43) | |