80ed7/3
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Prime factorization
24 × 5
Step size
18.3359¢
Octave
65\80ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth
104\80ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 79ed7/3 | 80ed7/3 | 81ed7/3 → |
80 equal divisions of 7/3 (abbreviated 80ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 80 equal parts of about 18.3 ¢ each. Each step represents a frequency ratio of (7/3)1/80, or the 80th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 18.3 | |
| 2 | 36.7 | |
| 3 | 55 | 31/30 |
| 4 | 73.3 | |
| 5 | 91.7 | 19/18, 39/37 |
| 6 | 110 | 33/31 |
| 7 | 128.4 | 14/13 |
| 8 | 146.7 | 25/23, 37/34 |
| 9 | 165 | 11/10 |
| 10 | 183.4 | |
| 11 | 201.7 | |
| 12 | 220 | |
| 13 | 238.4 | 39/34 |
| 14 | 256.7 | 29/25, 36/31 |
| 15 | 275 | 34/29 |
| 16 | 293.4 | |
| 17 | 311.7 | |
| 18 | 330 | 23/19 |
| 19 | 348.4 | |
| 20 | 366.7 | 21/17 |
| 21 | 385.1 | |
| 22 | 403.4 | 29/23 |
| 23 | 421.7 | 23/18, 37/29 |
| 24 | 440.1 | |
| 25 | 458.4 | 30/23 |
| 26 | 476.7 | 25/19 |
| 27 | 495.1 | |
| 28 | 513.4 | 39/29 |
| 29 | 531.7 | 19/14, 34/25 |
| 30 | 550.1 | |
| 31 | 568.4 | 25/18 |
| 32 | 586.7 | |
| 33 | 605.1 | |
| 34 | 623.4 | 33/23 |
| 35 | 641.8 | |
| 36 | 660.1 | 19/13 |
| 37 | 678.4 | 34/23, 37/25 |
| 38 | 696.8 | |
| 39 | 715.1 | |
| 40 | 733.4 | 29/19 |
| 41 | 751.8 | |
| 42 | 770.1 | 39/25 |
| 43 | 788.4 | 30/19 |
| 44 | 806.8 | |
| 45 | 825.1 | 29/18, 37/23 |
| 46 | 843.5 | |
| 47 | 861.8 | 23/14 |
| 48 | 880.1 | |
| 49 | 898.5 | |
| 50 | 916.8 | 39/23 |
| 51 | 935.1 | |
| 52 | 953.5 | 33/19 |
| 53 | 971.8 | |
| 54 | 990.1 | 23/13 |
| 55 | 1008.5 | 34/19 |
| 56 | 1026.8 | |
| 57 | 1045.1 | |
| 58 | 1063.5 | |
| 59 | 1081.8 | |
| 60 | 1100.2 | 17/9 |
| 61 | 1118.5 | |
| 62 | 1136.8 | |
| 63 | 1155.2 | 37/19 |
| 64 | 1173.5 | |
| 65 | 1191.8 | |
| 66 | 1210.2 | |
| 67 | 1228.5 | |
| 68 | 1246.8 | 37/18, 39/19 |
| 69 | 1265.2 | |
| 70 | 1283.5 | |
| 71 | 1301.8 | |
| 72 | 1320.2 | 15/7 |
| 73 | 1338.5 | 13/6 |
| 74 | 1356.9 | |
| 75 | 1375.2 | 31/14 |
| 76 | 1393.5 | |
| 77 | 1411.9 | |
| 78 | 1430.2 | |
| 79 | 1448.5 | 30/13 |
| 80 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.17 | +4.98 | +2.00 | +0.74 | -3.19 | +4.98 | -6.17 | -8.38 | -7.43 | -7.41 | +6.98 |
| Relative (%) | -44.5 | +27.1 | +10.9 | +4.0 | -17.4 | +27.1 | -33.6 | -45.7 | -40.5 | -40.4 | +38.1 | |
| Steps (reduced) |
65 (65) |
104 (24) |
131 (51) |
152 (72) |
169 (9) |
184 (24) |
196 (36) |
207 (47) |
217 (57) |
226 (66) |
235 (75) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.24 | -3.19 | +5.72 | +4.00 | +9.06 | +1.79 | -0.14 | +2.74 | -8.38 | +2.76 | -0.85 |
| Relative (%) | -17.7 | -17.4 | +31.2 | +21.8 | +49.4 | +9.7 | -0.7 | +15.0 | -45.7 | +15.1 | -4.6 | |
| Steps (reduced) |
242 (2) |
249 (9) |
256 (16) |
262 (22) |
268 (28) |
273 (33) |
278 (38) |
283 (43) |
287 (47) |
292 (52) |
296 (56) | |