85ed7/3
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Prime factorization
5 × 17
Step size
17.2573¢
Octave
70\85ed7/3 (1208.01¢) (→14\17ed7/3)
Twelfth
110\85ed7/3 (1898.3¢) (→22\17ed7/3)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 84ed7/3 | 85ed7/3 | 86ed7/3 → |
85 equal divisions of 7/3 (abbreviated 85ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 85 equal parts of about 17.3 ¢ each. Each step represents a frequency ratio of (7/3)1/85, or the 85th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 17.3 | |
| 2 | 34.5 | |
| 3 | 51.8 | 34/33 |
| 4 | 69 | |
| 5 | 86.3 | |
| 6 | 103.5 | |
| 7 | 120.8 | |
| 8 | 138.1 | |
| 9 | 155.3 | |
| 10 | 172.6 | 21/19 |
| 11 | 189.8 | 19/17, 29/26, 39/35 |
| 12 | 207.1 | |
| 13 | 224.3 | 33/29, 41/36 |
| 14 | 241.6 | 23/20, 31/27, 38/33 |
| 15 | 258.9 | |
| 16 | 276.1 | 34/29 |
| 17 | 293.4 | |
| 18 | 310.6 | |
| 19 | 327.9 | |
| 20 | 345.1 | |
| 21 | 362.4 | 37/30 |
| 22 | 379.7 | |
| 23 | 396.9 | 39/31 |
| 24 | 414.2 | 33/26 |
| 25 | 431.4 | |
| 26 | 448.7 | 35/27 |
| 27 | 465.9 | 17/13, 38/29 |
| 28 | 483.2 | |
| 29 | 500.5 | |
| 30 | 517.7 | |
| 31 | 535 | |
| 32 | 552.2 | |
| 33 | 569.5 | |
| 34 | 586.7 | |
| 35 | 604 | |
| 36 | 621.3 | |
| 37 | 638.5 | 13/9 |
| 38 | 655.8 | 19/13 |
| 39 | 673 | 31/21 |
| 40 | 690.3 | |
| 41 | 707.5 | |
| 42 | 724.8 | |
| 43 | 742.1 | |
| 44 | 759.3 | |
| 45 | 776.6 | 36/23 |
| 46 | 793.8 | |
| 47 | 811.1 | |
| 48 | 828.4 | 21/13, 29/18 |
| 49 | 845.6 | 31/19 |
| 50 | 862.9 | |
| 51 | 880.1 | |
| 52 | 897.4 | |
| 53 | 914.6 | |
| 54 | 931.9 | |
| 55 | 949.2 | |
| 56 | 966.4 | |
| 57 | 983.7 | 30/17 |
| 58 | 1000.9 | 41/23 |
| 59 | 1018.2 | 9/5 |
| 60 | 1035.4 | 20/11 |
| 61 | 1052.7 | |
| 62 | 1070 | 13/7 |
| 63 | 1087.2 | |
| 64 | 1104.5 | |
| 65 | 1121.7 | |
| 66 | 1139 | |
| 67 | 1156.2 | 37/19 |
| 68 | 1173.5 | |
| 69 | 1190.8 | |
| 70 | 1208 | |
| 71 | 1225.3 | |
| 72 | 1242.5 | 39/19, 41/20 |
| 73 | 1259.8 | 29/14 |
| 74 | 1277 | 23/11 |
| 75 | 1294.3 | 19/9 |
| 76 | 1311.6 | |
| 77 | 1328.8 | |
| 78 | 1346.1 | 37/17 |
| 79 | 1363.3 | |
| 80 | 1380.6 | |
| 81 | 1397.8 | |
| 82 | 1415.1 | |
| 83 | 1432.4 | |
| 84 | 1449.6 | 30/13 |
| 85 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.01 | -3.65 | -1.23 | -7.89 | +4.36 | -3.65 | +6.78 | -7.30 | +0.12 | +7.69 | -4.89 |
| Relative (%) | +46.4 | -21.2 | -7.2 | -45.7 | +25.3 | -21.2 | +39.3 | -42.3 | +0.7 | +44.6 | -28.3 | |
| Steps (reduced) |
70 (70) |
110 (25) |
139 (54) |
161 (76) |
180 (10) |
195 (25) |
209 (39) |
220 (50) |
231 (61) |
241 (71) |
249 (79) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.40 | +4.36 | +5.72 | -2.47 | -3.88 | +0.71 | -6.61 | +8.14 | -7.30 | -1.55 | +7.78 |
| Relative (%) | -31.3 | +25.3 | +33.1 | -14.3 | -22.5 | +4.1 | -38.3 | +47.1 | -42.3 | -9.0 | +45.1 | |
| Steps (reduced) |
257 (2) |
265 (10) |
272 (17) |
278 (23) |
284 (29) |
290 (35) |
295 (40) |
301 (46) |
305 (50) |
310 (55) |
315 (60) | |