65ed7/3
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Prime factorization
5 × 13
Step size
22.5672¢
Octave
53\65ed7/3 (1196.06¢)
Twelfth
84\65ed7/3 (1895.65¢)
Consistency limit
6
Distinct consistency limit
5
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| ← 64ed7/3 | 65ed7/3 | 66ed7/3 → |
65 equal divisions of 7/3 (abbreviated 65ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 65 equal parts of about 22.6 ¢ each. Each step represents a frequency ratio of (7/3)1/65, or the 65th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 22.6 | |
| 2 | 45.1 | 36/35 |
| 3 | 67.7 | 25/24 |
| 4 | 90.3 | |
| 5 | 112.8 | 16/15, 31/29 |
| 6 | 135.4 | 27/25 |
| 7 | 158 | 34/31, 35/32 |
| 8 | 180.5 | 10/9 |
| 9 | 203.1 | 9/8 |
| 10 | 225.7 | 33/29 |
| 11 | 248.2 | |
| 12 | 270.8 | 7/6 |
| 13 | 293.4 | 32/27 |
| 14 | 315.9 | 6/5 |
| 15 | 338.5 | 17/14 |
| 16 | 361.1 | |
| 17 | 383.6 | 5/4 |
| 18 | 406.2 | |
| 19 | 428.8 | 32/25 |
| 20 | 451.3 | 35/27 |
| 21 | 473.9 | 21/16 |
| 22 | 496.5 | 4/3 |
| 23 | 519 | 27/20 |
| 24 | 541.6 | 26/19 |
| 25 | 564.2 | |
| 26 | 586.7 | |
| 27 | 609.3 | |
| 28 | 631.9 | 36/25 |
| 29 | 654.5 | 19/13, 35/24 |
| 30 | 677 | 31/21 |
| 31 | 699.6 | 3/2 |
| 32 | 722.2 | |
| 33 | 744.7 | |
| 34 | 767.3 | 14/9 |
| 35 | 789.9 | |
| 36 | 812.4 | 8/5 |
| 37 | 835 | 34/21 |
| 38 | 857.6 | |
| 39 | 880.1 | |
| 40 | 902.7 | 27/16 |
| 41 | 925.3 | 29/17 |
| 42 | 947.8 | 19/11 |
| 43 | 970.4 | 7/4 |
| 44 | 993 | 16/9 |
| 45 | 1015.5 | 9/5 |
| 46 | 1038.1 | 31/17 |
| 47 | 1060.7 | |
| 48 | 1083.2 | 28/15 |
| 49 | 1105.8 | |
| 50 | 1128.4 | |
| 51 | 1150.9 | 33/17, 35/18 |
| 52 | 1173.5 | |
| 53 | 1196.1 | 2/1 |
| 54 | 1218.6 | |
| 55 | 1241.2 | |
| 56 | 1263.8 | 29/14 |
| 57 | 1286.3 | 21/10 |
| 58 | 1308.9 | 17/8, 32/15 |
| 59 | 1331.5 | |
| 60 | 1354 | 35/16 |
| 61 | 1376.6 | 31/14 |
| 62 | 1399.2 | |
| 63 | 1421.7 | |
| 64 | 1444.3 | |
| 65 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.94 | -6.31 | -7.87 | -10.54 | -10.24 | -6.31 | +10.76 | +9.95 | +8.09 | +1.06 | +8.39 |
| Relative (%) | -17.4 | -27.9 | -34.9 | -46.7 | -45.4 | -27.9 | +47.7 | +44.1 | +35.8 | +4.7 | +37.2 | |
| Steps (reduced) |
53 (53) |
84 (19) |
106 (41) |
123 (58) |
137 (7) |
149 (19) |
160 (30) |
169 (39) |
177 (47) |
184 (54) |
191 (61) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.22 | -10.24 | +5.72 | +6.82 | -7.86 | +6.02 | +2.68 | +4.15 | +9.95 | -2.88 | +10.43 |
| Relative (%) | +23.1 | -45.4 | +25.3 | +30.2 | -34.8 | +26.7 | +11.9 | +18.4 | +44.1 | -12.8 | +46.2 | |
| Steps (reduced) |
197 (2) |
202 (7) |
208 (13) |
213 (18) |
217 (22) |
222 (27) |
226 (31) |
230 (35) |
234 (39) |
237 (42) |
241 (46) | |