19ed7/3
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Prime factorization
19 (prime)
Step size
77.2037¢
Octave
16\19ed7/3 (1235.26¢)
Twelfth
25\19ed7/3 (1930.09¢)
Consistency limit
3
Distinct consistency limit
3
| ← 18ed7/3 | 19ed7/3 | 20ed7/3 → |
19 equal divisions of 7/3 (abbreviated 19ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 19 equal parts of about 77.2 ¢ each. Each step represents a frequency ratio of (7/3)1/19, or the 19th root of 7/3.
Intervals
| Degrees | Enneatonic | ed11\9~ed7/3 | ||
|---|---|---|---|---|
| 1 | Jb | Ab | 77.193 | 77.2037 |
| 2 | G# | 154.386 | 154.4075 | |
| 3 | J | A | 231.57895 | 231.6112 |
| 4 | A | B | 308.7719 | 308.8149 |
| 5 | Bb | Cb | 385.9649 | 386.0187 |
| 6 | A# | B# | 463.1579 | 463.2224 |
| 7 | B | C | 540.3509 | 540.4261 |
| 8 | C | Q | 617.5439 | 617.6299 |
| 9 | Qb | Db | 694.7368 | 694.8336 |
| 10 | C# | Q# | 771.9298 | 772.0373 |
| 11 | Q | D | 849.1228 | 849.24105 |
| 12 | D | S | 926.3158 | 926.4448 |
| 13 | Eb | 1003.5088 | 1003.6485 | |
| 14 | D# | S# | 1080.70175 | 1080.85225 |
| 15 | E | 1157.8947 | 1158.0559 | |
| 16 | Fb | 1235.0877 | 1235.2567 | |
| 17 | E# | 1312.2807 | 1312.4634 | |
| 18 | F | 1389.4737 | 1389.6672 | |
| 19 | G | 1466.6 | 1466.8709 | |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +35.3 | +28.1 | -6.7 | -7.0 | -13.8 | +28.1 | +28.6 | -20.9 | +28.3 | +17.7 | +21.5 |
| Relative (%) | +45.7 | +36.4 | -8.7 | -9.0 | -17.9 | +36.4 | +37.0 | -27.1 | +36.6 | +22.9 | +27.8 | |
| Steps (reduced) |
16 (16) |
25 (6) |
31 (12) |
36 (17) |
40 (2) |
44 (6) |
47 (9) |
49 (11) |
52 (14) |
54 (16) |
56 (18) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +37.3 | -13.8 | +21.2 | -13.4 | +36.1 | +14.3 | -2.1 | -13.7 | -20.9 | -24.3 | -24.0 |
| Relative (%) | +48.3 | -17.9 | +27.4 | -17.3 | +46.7 | +18.6 | -2.7 | -17.7 | -27.1 | -31.4 | -31.1 | |
| Steps (reduced) |
58 (1) |
59 (2) |
61 (4) |
62 (5) |
64 (7) |
65 (8) |
66 (9) |
67 (10) |
68 (11) |
69 (12) |
70 (13) | |