19ed7/4
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Prime factorization
19 (prime)
Step size
50.9908¢
Octave
24\19ed7/4 (1223.78¢)
Twelfth
37\19ed7/4 (1886.66¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 18ed7/4 | 19ed7/4 | 20ed7/4 → |
(semiconvergent)
19 equal divisions of 7/4 (abbreviated 19ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 19 equal parts of about 51 ¢ each. Each step represents a frequency ratio of (7/4)1/19, or the 19th root of 7/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 51 | |
| 2 | 102 | 18/17, 19/18 |
| 3 | 153 | 23/21 |
| 4 | 204 | 17/15, 19/17 |
| 5 | 255 | 7/6, 15/13, 22/19 |
| 6 | 305.9 | 6/5, 13/11 |
| 7 | 356.9 | 11/9, 21/17 |
| 8 | 407.9 | 19/15, 23/18 |
| 9 | 458.9 | 17/13, 22/17 |
| 10 | 509.9 | 23/17 |
| 11 | 560.9 | 18/13 |
| 12 | 611.9 | |
| 13 | 662.9 | 19/13, 22/15 |
| 14 | 713.9 | |
| 15 | 764.9 | 17/11 |
| 16 | 815.9 | 21/13 |
| 17 | 866.8 | 18/11 |
| 18 | 917.8 | 22/13 |
| 19 | 968.8 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +23.8 | -15.3 | -3.4 | +18.2 | +8.5 | -3.4 | +20.3 | +20.4 | -9.0 | -21.1 | -18.7 |
| Relative (%) | +46.6 | -30.0 | -6.7 | +35.7 | +16.6 | -6.7 | +39.9 | +40.0 | -17.7 | -41.3 | -36.7 | |
| Steps (reduced) |
24 (5) |
37 (18) |
47 (9) |
55 (17) |
61 (4) |
66 (9) |
71 (14) |
75 (18) |
78 (2) |
81 (5) |
84 (8) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.3 | +20.3 | +2.9 | -6.9 | -9.8 | -6.8 | +1.6 | +14.8 | -18.7 | +2.7 | -23.2 |
| Relative (%) | -8.5 | +39.9 | +5.7 | -13.5 | -19.3 | -13.4 | +3.1 | +28.9 | -36.7 | +5.3 | -45.6 | |
| Steps (reduced) |
87 (11) |
90 (14) |
92 (16) |
94 (18) |
96 (1) |
98 (3) |
100 (5) |
102 (7) |
103 (8) |
105 (10) |
106 (11) | |