19/16
19/16 is a 19-limit interval, 297.5 cents in size, the otonal minor third or octave-reduced 19th harmonic, which is extremely close to the minor third of 12edo (300 cents). It is an undevicesimal comma aka Boethius' comma (513/512) above the Pythagorean minor third.
| Interval information |
octave-reduced 19th harmonic
reduced harmonic
[sound info]
Approximation
Following edos (up to 200) contain good approximations of the interval 19/16.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 4 | 1\4 | 300.00 | +2.49 | +0.83 |
| 8 | 2\8 | 300.00 | +2.49 | +1.66 |
| 12 | 3\12 | 300.00 | +2.49 | +2.49 |
| 16 | 4\16 | 300.00 | +2.49 | +3.32 |
| 20 | 5\20 | 300.00 | +2.49 | +4.14 |
| 24 | 6\24 | 300.00 | +2.49 | +4.97 |
| 28 | 7\28 | 300.00 | +2.49 | +5.80 |
| 32 | 8\32 | 300.00 | +2.49 | +6.63 |
| 36 | 9\36 | 300.00 | +2.49 | +7.46 |
| 85 | 21\85 | 296.47 | -1.04 | -7.38 |
| 89 | 22\89 | 296.63 | -0.88 | -6.55 |
| 93 | 23\93 | 296.77 | -0.74 | -5.73 |
| 97 | 24\97 | 296.91 | -0.61 | -4.90 |
| 101 | 25\101 | 297.03 | -0.48 | -4.07 |
| 105 | 26\105 | 297.14 | -0.37 | -3.24 |
| 109 | 27\109 | 297.25 | -0.27 | -2.41 |
| 113 | 28\113 | 297.35 | -0.17 | -1.58 |
| 117 | 29\117 | 297.44 | -0.08 | -0.75 |
| 121 | 30\121 | 297.52 | +0.01 | +0.08 |
| 125 | 31\125 | 297.60 | +0.09 | +0.91 |
| 129 | 32\129 | 297.67 | +0.16 | +1.74 |
| 133 | 33\133 | 297.74 | +0.23 | +2.56 |
| 137 | 34\137 | 297.81 | +0.30 | +3.39 |
| 141 | 35\141 | 297.87 | +0.36 | +4.22 |
| 145 | 36\145 | 297.93 | +0.42 | +5.05 |
| 149 | 37\149 | 297.99 | +0.47 | +5.88 |
| 153 | 38\153 | 298.04 | +0.53 | +6.71 |
| 157 | 39\157 | 298.09 | +0.58 | +7.54 |