19edf
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Prime factorization
19 (prime)
Step size
36.945¢
Octave
32\19edf (1182.24¢)
Twelfth
51\19edf (1884.2¢)
Consistency limit
2
Distinct consistency limit
2
| ← 18edf | 19edf | 20edf → |
19EDF is the equal division of the just perfect fifth into 19 parts of 36.945 cents each, corresponding to 32.4807 edo (similar to every second step of 65edo). It tempers out the same commas as 65edo with the addition of |-103/19 65/19> (1.425 cents) resulting from its inexact 4/1.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.8 | -17.8 | +1.4 | -15.4 | +1.4 | -6.8 | -16.3 | +1.4 | +3.7 | -13.5 | -16.3 |
| Relative (%) | -48.1 | -48.1 | +3.9 | -41.8 | +3.9 | -18.5 | -44.2 | +3.9 | +10.1 | -36.5 | -44.2 | |
| Steps (reduced) |
32 (13) |
51 (13) |
65 (8) |
75 (18) |
84 (8) |
91 (15) |
97 (2) |
103 (8) |
108 (13) |
112 (17) |
116 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.1 | +12.4 | +3.7 | +2.9 | +8.7 | -16.3 | +0.9 | -14.0 | +12.4 | +5.7 | +2.6 |
| Relative (%) | -19.3 | +33.4 | +10.1 | +7.7 | +23.6 | -44.2 | +2.4 | -37.9 | +33.4 | +15.4 | +7.1 | |
| Steps (reduced) |
120 (6) |
124 (10) |
127 (13) |
130 (16) |
133 (0) |
135 (2) |
138 (5) |
140 (7) |
143 (10) |
145 (12) |
147 (14) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 36.945 | ||
| 2 | 73.89 | 24/23 | |
| 3 | 110.835 | 16/15 | |
| 4 | 147.78 | 12/11 | |
| 5 | 184.725 | 10/9 | |
| 6 | 221.67 | 25/22 | |
| 7 | 258.615 | 36/31 | |
| 8 | 295.56 | 19/16 | |
| 9 | 332.505 | 63/52, 40/33 | |
| 10 | 369.45 | 26/21 | |
| 11 | 406.395 | 24/19, 19/15 | |
| 12 | 443.34 | 31/24 | |
| 13 | 480.285 | 33/25 | |
| 14 | 517.23 | 27/20 | |
| 15 | 554.175 | 11/8 | |
| 16 | 591.12 | 45/32 | |
| 17 | 628.065 | 23/16 | |
| 18 | 665.01 | 22/15 | |
| 19 | 701.955 | exact 3/2 | just perfect fifth |
| 20 | 738.9 | ||
| 21 | 775.845 | ||
| 22 | 812.79 | 8/5 | |
| 23 | 849.735 | 18/11 | |
| 24 | 886.68 | 5/3 | |
| 25 | 923.625 | ||
| 26 | 960.57 | ||
| 27 | 997.515 | 16/9 | |
| 28 | 1034.46 | 20/11 | |
| 29 | 1071.405 | 13/7 | |
| 30 | 1108.35 | 36/19 | |
| 31 | 1145.295 | 31/16 | |
| 32 | 1182.24 | ||
| 33 | 1219.185 | ||
| 34 | 1256.13 | ||
| 35 | 1293.075 | ||
| 36 | 1330.02 | ||
| 37 | 1366.965 | ||
| 38 | 1403.91 | exact 9/4 | |