18edf
18EDF is the equal division of the just perfect fifth into 18 parts of 38.9975 cents each, corresponding to 30.7712 edo.
| ← 17edf | 18edf | 19edf → |
It is related to the regular temperament which tempers out 2401/2400 and 8589934592/8544921875 in the 7-limit; with 5632/5625, 46656/46585, and 166698/166375 in the 11-limit, which is supported by 31edo, 369edo, 400edo, 431edo, and 462edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.9 | +8.9 | -17.5 | -15.0 | -17.6 | +5.2 | +8.7 | +11.2 | -7.6 | -18.9 | -17.4 |
| Relative (%) | +22.9 | +22.9 | -44.9 | -38.6 | -45.1 | +13.3 | +22.4 | +28.6 | -19.5 | -48.6 | -44.7 | |
| Steps (reduced) |
31 (13) |
49 (13) |
71 (17) |
86 (14) |
106 (16) |
114 (6) |
126 (0) |
131 (5) |
139 (13) |
149 (5) |
152 (8) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 38.9975 | 45/44 | |
| 2 | 77.995 | ||
| 3 | 116.9925 | 16/15 | |
| 4 | 155.99 | 128/117 | |
| 5 | 194.9875 | 28/25 | |
| 6 | 233.985 | 8/7 | |
| 7 | 272.9825 | 7/6 | |
| 8 | 311.98 | 6/5 | |
| 9 | 350.9775 | 60/49, 49/40 | |
| 10 | 389.975 | 5/4 | |
| 11 | 428.9725 | 9/7 | |
| 12 | 467.97 | ||
| 13 | 506.9675 | 75/56 | |
| 14 | 545.965 | ||
| 15 | 584.9625 | ||
| 16 | 623.96 | ||
| 17 | 662.9575 | 22/15 | |
| 18 | 701.955 | exact 3/2 | just perfect fifth |
| 19 | 740.9525 | 135/88 | |
| 20 | 779.95 | ||
| 21 | 818.9475 | 8/5 | |
| 22 | 857.945 | 64/39 | |
| 23 | 896.9425 | 42/25 | |
| 24 | 935.94 | 12/7 | |
| 25 | 974.9375 | 7/4 | |
| 26 | 1013.935 | 9/5 | |
| 27 | 1052.9325 | 90/49, 147/80 | |
| 28 | 1091.93 | 15/8 | |
| 29 | 1130.9275 | 27/14 | |
| 30 | 1169.925 | ||
| 31 | 1208.9225 | 225/112 | |
| 32 | 1247.92 | ||
| 33 | 1286.9175 | ||
| 34 | 1325.915 | ||
| 35 | 1364.9125 | ||
| 36 | 1403.91 | exact 9/4 | |
Related regular temperaments
The rank-two regular temperament supported by 31edo and 369edo has three equal divisions of the interval which equals an octave minus the step interval of 18EDF as a generator.
7-limit 31&369
Commas: 2401/2400, 8589934592/8544921875
POTE generator: ~5/4 = 386.997
Mapping: [<1 19 2 7|, <0 -54 1 -13|]
11-limit 31&369
Commas: 2401/2400, 5632/5625, 46656/46585
POTE generator: ~5/4 = 386.999
Mapping: [<1 19 2 7 37|, <0 -54 1 -13 -104|]
EDOs: 31, 369, 400, 431, 462
13-limit 31&369
Commas: 1001/1000, 1716/1715, 4096/4095, 46656/46585
POTE generator: ~5/4 = 387.003
Mapping: [<1 19 2 7 37 -35|, <0 -54 1 -13 -104 120|]
EDOs: 31, 369, 400, 431, 462