18edf
| ← 17edf | 18edf | 19edf → |
18EDF is the equal division of the just perfect fifth into 18 parts of 38.9975 cents each, corresponding to 30.7712 edo.
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.
Lookalikes: 31edo, 49edt, 72ed5, 80ed6
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.9 | +8.9 | +17.8 | -17.5 | +17.8 | -15.0 | -12.2 | +17.8 | -8.6 | -17.6 | -12.2 |
| Relative (%) | +22.9 | +22.9 | +45.8 | -44.9 | +45.8 | -38.6 | -31.4 | +45.8 | -22.0 | -45.1 | -31.4 | |
| Steps (reduced) |
31 (13) |
49 (13) |
62 (8) |
71 (17) |
80 (8) |
86 (14) |
92 (2) |
98 (8) |
102 (12) |
106 (16) |
110 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.2 | -6.1 | -8.6 | -3.3 | +8.7 | -12.2 | +11.2 | +0.4 | -6.1 | -8.7 | -7.6 |
| Relative (%) | +13.3 | -15.7 | -22.0 | -8.5 | +22.4 | -31.4 | +28.6 | +0.9 | -15.7 | -22.2 | -19.5 | |
| Steps (reduced) |
114 (6) |
117 (9) |
120 (12) |
123 (15) |
126 (0) |
128 (2) |
131 (5) |
133 (7) |
135 (9) |
137 (11) |
139 (13) | |
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