# 18edf

 ← 17edf 18edf 19edf →
Prime factorization 2 × 32
Step size 38.9975¢
Octave 31\18edf (1208.92¢)
Twelfth 49\18edf (1910.88¢)
Consistency limit 4
Distinct consistency limit 4

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; 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

## Intervals

degree cents value corresponding
JI intervals
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|]

EDOs: 31, 369, 400, 431, 462

### 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