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	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|]

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