# 12edf

 ← 11edf 12edf 13edf →
Prime factorization 22 × 3
Step size 58.4963¢
Octave 21\12edf (1228.42¢) (→7\4edf)
Twelfth 33\12edf (1930.38¢) (→11\4edf)
Consistency limit 2
Distinct consistency limit 2
Special properties

12EDF is the equal division of the just perfect fifth into 12 parts of 58.49625 cents each, corresponding to 20.5141 edo (similar to every second step of 41edo). It is an intersection of 3edf~5edo and 4edf~7edo relations, and could pass as both 20edo and 21edo, with both relations nearly breaking down by this point. It is related to the dodecacot temperament, which tempers out 3087/3125 and 10976/10935 in the 7-limit.

It is a strong 3/2.5/2.7/2 subgroup system, a fact first noted by CompactStar, tempering out the commas 10976/10935 and 3125/3087, although the representation of 11/2 is more questionable. 24edf (effectively 41edo) provides a correction for 11/2. It contains the microdiatonic scale that corresponds to 12edo's diatonic scale with 2/1 compressed to 3/2.

## Intervals

degree cents value corresponding
JI intervals
0 exact 1/1
1 58.49625 28/27, 91/88, 88/85
2 116.9925 15/14
3 175.48875 10/9, 21/19
4 233.9850 8/7
5 292.48125 45/38
6 350.9775 11/9, 27/22
7 409.47375 19/15, 63/50
8 467.9700 21/16
9 526.46625 19/14
10 584.9625 7/5
11 643.4588 13/9
12 701.9550 exact 3/2 just perfect fifth
13 760.45125 273/176, 132/85
14 818.9475 8/5
15 877.44375 63/38
16 935.94 12/7
17 994.43625 135/76
18 1052.9325 11/6, 81/44
19 1111.42875 19/10
20 1169.925 63/32
21 1228.42125 57/28
22 1286.9175 21/10
23 1345.41375 13/6
24 1403.91 exact 9/4