24ed5

Division of the 5th harmonic into 24 equal parts (24ed5) is related to the miracle temperament. The step size about 116.0964 cents. It is similar to every third step of 31edo, but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	116.0964	16/15, 15/14
2	232.1928	8/7
3	348.2892	11/9
4	464.3856	17/13
5	580.4820	7/5
6	696.5784		meantone fifth (pseudo-3/2)
7	812.6748	8/5
8	928.7712	65/38
9	1044.8676	11/6
10	1160.9640	45/23
11	1277.0605	23/11
12	1393.1569	38/17, 85/38	meantone major second plus an octave
13	1509.2533	55/23
14	1625.3497	23/9
15	1741.4461	30/11
16	1857.5425	38/13
17	1973.6389	25/8
18	2089.7353		meantone major sixth plus an octave (pseudo-10/3)
19	2205.8317	25/7
20	2321.9281	65/17
21	2438.0245	45/11
22	2554.1209	35/8
23	2670.2173	14/3
24	2786.3137	exact 5/1	just major third plus two octaves

24ed5 as a generator

24ed5 can also be thought of as a generator of the 2.3.5.7.11.23 subgroup temperament which tempers out 225/224, 243/242, 385/384, and 529/528, which is a cluster temperament with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44 ~ 46/45 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by 31edo, 82edo, 113edo, and 144edo.