24edt

← 23edt

24edt

25edt →

Prime factorization	23 × 3
Step size	79.2481¢
Octave	15\24edt (1188.72¢) (→5\8edt)
Consistency limit	5
Distinct consistency limit	5
Special properties	highly composite

24EDT is the equal division of the third harmonic into 24 parts of 79.2481 cents each, corresponding to 15.1423 edo (similar to every seventh step of 106edo). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by 15, 106, 121, 212, and 227 EDOs.

degree	cents value	hekts	corresponding JI intervals	comments
0			exact 1/1
1	79.2481	54.167	22/21
2	158.4963	108.333		pseudo-12/11
3	237.7444	162.5	39/34, 8/7
4	316.9925	216.667	6/5
5	396.2406	270.833	44/35	pseudo-5/4
6	475.4888	325	21/16	pseudo-4/3
7	554.7369	379.167	11/8
8	633.985	433.333	75/52, 13/9
9	713.2331	487.5		pseudo-3/2
10	792.4813	541.667	30/19, 19/12
11	871.7294	595.833		pseudo-5/3
12	950.9775	650	45/26, 26/15
13	1030.2256	704.167		pseudo-9/5
14	1109.4738	758.333	36/19, 19/10
15	1188.7219	812.5		pseudooctave
16	1267.97	866.667	52/25, 27/13
17	1347.2181	920.833	24/11
18	1426.4663	975	16/7	pseudo-9/4
19	1505.7144	1029.167	105/44	pseudo-12/5 (6/5 plus pseudooctave)
20	1584.9625	1083.333	5/2
21	1664.2106	1137.5	34/13, 21/8	φ2
22	1743.4588	1191.667		pseudo-11/4 (11/8 plus pseudooctave)
23	1822.7069	1245.833.	63/22
24	1901.955	1300	exact 3/1	just perfect fifth plus an octave

Related regular temperaments

11-limit 15&106&212

Commas: 15625/15552, 585640/583443

POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597

Mapping: [<1 0 1 0 -1|, <0 24 20 0 25|, <0 0 0 1 1|]

EDOs: 15, 106, 121, 212, 227

13-limit 15&106&212

Commas: 325/324, 625/624, 468512/468195

POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727

Mapping: [<1 0 1 0 -1 0|, <0 24 20 0 25 56|, <0 0 0 1 1 0|]

EDOs: 15, 106, 121, 212, 227