24ed7

← 23ed7

24ed7

25ed7 →

Prime factorization	23 × 3
Step size	140.368¢
Octave	9\24ed7 (1263.31¢) (→3\8ed7)
Twelfth	14\24ed7 (1965.15¢) (→7\12ed7)
Consistency limit	3
Distinct consistency limit	3
Special properties	Highly composite

Division of the 7th harmonic into 24 equal parts (24ed7) is related to the quanic temperament, which tempers out 352/351, 540/539, 729/728, and 1331/1323 in the 13-limit; 352/351, 442/441, 540/539, 561/560, and 715/714 in the 17-limit. The step size is about 140.3677 cents, corresponding to 8.5490 edo.

Intervals

Intervals of 24ed7

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	140.3677	13/12, 25/23
2	280.7355	20/17
3	421.1032	14/11, 65/51, 51/40, 23/18, 32/25
4	561.4710	18/13
5	701.8387	3/2
6	842.2065	13/8, 80/49
7	982.5742	30/17
8	1122.9420	21/11
9	1263.3097	56/27, 27/13
10	1403.6775	9/4
11	1544.0452	56/23, 39/16, 22/9, 120/49
12	1684.4130	119/45, 45/17
13	1824.7807	63/22, 112/39, 23/8
14	1965.1484	28/9
15	2105.5162	91/27, 27/8
16	2245.8839	11/3
17	2386.2517	119/30, 143/36
18	2526.6194	56/13
19	2666.9872	14/3
20	2807.3549	91/18
21	2947.7227	11/2
22	3088.0904	119/20
23	3228.4582	84/13
24	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of harmonics in 24ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+63.3	+63.2	-13.7	+21.0	-13.9	+0.0	+49.6	-14.0	-56.0	+59.7	+49.4
	Relative (%)	+45.1	+45.0	-9.8	+15.0	-9.9	+0.0	+35.3	-10.0	-39.9	+42.5	+35.2
Steps (reduced)		9 (9)	14 (14)	17 (17)	20 (20)	22 (22)	24 (0)	26 (2)	27 (3)	28 (4)	30 (6)	31 (7)

Approximation of harmonics in 24ed7

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+51.2	+63.3	-56.1	-27.5	+7.9	+49.3	-44.3	+7.3	+63.2	-17.3	+46.1
	Relative (%)	+36.5	+45.1	-40.0	-19.6	+5.6	+35.1	-31.5	+5.2	+45.0	-12.4	+32.8
Steps (reduced)		32 (8)	33 (9)	33 (9)	34 (10)	35 (11)	36 (12)	36 (12)	37 (13)	38 (14)	38 (14)	39 (15)

Music

Ambient Esoterica

• SQRT(7):1 | Irrational Octave Microtones (2023)