24edf

← 23edf

24edf

25edf →

Prime factorization	23 × 3
Step size	29.2481¢
Octave	41\24edf (1199.17¢) (convergent)
Twelfth	65\24edf (1901.13¢) (convergent)
Consistency limit	16
Distinct consistency limit	7
Special properties	Highly composite

Division of the just perfect fifth into 24 equal parts (24EDF) is related to 41 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 0.8269 cents compressed and the step size is about 29.2481 cents. It is consistent to the 16-integer-limit.

Lookalikes: 41edo, 65edt, 95ed5

Harmonics

Approximation of prime harmonics in 24edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.8	-0.8	-7.7	-5.3	+1.9	+5.2	+8.7	-8.3	+11.9	-9.2	-7.7
	Relative (%)	-2.8	-2.8	-26.5	-18.1	+6.6	+17.7	+29.8	-28.5	+40.6	-31.5	-26.2
Steps (reduced)		41 (17)	65 (17)	95 (23)	115 (19)	142 (22)	152 (8)	168 (0)	174 (6)	186 (18)	199 (7)	203 (11)

Approximation of prime harmonics in 24edf

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+7.8	+5.5	+10.8	+3.1	-0.2	-10.4	-9.6	+3.5	-9.2	+1.2	+10.7
	Relative (%)	+26.5	+18.9	+37.0	+10.5	-0.7	-35.5	-32.8	+11.9	-31.3	+4.2	+36.7
Steps (reduced)		214 (22)	220 (4)	223 (7)	228 (12)	235 (19)	241 (1)	243 (3)	249 (9)	252 (12)	254 (14)	259 (19)

Intervals

Intervals of 24edf

	Cents Value	Approximate Ratios in the 11-limit
0		1/1
1	29.2481	81/80
2	58.49625	25/24, 28/27, 33/32
3	87.7444	21/20, 22/21
4	116.9925	16/15, 15/14
5	146.2406	12/11
6	175.48875	10/9, 11/10
7	204.7369	9/8
8	233.985	8/7
9	263.2331	7/6, 32/25
10	292.48125	32/27
11	321.7293	6/5
12	350.9775	11/9,27/22
13	380.2256	5/4
14	409.47375	14/11, 81/64
15	438.7219	9/7
16	467.97	21/16
17	497.2181	4/3
18	526.46625	15/11, 27/20
19	556.7144	11/8
20	584.9625	7/5
21	614.2106	10/7
22	643.45875	16/11
23	671.7069	22/15, 40/27
24	701.955	3/2
25	731.2031	32/21
26	760.45125	14/9, 25/16
27	789.6994	11/7, 128/81
28	818.9475	8/5
29	848.1956	18/11, 44/27
30	877.44375	5/3
31	906.6919	27/16
32	935.94	12/7
33	965.1881	7/4
34	994.43625	16/9
35	1023.6844	9/5, 20/11
36	1052.9325	11/6
37	1082.1806	15/8
38	1111.42875	40/21, 21/11
39	1140.6769	48/25, 27/14, 64/33
40	1169.925	160/81
41	1199.1731	2/1
42	1228.42125	81/40
43	1257.6694	25/12, 56/27, 33/16
44	1286.9175	21/10, 44/21
45	1316.1656	32/15, 15/7
46	1345.41375	24/11
47	1374.6619	20/9, 11/5
48	1403.91	9/4

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