43ed5/2

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43ed5/2

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Prime factorization	43 (prime)
Step size	36.891¢
Octave	33\43ed5/2 (1217.4¢)
Twelfth	52\43ed5/2 (1918.33¢)
Consistency limit	3
Distinct consistency limit	3

43 equal divisions of 5/2 (abbreviated 43ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 43 equal parts of about 36.9 ¢ each. Each step represents a frequency ratio of (5/2)^1/43, or the 43rd root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	36.9
2	73.8
3	110.7
4	147.6
5	184.5	10/9, 29/26
6	221.3	25/22
7	258.2
8	295.1
9	332	17/14, 23/19
10	368.9	21/17, 26/21
11	405.8	29/23
12	442.7
13	479.6
14	516.5	27/20
15	553.4	29/21
16	590.3
17	627.1
18	664	22/15
19	700.9	3/2
20	737.8	26/17, 29/19
21	774.7
22	811.6
23	848.5
24	885.4	5/3
25	922.3	29/17
26	959.2
27	996.1
28	1032.9
29	1069.8	13/7
30	1106.7
31	1143.6
32	1180.5
33	1217.4
34	1254.3	29/14
35	1291.2
36	1328.1
37	1365	11/5
38	1401.9	9/4
39	1438.7
40	1475.6
41	1512.5
42	1549.4	22/9
43	1586.3	5/2

Harmonics

Approximation of harmonics in 43ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+17.4	+16.4	-2.1	+17.4	-3.1	-11.7	+15.3	-4.1	-2.1	+17.4	+14.3
	Relative (%)	+47.2	+44.4	-5.6	+47.2	-8.4	-31.8	+41.5	-11.2	-5.6	+47.1	+38.7
Steps (reduced)		33 (33)	52 (9)	65 (22)	76 (33)	84 (41)	91 (5)	98 (12)	103 (17)	108 (22)	113 (27)	117 (31)

Approximation of harmonics in 43ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-13.6	+5.7	-3.1	-4.2	+1.5	+13.3	-6.6	+15.3	+4.6	-2.1	-5.3
	Relative (%)	-36.9	+15.3	-8.4	-11.3	+4.2	+36.0	-17.8	+41.5	+12.6	-5.7	-14.4
Steps (reduced)		120 (34)	124 (38)	127 (41)	130 (1)	133 (4)	136 (7)	138 (9)	141 (12)	143 (14)	145 (16)	147 (18)