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	36.891
2	73.782
3	110.673
4	147.564
5	184.455	10/9, 29/26
6	221.346	25/22
7	258.237
8	295.128
9	332.019	17/14, 23/19
10	368.91	21/17, 26/21
11	405.801	29/23
12	442.692
13	479.583
14	516.474	27/20
15	553.365	29/21
16	590.256
17	627.147
18	664.038	22/15
19	700.929	3/2
20	737.82	26/17, 29/19
21	774.711
22	811.602
23	848.493
24	885.384	5/3
25	922.275	29/17
26	959.166
27	996.057
28	1032.948
29	1069.839	13/7
30	1106.73
31	1143.622
32	1180.513
33	1217.404
34	1254.295	29/14
35	1291.186
36	1328.077
37	1364.968	11/5
38	1401.859	9/4
39	1438.75
40	1475.641
41	1512.532
42	1549.423	22/9
43	1586.314	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)