42ed11/5

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42ed11/5

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Prime factorization	2 × 3 × 7
Step size	32.5001¢
Octave	37\42ed11/5 (1202.5¢)
Twelfth	59\42ed11/5 (1917.51¢)
Consistency limit	5
Distinct consistency limit	4

42 equal divisions of 11/5 (abbreviated 42ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 42 equal parts of about 32.5⁠ ⁠¢ each. Each step represents a frequency ratio of (11/5)^1/42, or the 42nd root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	32.5
2	65	25/24, 26/25
3	97.5
4	130	14/13
5	162.5	11/10
6	195	19/17, 28/25
7	227.5	8/7, 25/22
8	260	22/19
9	292.5	13/11, 19/16
10	325	23/19
11	357.5	16/13
12	390	5/4
13	422.5	14/11
14	455	13/10
15	487.5
16	520	23/17
17	552.5	11/8
18	585	7/5
19	617.5	10/7
20	650	16/11
21	682.5
22	715
23	747.5	17/11, 20/13
24	780	11/7
25	812.5	8/5
26	845	13/8
27	877.5
28	910	22/13
29	942.5	19/11
30	975	7/4
31	1007.5	25/14
32	1040	20/11
33	1072.5	13/7
34	1105	19/10
35	1137.5	25/13
36	1170
37	1202.5	2/1
38	1235
39	1267.5	25/12
40	1300	17/8
41	1332.5	13/6, 28/13
42	1365	11/5

Harmonics

Approximation of harmonics in 42ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.5	+15.6	+5.0	+8.7	-14.4	+11.2	+7.5	-1.4	+11.2	+8.7	-11.9
	Relative (%)	+7.7	+47.8	+15.4	+26.8	-44.4	+34.4	+23.1	-4.3	+34.5	+26.8	-36.7
Steps (reduced)		37 (37)	59 (17)	74 (32)	86 (2)	95 (11)	104 (20)	111 (27)	117 (33)	123 (39)	128 (2)	132 (6)

Approximation of harmonics in 42ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+12.0	+13.7	-8.3	+10.0	+2.6	+1.1	+5.0	+13.7	-5.8	+11.2	-0.8
	Relative (%)	+36.9	+42.1	-25.4	+30.8	+7.9	+3.4	+15.4	+42.2	-17.7	+34.5	-2.3
Steps (reduced)		137 (11)	141 (15)	144 (18)	148 (22)	151 (25)	154 (28)	157 (31)	160 (34)	162 (36)	165 (39)	167 (41)