42ed11/5

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 41ed11/5

42ed11/5

43ed11/5 →

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	162.501	11/10
6	195.001	19/17, 28/25
7	227.501	8/7, 25/22
8	260.001	22/19
9	292.501	13/11, 19/16
10	325.001	23/19
11	357.501	16/13
12	390.001	5/4
13	422.501	14/11
14	455.001	13/10
15	487.502
16	520.002	23/17
17	552.502	11/8
18	585.002	7/5
19	617.502	10/7
20	650.002	16/11
21	682.502
22	715.002
23	747.502	17/11, 20/13
24	780.002	11/7
25	812.503	8/5
26	845.003	13/8
27	877.503
28	910.003	22/13
29	942.503	19/11
30	975.003	7/4
31	1007.503	25/14
32	1040.003	20/11
33	1072.503	13/7
34	1105.003	19/10
35	1137.504	25/13
36	1170.004
37	1202.504	2/1
38	1235.004
39	1267.504	25/12
40	1300.004	17/8
41	1332.504	13/6, 28/13
42	1365.004	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)