40ed11/5

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40ed11/5

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Prime factorization	23 × 5
Step size	34.1251¢
Octave	35\40ed11/5 (1194.38¢) (→7\8ed11/5)
Twelfth	56\40ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit	3
Distinct consistency limit	3

40 equal divisions of 11/5 (abbreviated 40ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 40 equal parts of about 34.1 ¢ each. Each step represents a frequency ratio of (11/5)^1/40, or the 40th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	34.125
2	68.25	24/23
3	102.375	18/17
4	136.5	13/12, 27/25
5	170.626	11/10
6	204.751
7	238.876	23/20
8	273.001	7/6
9	307.126	25/21
10	341.251	11/9, 17/14, 28/23
11	375.376
12	409.501	24/19
13	443.626	22/17
14	477.751	29/22
15	511.877
16	546.002	26/19
17	580.127	7/5
18	614.252	10/7
19	648.377	29/20
20	682.502
21	716.627
22	750.752	17/11, 20/13
23	784.877	11/7
24	819.003	29/18
25	853.128	18/11, 23/14
26	887.253	5/3
27	921.378	17/10, 29/17
28	955.503
29	989.628	23/13, 30/17
30	1023.753	9/5
31	1057.878	24/13
32	1092.003
33	1126.128	21/11, 23/12
34	1160.254
35	1194.379	2/1
36	1228.504
37	1262.629	29/14
38	1296.754
39	1330.879	28/13
40	1365.004	11/5

Harmonics

Approximation of harmonics in 40ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.6	+9.1	-11.2	+11.9	+3.4	+9.6	-16.9	-16.0	+6.3	+11.9	-2.2
	Relative (%)	-16.5	+26.5	-32.9	+35.0	+10.1	+28.0	-49.4	-47.0	+18.5	+35.0	-6.4
Steps (reduced)		35 (35)	56 (16)	70 (30)	82 (2)	91 (11)	99 (19)	105 (25)	111 (31)	117 (37)	122 (2)	126 (6)

Approximation of harmonics in 40ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	+3.9	-13.1	+11.6	+9.1	+12.5	-12.9	+0.7	-15.5	+6.3	-2.4
	Relative (%)	-12.5	+11.5	-38.5	+34.1	+26.5	+36.6	-37.7	+2.1	-45.5	+18.5	-7.0
Steps (reduced)		130 (10)	134 (14)	137 (17)	141 (21)	144 (24)	147 (27)	149 (29)	152 (32)	154 (34)	157 (37)	159 (39)