36ed11/5

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36ed11/5

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Prime factorization	22 × 32
Step size	37.9168¢
Octave	32\36ed11/5 (1213.34¢) (→8\9ed11/5)
Twelfth	50\36ed11/5 (1895.84¢) (→25\18ed11/5)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

36 equal divisions of 11/5 (abbreviated 36ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 36 equal parts of about 37.9 ¢ each. Each step represents a frequency ratio of (11/5)^1/36, or the 36th root of 11/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	37.917
2	75.834	22/21, 23/22
3	113.75
4	151.667	23/21
5	189.584	10/9, 19/17, 29/26
6	227.501
7	265.417	7/6
8	303.334
9	341.251	11/9
10	379.168
11	417.085	19/15, 23/18
12	455.001	13/10
13	492.918
14	530.835	15/11, 23/17
15	568.752	18/13
16	606.669	27/19
17	644.585	13/9, 29/20
18	682.502
19	720.419
20	758.336	17/11
21	796.252	27/17
22	834.169	21/13
23	872.086
24	910.003	22/13
25	947.92	19/11
26	985.836	23/13
27	1023.753	9/5
28	1061.67
29	1099.587	17/9
30	1137.504
31	1175.42
32	1213.337
33	1251.254
34	1289.171	19/9, 21/10
35	1327.087
36	1365.004	11/5

Harmonics

Approximation of harmonics in 36ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.3	-6.1	-11.2	-18.4	+7.2	+5.8	+2.1	-12.2	-5.1	-18.4	-17.4
	Relative (%)	+35.2	-16.1	-29.7	-48.5	+19.0	+15.2	+5.5	-32.3	-13.3	-48.5	-45.8
Steps (reduced)		32 (32)	50 (14)	63 (27)	73 (1)	82 (10)	89 (17)	95 (23)	100 (28)	105 (33)	109 (1)	113 (5)

Approximation of harmonics in 36ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	-18.8	+13.4	+15.4	-13.7	+1.1	-16.7	+8.3	-0.3	-5.1	-6.2
	Relative (%)	-11.2	-49.6	+35.4	+40.7	-36.1	+2.9	-43.9	+21.9	-0.9	-13.3	-16.3
Steps (reduced)		117 (9)	120 (12)	124 (16)	127 (19)	129 (21)	132 (24)	134 (26)	137 (29)	139 (31)	141 (33)	143 (35)