32ed11/5

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32ed11/5

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Prime factorization	25
Step size	42.6564¢
Octave	28\32ed11/5 (1194.38¢) (→7\8ed11/5)
Twelfth	45\32ed11/5 (1919.54¢)
Consistency limit	2
Distinct consistency limit	2

32 equal divisions of 11/5 (abbreviated 32ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 32 equal parts of about 42.7 ¢ each. Each step represents a frequency ratio of (11/5)^1/32, or the 32nd root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	42.656
2	85.313	19/18, 23/22
3	127.969	14/13, 15/14
4	170.626	11/10, 21/19
5	213.282	17/15, 25/22, 26/23
6	255.938	15/13
7	298.595
8	341.251	17/14, 28/23
9	383.907	5/4
10	426.564	14/11
11	469.22	17/13
12	511.877
13	554.533	11/8
14	597.189	17/12, 24/17
15	639.846	16/11
16	682.502
17	725.158
18	767.815	25/16
19	810.471	8/5
20	853.128	23/14
21	895.784
22	938.44	12/7
23	981.097	23/13
24	1023.753
25	1066.41	13/7, 24/13
26	1109.066
27	1151.722
28	1194.379	2/1
29	1237.035
30	1279.691	23/11
31	1322.348	15/7, 28/13
32	1365.004	11/5

Harmonics

Approximation of harmonics in 32ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.6	+17.6	-11.2	-13.6	+12.0	+1.0	-16.9	-7.5	-19.3	-13.6	+6.3
	Relative (%)	-13.2	+41.2	-26.4	-32.0	+28.0	+2.4	-39.5	-17.6	-45.2	-32.0	+14.9
Steps (reduced)		28 (28)	45 (13)	56 (24)	65 (1)	73 (9)	79 (15)	84 (20)	89 (25)	93 (29)	97 (1)	101 (5)

Approximation of harmonics in 32ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	-4.6	+3.9	+20.2	+0.5	-13.1	+21.3	+17.8	+18.6	-19.3	-10.9
	Relative (%)	-10.0	-10.8	+9.2	+47.3	+1.2	-30.7	+49.8	+41.6	+43.6	-45.2	-25.6
Steps (reduced)		104 (8)	107 (11)	110 (14)	113 (17)	115 (19)	117 (21)	120 (24)	122 (26)	124 (28)	125 (29)	127 (31)