27ed11/5

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27ed11/5

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Prime factorization	33
Step size	50.5557¢
Octave	24\27ed11/5 (1213.34¢) (→8\9ed11/5)
Twelfth	38\27ed11/5 (1921.12¢)
Consistency limit	3
Distinct consistency limit	3

27 equal divisions of 11/5 (abbreviated 27ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 27 equal parts of about 50.6 ¢ each. Each step represents a frequency ratio of (11/5)^1/27, or the 27th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	50.556
2	101.111
3	151.667	25/23
4	202.223	9/8, 19/17
5	252.779	15/13, 22/19
6	303.334
7	353.89
8	404.446	19/15
9	455.001	13/10, 17/13, 22/17
10	505.557	4/3
11	556.113
12	606.669	10/7
13	657.224	19/13, 22/15, 25/17
14	707.78	3/2
15	758.336	14/9, 17/11
16	808.891
17	859.447
18	910.003	17/10, 22/13
19	960.559	7/4, 26/15
20	1011.114
21	1061.67	13/7
22	1112.226	19/10
23	1162.781
24	1213.337
25	1263.893
26	1314.449	15/7
27	1365.004	11/5

Harmonics

Approximation of harmonics in 27ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.3	+19.2	-23.9	-5.7	-18.1	+18.4	-10.5	-12.2	+7.6	-5.7	-4.7
	Relative (%)	+26.4	+37.9	-47.2	-11.4	-35.7	+36.4	-20.9	-24.2	+15.0	-11.4	-9.3
Steps (reduced)		24 (24)	38 (11)	47 (20)	55 (1)	61 (7)	67 (13)	71 (17)	75 (21)	79 (25)	82 (1)	85 (4)

Approximation of harmonics in 27ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+8.4	-18.8	+13.4	+2.8	-1.1	+1.1	+8.6	+20.9	-13.0	+7.6	-18.8
	Relative (%)	+16.6	-37.2	+26.5	+5.5	-2.1	+2.2	+17.0	+41.4	-25.7	+15.0	-37.2
Steps (reduced)		88 (7)	90 (9)	93 (12)	95 (14)	97 (16)	99 (18)	101 (20)	103 (22)	104 (23)	106 (25)	107 (26)