27ed5/2

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27ed5/2

28ed5/2 →

Prime factorization	33
Step size	58.7524¢
Octave	20\27ed5/2 (1175.05¢)
Twelfth	32\27ed5/2 (1880.08¢)
Consistency limit	3
Distinct consistency limit	3

27 equal divisions of 5/2 (abbreviated 27ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 27 equal parts of about 58.8 ¢ each. Each step represents a frequency ratio of (5/2)^1/27, or the 27th root of 5/2.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	58.752
2	117.505	15/14
3	176.257	10/9
4	235.009
5	293.762	13/11, 25/21
6	352.514
7	411.267
8	470.019
9	528.771	23/17
10	587.524	7/5
11	646.276	19/13
12	705.028	3/2
13	763.781	14/9
14	822.533
15	881.285	5/3
16	940.038	19/11
17	998.79	25/14
18	1057.542
19	1116.295
20	1175.047
21	1233.8
22	1292.552	21/10
23	1351.304
24	1410.057	9/4
25	1468.809	7/3
26	1527.561	17/7
27	1586.314	5/2

Harmonics

Approximation of harmonics in 27ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-25.0	-21.9	+8.8	-25.0	+11.9	-19.9	-16.1	+15.0	+8.8	+20.1	-13.0
	Relative (%)	-42.5	-37.2	+15.1	-42.5	+20.3	-33.9	-27.4	+25.5	+15.1	+34.2	-22.2
Steps (reduced)		20 (20)	32 (5)	41 (14)	47 (20)	53 (26)	57 (3)	61 (7)	65 (11)	68 (14)	71 (17)	73 (19)

Approximation of harmonics in 27ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+24.7	+13.9	+11.9	+17.7	-28.5	-10.0	+13.9	-16.1	+16.9	-4.9	-23.1
	Relative (%)	+42.0	+23.6	+20.3	+30.1	-48.5	-17.0	+23.7	-27.4	+28.8	-8.3	-39.2
Steps (reduced)		76 (22)	78 (24)	80 (26)	82 (1)	83 (2)	85 (4)	87 (6)	88 (7)	90 (9)	91 (10)	92 (11)