27ed5/4

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27ed5/4

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Prime factorization	33
Step size	14.3079¢
Octave	84\27ed5/4 (1201.86¢) (→28\9ed5/4)
Twelfth	133\27ed5/4 (1902.95¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	6

27 equal divisions of 5/4 (abbreviated 27ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 27 equal parts of about 14.3 ¢ each. Each step represents a frequency ratio of (5/4)^1/27, or the 27th root of 5/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	14.3
2	28.6
3	42.9
4	57.2	26/25
5	71.5	23/22, 25/24
6	85.8	19/18, 22/21
7	100.2	17/16, 18/17, 20/19
8	114.5	16/15
9	128.8	13/12, 14/13, 15/14
10	143.1
11	157.4	11/10, 12/11, 23/21
12	171.7	21/19
13	186	10/9, 19/17
14	200.3	9/8
15	214.6	17/15, 26/23
16	228.9	25/22
17	243.2
18	257.5	7/6, 15/13, 22/19
19	271.9
20	286.2	13/11, 19/16, 20/17
21	300.5
22	314.8	6/5
23	329.1	23/19
24	343.4	11/9, 17/14
25	357.7	21/17
26	372	26/21
27	386.3	5/4

Harmonics

Approximation of harmonics in 27ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.86	+1.00	+3.73	+3.73	+2.86	-6.47	+5.59	+2.00	+5.59	-2.02	+4.73
	Relative (%)	+13.0	+7.0	+26.1	+26.1	+20.0	-45.2	+39.1	+13.9	+39.1	-14.1	+33.0
Steps (reduced)		84 (3)	133 (25)	168 (6)	195 (6)	217 (1)	235 (19)	252 (9)	266 (23)	279 (9)	290 (20)	301 (4)

Approximation of harmonics in 27ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.07	-4.60	+4.73	-6.85	+2.66	+3.86	-3.90	-6.85	-5.47	-0.16	-5.57
	Relative (%)	-35.5	-32.2	+33.0	-47.9	+18.6	+27.0	-27.2	-47.9	-38.2	-1.1	-39.0
Steps (reduced)		310 (13)	319 (22)	328 (4)	335 (11)	343 (19)	350 (26)	356 (5)	362 (11)	368 (17)	374 (23)	379 (1)