27ed7/4

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27ed7/4

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Prime factorization	33
Step size	35.8824¢
Octave	33\27ed7/4 (1184.12¢) (→11\9ed7/4)
Twelfth	53\27ed7/4 (1901.77¢) (convergent)
Consistency limit	3
Distinct consistency limit	3

27 equal divisions of 7/4 (abbreviated 27ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 27 equal parts of about 35.9 ¢ each. Each step represents a frequency ratio of (7/4)^1/27, or the 27th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	35.882
2	71.765	22/21, 23/22
3	107.647
4	143.53
5	179.412	10/9, 21/19
6	215.295	17/15, 26/23
7	251.177	15/13, 22/19, 23/20
8	287.06	13/11
9	322.942	23/19
10	358.824	21/17, 26/21
11	394.707
12	430.589	9/7, 23/18
13	466.472	17/13
14	502.354
15	538.237	15/11, 19/14, 26/19
16	574.119	7/5
17	610.001	10/7
18	645.884	13/9, 19/13
19	681.766
20	717.649
21	753.531	17/11
22	789.414	11/7
23	825.296	21/13
24	861.179	23/14
25	897.061
26	932.943
27	968.826

Harmonics

Approximation of harmonics in 27ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-15.9	-0.2	+4.1	+12.5	-16.1	+4.1	-11.8	-0.4	-3.4	+11.0	+3.9
	Relative (%)	-44.3	-0.5	+11.5	+34.9	-44.8	+11.5	-32.8	-1.0	-9.4	+30.8	+11.0
Steps (reduced)		33 (6)	53 (26)	67 (13)	78 (24)	86 (5)	94 (13)	100 (19)	106 (25)	111 (3)	116 (8)	120 (12)

Approximation of harmonics in 27ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+8.9	-11.8	+12.3	+8.2	+10.9	-16.3	-2.2	+16.6	+3.9	-4.8	-10.0
	Relative (%)	+24.8	-32.8	+34.4	+23.0	+30.5	-45.3	-6.1	+46.4	+11.0	-13.5	-27.9
Steps (reduced)		124 (16)	127 (19)	131 (23)	134 (26)	137 (2)	139 (4)	142 (7)	145 (10)	147 (12)	149 (14)	151 (16)