27ed7/3

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27ed7/3

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Prime factorization	33
Step size	54.3286¢
Octave	22\27ed7/3 (1195.23¢) (semiconvergent)
Twelfth	35\27ed7/3 (1901.5¢) (convergent)
Consistency limit	12
Distinct consistency limit	5

27 equal divisions of 7/3 (abbreviated 27ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 27 equal parts of about 54.3 ¢ each. Each step represents a frequency ratio of (7/3)^1/27, or the 27th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	54.329
2	108.657	15/14, 16/15, 17/16, 18/17
3	162.986	11/10, 21/19, 23/21
4	217.314	17/15, 25/22, 26/23
5	271.643	7/6, 20/17
6	325.971	6/5, 17/14, 23/19
7	380.3	5/4, 26/21
8	434.628	9/7, 23/18
9	488.957	4/3
10	543.286	11/8, 15/11, 26/19
11	597.614	17/12, 24/17
12	651.943	16/11, 19/13, 22/15
13	706.271	3/2
14	760.6	14/9, 17/11
15	814.928	8/5
16	869.257	23/14
17	923.585	12/7, 17/10
18	977.914	7/4, 23/13
19	1032.242	20/11
20	1086.571	15/8
21	1140.9
22	1195.228	2/1
23	1249.557
24	1303.885	17/8, 19/9
25	1358.214	11/5, 24/11
26	1412.542	9/4, 25/11
27	1466.871	7/3

Harmonics

Approximation of harmonics in 27ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.8	-0.5	-9.5	-15.6	-5.2	-0.5	-14.3	-0.9	-20.3	-22.3	-10.0
	Relative (%)	-8.8	-0.8	-17.6	-28.6	-9.6	-0.8	-26.3	-1.7	-37.4	-41.1	-18.4
Steps (reduced)		22 (22)	35 (8)	44 (17)	51 (24)	57 (3)	62 (8)	66 (12)	70 (16)	73 (19)	76 (22)	79 (25)

Approximation of harmonics in 27ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+14.4	-5.2	-16.0	-19.1	-15.4	-5.7	+9.4	-25.1	-0.9	-27.1	+4.6
	Relative (%)	+26.5	-9.6	-29.5	-35.1	-28.3	-10.5	+17.2	-46.2	-1.7	-49.9	+8.4
Steps (reduced)		82 (1)	84 (3)	86 (5)	88 (7)	90 (9)	92 (11)	94 (13)	95 (14)	97 (16)	98 (17)	100 (19)