21ed11/5

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21ed11/5

22ed11/5 →

Prime factorization	3 × 7
Step size	65.0002¢
Octave	18\21ed11/5 (1170¢) (→6\7ed11/5)
Twelfth	29\21ed11/5 (1885.01¢)
Consistency limit	3
Distinct consistency limit	3

21 equal divisions of 11/5 (abbreviated 21ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 21 equal parts of about 65 ¢ each. Each step represents a frequency ratio of (11/5)^1/21, or the 21st root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	65
2	130	14/13, 15/14, 25/23
3	195.001	10/9, 19/17
4	260.001	15/13, 22/19
5	325.001	17/14
6	390.001
7	455.001	13/10, 17/13, 22/17
8	520.002	19/14
9	585.002	7/5
10	650.002	13/9, 19/13, 22/15
11	715.002	3/2
12	780.002	11/7, 14/9
13	845.003	21/13
14	910.003	17/10, 22/13
15	975.003
16	1040.003
17	1105.003	17/9, 19/10, 21/11
18	1170.004
19	1235.004
20	1300.004	19/9
21	1365.004	11/5

Harmonics

Approximation of harmonics in 21ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-30.0	-16.9	+5.0	+8.7	+18.1	+11.2	-25.0	+31.1	-21.3	+8.7	-11.9
	Relative (%)	-46.1	-26.1	+7.7	+13.4	+27.8	+17.2	-38.4	+47.8	-32.8	+13.4	-18.4
Steps (reduced)		18 (18)	29 (8)	37 (16)	43 (1)	48 (6)	52 (10)	55 (13)	59 (17)	61 (19)	64 (1)	66 (3)

Approximation of harmonics in 21ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-20.5	-18.8	-8.3	+10.0	-29.9	+1.1	-27.5	+13.7	-5.8	-21.3	+31.7
	Relative (%)	-31.6	-28.9	-12.7	+15.4	-46.1	+1.7	-42.3	+21.1	-8.9	-32.8	+48.8
Steps (reduced)		68 (5)	70 (7)	72 (9)	74 (11)	75 (12)	77 (14)	78 (15)	80 (17)	81 (18)	82 (19)	84 (0)