21ed7/4

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21ed7/4

22ed7/4 →

Prime factorization	3 × 7
Step size	46.1346¢
Octave	26\21ed7/4 (1199.5¢) (convergent)
Twelfth	41\21ed7/4 (1891.52¢) (semiconvergent)
Consistency limit	14
Distinct consistency limit	3

21 equal divisions of 7/4 (abbreviated 21ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 21 equal parts of about 46.1 ¢ each. Each step represents a frequency ratio of (7/4)^1/21, or the 21st root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	46.135
2	92.269	17/16, 18/17, 19/18, 20/19, 21/20, 22/21
3	138.404	12/11, 13/12, 14/13
4	184.538	10/9, 19/17, 21/19
5	230.673	8/7, 17/15
6	276.807	7/6, 13/11, 20/17
7	322.942	6/5, 17/14
8	369.077	16/13, 21/17
9	415.211	14/11, 19/15, 24/19
10	461.346	13/10, 17/13, 21/16, 22/17, 25/19
11	507.48	4/3
12	553.615	11/8, 18/13, 25/18
13	599.749	17/12, 24/17
14	645.884	13/9, 16/11, 19/13
15	692.019	3/2
16	738.153	20/13
17	784.288	11/7, 19/12
18	830.422	13/8, 21/13
19	876.557	5/3
20	922.691	12/7, 17/10, 22/13
21	968.826	7/4

Harmonics

Approximation of harmonics in 21ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.5	-10.4	-1.0	-18.2	-10.9	-1.0	-1.5	-20.9	-18.7	+0.8	-11.4
	Relative (%)	-1.1	-22.6	-2.2	-39.5	-23.7	-2.2	-3.3	-45.2	-40.6	+1.7	-24.8
Steps (reduced)		26 (5)	41 (20)	52 (10)	60 (18)	67 (4)	73 (10)	78 (15)	82 (19)	86 (2)	90 (6)	93 (9)

Approximation of harmonics in 21ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.6	-1.5	+17.5	-2.0	-14.7	-21.4	-22.7	-19.2	-11.4	+0.3	+15.6
	Relative (%)	-25.2	-3.3	+37.8	-4.3	-31.8	-46.3	-49.2	-41.7	-24.8	+0.6	+33.8
Steps (reduced)		96 (12)	99 (15)	102 (18)	104 (20)	106 (1)	108 (3)	110 (5)	112 (7)	114 (9)	116 (11)	118 (13)