21ed7/3

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21ed7/3

22ed7/3 →

Prime factorization	3 × 7
Step size	69.851¢
Octave	17\21ed7/3 (1187.47¢)
Twelfth	27\21ed7/3 (1885.98¢) (→9\7ed7/3)
Consistency limit	5
Distinct consistency limit	4

21 equal divisions of 7/3 (abbreviated 21ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 21 equal parts of about 69.9⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/21, or the 21st root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	69.9	21/20, 22/21
2	139.7	12/11, 25/23
3	209.6	9/8, 17/15
4	279.4	7/6, 20/17
5	349.3	11/9, 17/14
6	419.1	14/11, 19/15
7	489	4/3, 25/19
8	558.8	11/8
9	628.7	10/7
10	698.5	3/2
11	768.4	11/7, 14/9, 17/11
12	838.2	18/11
13	908.1	17/10
14	977.9	7/4, 23/13
15	1047.8	11/6, 20/11
16	1117.6	19/10, 21/11, 25/13
17	1187.5	2/1
18	1257.3
19	1327.2	15/7
20	1397	9/4, 20/9
21	1466.9	7/3

Harmonics

Approximation of harmonics in 21ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-12.5	-16.0	-25.1	+7.7	-28.5	-16.0	+32.3	-32.0	-4.8	-30.1	+28.8
	Relative (%)	-17.9	-22.9	-35.9	+11.1	-40.8	-22.9	+46.2	-45.7	-6.9	-43.1	+41.2
Steps (reduced)		17 (17)	27 (6)	34 (13)	40 (19)	44 (2)	48 (6)	52 (10)	54 (12)	57 (15)	59 (17)	62 (20)

Approximation of harmonics in 21ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+29.9	-28.5	-8.3	+19.7	-15.4	+25.4	+1.6	-17.3	-32.0	+27.2	+20.1
	Relative (%)	+42.9	-40.8	-11.8	+28.2	-22.0	+36.3	+2.3	-24.8	-45.7	+39.0	+28.8
Steps (reduced)		64 (1)	65 (2)	67 (4)	69 (6)	70 (7)	72 (9)	73 (10)	74 (11)	75 (12)	77 (14)	78 (15)