21ed5/2

← 20ed5/2

21ed5/2

22ed5/2 →

Prime factorization	3 × 7
Step size	75.5387 ¢
Octave	16\21ed5/2 (1208.62 ¢) (semiconvergent)
Twelfth	25\21ed5/2 (1888.47 ¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	6

21ed5/2 is the equal division of the 5/2 interval into 21 parts of approximately 75.539 cents each. It roughly corresponds to 16edo.

Theory

From a no-threes point of view, 21ed5/2 tempers out 50/49 in the 7-limit (being a jubilic system similar to 13ed5/2), 625/616 and 176/175 in the 11-limit, and 143/140, 715/686 and 847/845 in the 13-limit. It is not particularly excellent as a no-threes system with the 5/4 and 7/4 being noticeably off, but can work for 5/2-equivalent jubilic.

Harmonics

Approximation of harmonics in 21ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.6	-13.5	+17.2	+8.6	-4.9	+30.4	+25.9	-27.0	+17.2	+3.3	+3.8
	Relative (%)	+11.4	-17.9	+22.8	+11.4	-6.4	+40.3	+34.2	-35.7	+22.8	+4.4	+5.0
Steps (reduced)		16 (16)	25 (4)	32 (11)	37 (16)	41 (20)	45 (3)	48 (6)	50 (8)	53 (11)	55 (13)	57 (15)

Interval table

Steps	Cents	Jubilic[8] notation	Approximate ratios*
0	0.000	J	1/1
1	75.539	J&	26/25
2	151.078	K@	35/32
3			8/7, 28/25
4			13/11, 77/64
5			5/4, 11/9, 16/13, 49/40
6				13/10, 32/25
7				11/8, 35/26
8				7/5, 10/7
9				16/11, 52/35
10				11/7, 20/13, 25/16, 49/32
11				8/5, 13/8
12				22/13, 55/32
13				} * Based on treating 21ed5/2 as a no-threes 13-limit temperament Steps Cents Approximate ratios 0 0 1/1 1 75.5 21/20, 22/21, 23/22, 24/23, 25/24 2 151.1 11/10, 12/11, 13/12, 23/21, 25/23 3 226.6 8/7, 17/15, 25/22 4 302.2 6/5, 13/11, 25/21 5 377.7 5/4, 21/17 6 453.2 13/10, 17/13, 22/17 7 528.8 15/11, 23/17 8 604.3 10/7, 17/12, 24/17 9 679.8 25/17 10 755.4 17/11, 20/13 11 830.9 13/8, 21/13 12 906.5 17/10, 22/13 13 982 7/4, 23/13 14 1057.5 11/6, 13/7, 24/13 15 1133.1 21/11, 23/12, 25/13 16 1208.6 2/1 17 1284.2 19/9, 21/10, 23/11, 25/12 18 1359.7 11/5, 24/11 19 1435.2 16/7, 23/10, 25/11 20 1510.8 12/5 21 1586.3 5/2