21ed4

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21ed4

23ed4 →

Prime factorization	3 × 7
Step size	114.286¢
Octave	11\21ed4 (1257.14¢)
Twelfth	17\21ed4 (1942.86¢)
Consistency limit	1
Distinct consistency limit	1

21 equal divisions of the 4th harmonic (abbreviated 21ed4) is a nonoctave tuning system that divides the interval of 4/1 into 21 equal parts of about 114⁠ ⁠¢ each. Each step represents a frequency ratio of 4^1/21, or the 21st root of 4. It represents every second step of 21edo.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	114.3	14/13, 15/14
2	228.6	17/15
3	342.9	17/14
4	457.1	13/10, 17/13, 22/17
5	571.4	7/5
6	685.7
7	800
8	914.3	17/10, 22/13
9	1028.6
10	1142.9
11	1257.1
12	1371.4	11/5, 20/9
13	1485.7
14	1600
15	1714.3
16	1828.6
17	1942.9
18	2057.1	23/7
19	2171.4
20	2285.7
21	2400

Harmonics

Approximation of harmonics in 21ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+57.1	+40.9	+0.0	-43.5	-16.2	-54.5	+57.1	-32.5	+13.7	-37.0	+40.9
	Relative (%)	+50.0	+35.8	+0.0	-38.0	-14.2	-47.7	+50.0	-28.4	+12.0	-32.4	+35.8
Steps (reduced)		11 (11)	17 (17)	21 (0)	24 (3)	27 (6)	29 (8)	32 (11)	33 (12)	35 (14)	36 (15)	38 (17)

Approximation of harmonics in 21ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.6	+2.6	-2.6	+0.0	+9.3	+24.7	+45.3	-43.5	-13.6	+20.1	-56.8
	Relative (%)	+14.5	+2.3	-2.2	+0.0	+8.2	+21.6	+39.7	-38.0	-11.9	+17.6	-49.7
Steps (reduced)		39 (18)	40 (19)	41 (20)	42 (0)	43 (1)	44 (2)	45 (3)	45 (3)	46 (4)	47 (5)	47 (5)

Music

• Sister equal by Chris Vaisvil — 3rd Song on that page is in 21ED4