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	114.286	14/13, 15/14
2	228.571	17/15
3	342.857	17/14
4	457.143	13/10, 17/13, 22/17
5	571.429	7/5
6	685.714
7	800
8	914.286	17/10, 22/13
9	1028.571
10	1142.857
11	1257.143
12	1371.429	11/5, 20/9
13	1485.714
14	1600
15	1714.286
16	1828.571
17	1942.857
18	2057.143	23/7
19	2171.429
20	2285.714
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