21ed5/3

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 20ed5/3

21ed5/3

22ed5/3 →

Prime factorization	3 × 7
Step size	42.1123¢
Octave	28\21ed5/3 (1179.14¢) (→4\3ed5/3)
Twelfth	45\21ed5/3 (1895.05¢) (→15\7ed5/3)
Consistency limit	3
Distinct consistency limit	3

21 equal divisions of 5/3 (abbreviated 21ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 21 equal parts of about 42.1 ¢ each. Each step represents a frequency ratio of (5/3)^1/21, or the 21st root of 5/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	42.112
2	84.225	18/17, 22/21, 23/22
3	126.337	14/13, 15/14
4	168.449	10/9, 21/19, 23/21
5	210.562	17/15, 25/22
6	252.674	15/13, 22/19
7	294.786	25/21
8	336.899	17/14, 23/19
9	379.011	21/17
10	421.123	9/7, 19/15
11	463.236	13/10, 17/13, 25/19
12	505.348
13	547.46
14	589.572	7/5
15	631.685	13/9
16	673.797	22/15, 25/17
17	715.909	3/2
18	758.022	14/9
19	800.134
20	842.246	21/13
21	884.359	5/3

Harmonics

Approximation of harmonics in 21ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-20.9	-6.9	+0.4	-6.9	+14.4	+0.2	-20.5	-13.8	+14.4	+17.8	-6.5
	Relative (%)	-49.5	-16.4	+1.0	-16.4	+34.1	+0.4	-48.6	-32.8	+34.1	+42.3	-15.4
Steps (reduced)		28 (7)	45 (3)	57 (15)	66 (3)	74 (11)	80 (17)	85 (1)	90 (6)	95 (11)	99 (15)	102 (18)

Approximation of harmonics in 21ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	-20.7	-13.8	+0.8	-19.9	+7.5	-1.9	-6.5	-6.7	-3.1	+4.2
	Relative (%)	-44.5	-49.1	-32.8	+1.9	-47.3	+17.7	-4.6	-15.4	-16.0	-7.3	+10.0
Steps (reduced)		105 (0)	108 (3)	111 (6)	114 (9)	116 (11)	119 (14)	121 (16)	123 (18)	125 (20)	127 (1)	129 (3)