20ed7/3

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20ed7/3

21ed7/3 →

Prime factorization	22 × 5
Step size	73.3435¢
Octave	16\20ed7/3 (1173.5¢) (→4\5ed7/3)
Twelfth	26\20ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	3
Distinct consistency limit	2

20 equal divisions of 7/3 (abbreviated 20ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 20 equal parts of about 73.3 ¢ each. Each step represents a frequency ratio of (7/3)^1/20, or the 20th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	73.344	22/21, 23/22
2	146.687	23/21, 25/23
3	220.031	17/15, 25/22
4	293.374	13/11, 25/21
5	366.718	21/17
6	440.061	9/7, 22/17, 23/18
7	513.405	23/17
8	586.748	7/5
9	660.092	19/13, 22/15, 25/17
10	733.435	23/15
11	806.779
12	880.123	5/3
13	953.466	19/11
14	1026.81	9/5
15	1100.153	17/9
16	1173.497
17	1246.84
18	1320.184	15/7
19	1393.527
20	1466.871	7/3

Harmonics

Approximation of harmonics in 20ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-26.5	+5.0	+20.3	+0.7	-21.5	+5.0	-6.2	+10.0	-25.8	+29.3	+25.3
	Relative (%)	-36.1	+6.8	+27.7	+1.0	-29.3	+6.8	-8.4	+13.6	-35.1	+39.9	+34.5
Steps (reduced)		16 (16)	26 (6)	33 (13)	38 (18)	42 (2)	46 (6)	49 (9)	52 (12)	54 (14)	57 (17)	59 (19)

Approximation of harmonics in 20ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+33.4	-21.5	+5.7	-32.7	+9.1	-16.5	+36.5	+21.1	+10.0	+2.8	-0.9
	Relative (%)	+45.6	-29.3	+7.8	-44.5	+12.4	-22.6	+49.8	+28.7	+13.6	+3.8	-1.2
Steps (reduced)		61 (1)	62 (2)	64 (4)	65 (5)	67 (7)	68 (8)	70 (10)	71 (11)	72 (12)	73 (13)	74 (14)