20edt

← 19edt

20edt

21edt →

Prime factorization	22 × 5
Step size	95.0978¢
Octave	13\20edt (1236.27¢)
Consistency limit	2
Distinct consistency limit	2

20 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 20edt or 20ed3), is a nonoctave tuning system that divides the interval of 3/1 into 20 equal parts of about 95.1 ¢ each. Each step represents a frequency ratio of 3^1/20, or the 20th root of 3. It corresponds to 12.6186 edo.

Intervals

degree	cents value	hekts	corresponding JI intervals	comments
0			exact 1/1
1	95.0978	65
2	190.1955	130
3	285.2933	195	33/28, 13/11
4	380.391	260	5/4
5	475.4888	325
6	570.5865	390	39/28
7	665.6843	455	22/15
8	760.7820	520
9	855.8798	585	18/11
10	950.9775	650	45/26, 26/15
11	1046.0753	725	11/6
12	1141.173	780
13	1236.2708	845	45/22
14	1331.3685	910	28/13
15	1426.4663	975
16	1521.564	1040	12/5
17	1616.6618	1105	33/13, 28/11
18	1711.7595	1170
19	1806.8573	1235
20	1901.955	1300	exact 3/1	just perfect fifth plus an octave

Harmonics

Approximation of harmonics in 20edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+36.3	+0.0	-22.6	-28.5	+36.3	-40.4	+13.7	+0.0	+7.8	+33.0	-22.6
	Relative (%)	+38.1	+0.0	-23.7	-29.9	+38.1	-42.5	+14.4	+0.0	+8.2	+34.7	-23.7
Steps (reduced)		13 (13)	20 (0)	25 (5)	29 (9)	33 (13)	35 (15)	38 (18)	40 (0)	42 (2)	44 (4)	45 (5)

Approximation of harmonics in 20edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+29.1	-4.1	-28.5	-45.1	+40.1	+36.3	+37.8	+44.1	-40.4	-25.8	-7.7
	Relative (%)	+30.6	-4.3	-29.9	-47.4	+42.2	+38.1	+39.7	+46.3	-42.5	-27.2	-8.1
Steps (reduced)		47 (7)	48 (8)	49 (9)	50 (10)	52 (12)	53 (13)	54 (14)	55 (15)	55 (15)	56 (16)	57 (17)