19edf

← 18edf

19edf

20edf →

Prime factorization	19 (prime)
Step size	36.945 ¢
Octave	32\19edf (1182.24 ¢)
Twelfth	51\19edf (1884.2 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

19edf corresponds to 32.4807 edo (similar to every second step of 65edo). It tempers out the same commas as 65edo with the addition of [-103/19 65/19⟩ (1.425 ¢) resulting from its inexact 4/1. It is not as similar to 32edo as 13edf and 16edf are to 22edo and 27edo.

Harmonics

Approximation of harmonics in 19edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-17.8	-17.8	+1.4	-15.4	+1.4	-6.8	-16.3	+1.4	+3.7	-13.5	-16.3
	Relative (%)	-48.1	-48.1	+3.9	-41.8	+3.9	-18.5	-44.2	+3.9	+10.1	-36.5	-44.2
Steps (reduced)		32 (13)	51 (13)	65 (8)	75 (18)	84 (8)	91 (15)	97 (2)	103 (8)	108 (13)	112 (17)	116 (2)

Approximation of harmonics in 19edf

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-7.1	+12.4	+3.7	+2.9	+8.7	-16.3	+0.9	-14.0	+12.4	+5.7	+2.6
	Relative (%)	-19.3	+33.4	+10.1	+7.7	+23.6	-44.2	+2.4	-37.9	+33.4	+15.4	+7.1
Steps (reduced)		120 (6)	124 (10)	127 (13)	130 (16)	133 (0)	135 (2)	138 (5)	140 (7)	143 (10)	145 (12)	147 (14)

Intervals

Intervals of 19edf

Degree	Cents	Corresponding JI intervals	comments
0		exact 1/1
1	36.945
2	73.89	24/23
3	110.835	16/15
4	147.78	12/11
5	184.725	10/9
6	221.67	25/22
7	258.615	36/31
8	295.56	19/16
9	332.505	63/52, 40/33
10	369.45	26/21
11	406.395	24/19, 19/15
12	443.34	31/24
13	480.285	33/25
14	517.23	27/20
15	554.175	11/8
16	591.12	45/32
17	628.065	23/16
18	665.01	22/15
19	701.955	exact 3/2	just perfect fifth
20	738.9
21	775.845
22	812.79	8/5
23	849.735	18/11
24	886.68	5/3
25	923.625
26	960.57
27	997.515	16/9
28	1034.46	20/11
29	1071.405	13/7
30	1108.35	36/19
31	1145.295	31/16
32	1182.24
33	1219.185
34	1256.13
35	1293.075
36	1330.02
37	1366.965
38	1403.91	exact 9/4