19ed11

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19ed11

20ed11 →

Prime factorization	19 (prime)
Step size	218.49¢
Octave	5\19ed11 (1092.45¢)
Twelfth	9\19ed11 (1966.41¢)
Consistency limit	2
Distinct consistency limit	2

19 equal divisions of the 11th harmonic (abbreviated 19ed11) is a nonoctave tuning system that divides the interval of 11/1 into 19 equal parts of about 218 ¢ each. Each step represents a frequency ratio of 11^1/19, or the 19th root of 11. It is similar to every second step of 11edo.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	218.4904	(17/15)
2	436.9808	(9/7)
3	655.4713	187/128, 19/13
4	873.9617	48/29, 53/32, 58/35
5	1092.4521	(15/8), 216/115, (32/17)
6	1310.9425	32/15
7	1529.4329	121/50, 46/19
8	1747.9233	(11/4)
9	1966.4138	28/9, 187/60
10	2184.9042	60/17, 272/77, 99/28
11	2403.3946	(4/1)
12	2621.8850	209/46, 50/11
13	2840.3754	165/32
14	3058.8659
15	3277.3563
16	3495.8467	143/19, 128/17
17	3714.3371	1000/117
18	3932.8275
19	4151.3179	exact 11/1	undecimal fourth plus three octaves

Harmonics

Approximation of harmonics in 19ed11

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-107.5	+64.5	+3.4	+54.1	-43.1	-91.5	-104.2	-89.6	-53.5	+0.0	+67.9
	Relative (%)	-49.2	+29.5	+1.6	+24.7	-19.7	-41.9	-47.7	-41.0	-24.5	+0.0	+31.1
Steps (reduced)		5 (5)	9 (9)	11 (11)	13 (13)	14 (14)	15 (15)	16 (16)	17 (17)	18 (18)	19 (0)	20 (1)

Approximation of harmonics in 19ed11

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-70.7	+19.5	-100.0	+6.8	-98.2	+21.4	-72.2	+57.5	-27.0	-107.5	+34.0
	Relative (%)	-32.4	+8.9	-45.8	+3.1	-44.9	+9.8	-33.1	+26.3	-12.4	-49.2	+15.6
Steps (reduced)		20 (1)	21 (2)	21 (2)	22 (3)	22 (3)	23 (4)	23 (4)	24 (5)	24 (5)	24 (5)	25 (6)