11edf

← 10edf

11edf

12edf →

Prime factorization	11 (prime)
Step size	63.8141¢
Octave	19\11edf (1212.47¢)
Twelfth	30\11edf (1914.42¢)
Consistency limit	7
Distinct consistency limit	4

11 equal divisions of the perfect fifth (abbreviated 11edf or 11ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 11 equal parts of about 63.8⁠ ⁠¢ each. Each step represents a frequency ratio of (3/2)^1/11, or the 11th root of 3/2. It corresponds to 18.8046edo, is is similar to 19edo, and nearly identical to Carlos Beta.

While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo, being about four cents flat of that of 7edo.

11edf represents the upper bound of the phoenix tuning range. 11edf benefits from all the desirable properties of phoenix tuning systems.

Harmonics

Approximation of harmonics in 11edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Error	Absolute (¢)	+12.47	+12.47	+24.94	+21.51	+24.94	+13.32	-26.41	+24.94	-29.84	-3.40	-26.41	+26.46	+25.79	-29.84	-13.94
	Relative (%)	+19.5	+19.5	+39.1	+33.7	+39.1	+20.9	-41.4	+39.1	-46.8	-5.3	-41.4	+41.5	+40.4	-46.8	-21.8
Steps (reduced)		19 (8)	30 (8)	38 (5)	44 (0)	49 (5)	53 (9)	56 (1)	60 (5)	62 (7)	65 (10)	67 (1)	70 (4)	72 (6)	73 (7)	75 (9)

Intervals

Degree	Cent value	Corresponding JI intervals	Comments
0		exact 1/1
1	63.8141	(28/27), (27/26)
2	127.6282	14/13
3	191.4423
4	255.2564
5	319.07045	6/5
6	382.8845	5/4
7	446.6986
8	510.5127
9	574.3268	39/28
10	638.1409	(13/9)
11	701.955	exact 3/2	just perfect fifth
12	765.7691	14/9, 81/52
13	828.5732	21/13
14	893.3973
15	956.2114
16	1020.0255	9/5
17	1084.8395	15/8
18	1148.6536
19	1211.4677
20	1276.2816	117/56
21	1340.0959	13/6
22	1403.91	exact 9/4