23ed11/5

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 22ed11/5

23ed11/5

24ed11/5 →

Prime factorization	23 (prime)
Step size	59.348¢
Octave	20\23ed11/5 (1186.96¢)
Twelfth	32\23ed11/5 (1899.14¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	4

23 equal divisions of 11/5 (abbreviated 23ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 23 equal parts of about 59.3 ¢ each. Each step represents a frequency ratio of (11/5)^1/23, or the 23rd root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	59.348
2	118.696	14/13, 15/14
3	178.044	10/9, 11/10, 21/19
4	237.392	15/13, 23/20
5	296.74	13/11, 25/21
6	356.088	11/9, 21/17
7	415.436	14/11, 19/15, 23/18
8	474.784	17/13, 25/19
9	534.132	15/11, 19/14
10	593.48	7/5
11	652.828	19/13, 22/15
12	712.176	3/2
13	771.524	11/7, 14/9
14	830.872	21/13
15	890.22	5/3
16	949.568	19/11
17	1008.916	9/5, 25/14
18	1068.264	13/7
19	1127.612	21/11, 23/12, 25/13
20	1186.96	2/1
21	1246.308
22	1305.656	19/9
23	1365.004	11/5

Harmonics

Approximation of harmonics in 23ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-13.0	-2.8	-26.1	+3.0	-15.9	+14.0	+20.2	-5.6	-10.0	+3.0	-28.9
	Relative (%)	-22.0	-4.7	-43.9	+5.1	-26.7	+23.6	+34.1	-9.5	-16.8	+5.1	-48.7
Steps (reduced)		20 (20)	32 (9)	40 (17)	47 (1)	52 (6)	57 (11)	61 (15)	64 (18)	67 (21)	70 (1)	72 (3)

Approximation of harmonics in 23ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.6	+1.0	+0.2	+7.2	+20.9	-18.7	+6.4	-23.0	+11.2	-10.0	-27.6
	Relative (%)	+17.8	+1.6	+0.4	+12.1	+35.3	-31.5	+10.8	-38.8	+18.9	-16.8	-46.5
Steps (reduced)		75 (6)	77 (8)	79 (10)	81 (12)	83 (14)	84 (15)	86 (17)	87 (18)	89 (20)	90 (21)	91 (22)