23ed7/3

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23ed7/3

24ed7/3 →

Prime factorization	23 (prime)
Step size	63.777¢
Octave	19\23ed7/3 (1211.76¢)
Twelfth	30\23ed7/3 (1913.31¢)
Consistency limit	6
Distinct consistency limit	3

23 equal divisions of 7/3 (abbreviated 23ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 23 equal parts of about 63.8 ¢ each. Each step represents a frequency ratio of (7/3)^1/23, or the 23rd root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	63.777	23/22, 25/24
2	127.554	13/12, 14/13, 15/14
3	191.331	9/8, 10/9, 19/17
4	255.108	7/6, 15/13, 22/19
5	318.885	6/5, 23/19
6	382.662	5/4
7	446.439	9/7, 13/10, 22/17
8	510.216	4/3, 23/17
9	573.993	7/5, 18/13, 25/18
10	637.77	13/9
11	701.547	3/2
12	765.324	14/9, 17/11, 25/16
13	829.101	13/8, 21/13
14	892.878	5/3
15	956.655	7/4, 19/11
16	1020.432	9/5
17	1084.209	13/7, 15/8
18	1147.986
19	1211.763	2/1
20	1275.54	21/10, 23/11, 25/12
21	1339.317	13/6
22	1403.094	9/4
23	1466.871	7/3

Harmonics

Approximation of harmonics in 23ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.8	+11.4	+23.5	+19.9	+23.1	+11.4	-28.5	+22.7	+31.6	-5.8	-28.9
	Relative (%)	+18.4	+17.8	+36.9	+31.2	+36.2	+17.8	-44.7	+35.6	+49.6	-9.1	-45.3
Steps (reduced)		19 (19)	30 (7)	38 (15)	44 (21)	49 (3)	53 (7)	56 (10)	60 (14)	63 (17)	65 (19)	67 (21)

Approximation of harmonics in 23ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+23.9	+23.1	+31.2	-16.7	+5.9	-29.3	+4.6	-20.4	+22.7	+5.9	-7.2
	Relative (%)	+37.4	+36.2	+49.0	-26.2	+9.2	-45.9	+7.3	-32.0	+35.6	+9.3	-11.3
Steps (reduced)		70 (1)	72 (3)	74 (5)	75 (6)	77 (8)	78 (9)	80 (11)	81 (12)	83 (14)	84 (15)	85 (16)