23ed5/2

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23ed5/2

24ed5/2 →

Prime factorization	23 (prime)
Step size	68.9702¢
Octave	17\23ed5/2 (1172.49¢)
Twelfth	28\23ed5/2 (1931.16¢)
Consistency limit	2
Distinct consistency limit	2

23 equal divisions of 5/2 (abbreviated 23ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 23 equal parts of about 69 ¢ each. Each step represents a frequency ratio of (5/2)^1/23, or the 23rd root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	68.97	25/24
2	137.94	12/11, 13/12, 14/13
3	206.91	17/15
4	275.881	7/6, 13/11
5	344.851	17/14
6	413.821	14/11, 19/15, 23/18
7	482.791
8	551.761
9	620.731
10	689.702
11	758.672	17/11
12	827.642
13	896.612
14	965.582
15	1034.552
16	1103.523
17	1172.493
18	1241.463
19	1310.433	15/7
20	1379.403
21	1448.373
22	1517.344	12/5
23	1586.314	5/2

Harmonics

Approximation of harmonics in 23ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-27.5	+29.2	+14.0	-27.5	+1.7	+10.7	-13.6	-10.6	+14.0	-13.1	-25.8
	Relative (%)	-39.9	+42.4	+20.2	-39.9	+2.5	+15.5	-19.6	-15.3	+20.2	-19.0	-37.4
Steps (reduced)		17 (17)	28 (5)	35 (12)	40 (17)	45 (22)	49 (3)	52 (6)	55 (9)	58 (12)	60 (14)	62 (16)

Approximation of harmonics in 23ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-26.4	-16.8	+1.7	+27.9	-8.1	+30.9	+6.3	-13.6	-29.0	+28.4	+20.4
	Relative (%)	-38.3	-24.4	+2.5	+40.5	-11.7	+44.8	+9.1	-19.6	-42.1	+41.1	+29.5
Steps (reduced)		64 (18)	66 (20)	68 (22)	70 (1)	71 (2)	73 (4)	74 (5)	75 (6)	76 (7)	78 (9)	79 (10)