23edt

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23edt

24edt →

Prime factorization	23 (prime)
Step size	82.6937¢
Octave	15\23edt (1240.41¢)
Consistency limit	2
Distinct consistency limit	2

23EDT is the equal division of the third harmonic into 23 parts of 82.6937 cents each, corresponding to 14.5114 edo (similar to every second step of 29edo).

Intervals

degree	cents value	hekts	corresponding JI intervals	comments
0			exact 1/1
1	82.6937	56.522	150/143
2	165.3874	113.0435	11/10
3	248.0811	169.565	15/13
4	330.7748	226.087	23/19
5	413.4685	282.609	33/26, 80/63
6	496.1622	339.13	(4/3)
7	578.8559	395.652	88/63, 95/68	pseudo-7/5
8	661.5496	452.174	63/43
9	744.2433	508.696	135/88
10	826.937	565.217	50/31, 408/253, 129/80, 108/67
11	909.6307	621.739	(27/16)	pseudo-5/3
12	992.3243	678.261	(16/9)
13	1075.018	734.783	93/50, 253/136, 80/43, 67/36
14	1157.7117	791.304	88/45
15	1240.4054	847.826	43/21
16	1323.0991	904.348	189/88, 204/95
17	1405.7928	960.87	(9/4)
18	1488.4865	1017.391	26/11, 189/80	pseudo-7/3
19	1571.1802	1073.913	57/23
20	1653.8739	1130.435.	13/5
21	1736.5676	1186.9565	30/11
22	1819.2613	1243.478	143/50
23	1901.9550	1300	exact 3/1	just perfect fifth plus an octave

Harmonics

Approximation of harmonics in 23edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+40.4	+0.0	-1.9	+25.3	+40.4	+21.6	+38.5	+0.0	-17.0	-16.6	-1.9
	Relative (%)	+48.9	+0.0	-2.3	+30.6	+48.9	+26.1	+46.6	+0.0	-20.6	-20.1	-2.3
Steps (reduced)		15 (15)	23 (0)	29 (6)	34 (11)	38 (15)	41 (18)	44 (21)	46 (0)	48 (2)	50 (4)	52 (6)

Approximation of harmonics in 23edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+24.9	-20.7	+25.3	-3.8	-26.0	+40.4	+29.5	+23.4	+21.6	+23.8	+29.5
	Relative (%)	+30.1	-25.0	+30.6	-4.6	-31.5	+48.9	+35.7	+28.3	+26.1	+28.7	+35.7
Steps (reduced)		54 (8)	55 (9)	57 (11)	58 (12)	59 (13)	61 (15)	62 (16)	63 (17)	64 (18)	65 (19)	66 (20)