41ed5/2

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41ed5/2

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Prime factorization	41 (prime)
Step size	38.6906¢
Octave	31\41ed5/2 (1199.41¢) (semiconvergent)
Twelfth	49\41ed5/2 (1895.84¢) (semiconvergent)
Consistency limit	12
Distinct consistency limit	7

41 equal divisions of 5/2 (abbreviated 41ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 41 equal parts of about 38.7⁠ ⁠¢ each. Each step represents a frequency ratio of (5/2)^1/41, or the 41st root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	38.7
2	77.4	22/21, 23/22, 24/23, 25/24
3	116.1	15/14, 16/15
4	154.8	12/11, 23/21
5	193.5	19/17, 28/25, 29/26
6	232.1	8/7
7	270.8	7/6, 27/23
8	309.5	6/5
9	348.2	11/9, 27/22
10	386.9	5/4
11	425.6	23/18
12	464.3	17/13, 21/16, 30/23
13	503	4/3
14	541.7	15/11, 26/19
15	580.4	7/5
16	619	10/7
17	657.7	19/13, 22/15
18	696.4	3/2
19	735.1	23/15, 26/17, 29/19
20	773.8	25/16
21	812.5	8/5
22	851.2	18/11
23	889.9	5/3
24	928.6	12/7, 29/17
25	967.3	7/4
26	1006	25/14
27	1044.6	11/6
28	1083.3	15/8, 28/15
29	1122	21/11, 23/12
30	1160.7
31	1199.4	2/1
32	1238.1
33	1276.8	23/11, 25/12
34	1315.5	15/7
35	1354.2	24/11
36	1392.9	29/13
37	1431.6	16/7
38	1470.2	7/3
39	1508.9	12/5
40	1547.6	22/9, 27/11
41	1586.3	5/2

Harmonics

Approximation of harmonics in 41ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.6	-6.1	-1.2	-0.6	-6.7	-2.7	-1.8	-12.2	-1.2	-11.4	-7.3
	Relative (%)	-1.5	-15.8	-3.1	-1.5	-17.3	-7.1	-4.6	-31.6	-3.1	-29.5	-18.9
Steps (reduced)		31 (31)	49 (8)	62 (21)	72 (31)	80 (39)	87 (5)	93 (11)	98 (16)	103 (21)	107 (25)	111 (29)

Approximation of harmonics in 41ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+8.9	-3.3	-6.7	-2.4	+8.7	-12.8	+9.6	-1.8	-8.9	-12.0	-11.6
	Relative (%)	+23.0	-8.6	-17.3	-6.1	+22.6	-33.1	+24.9	-4.6	-22.9	-31.1	-30.0
Steps (reduced)		115 (33)	118 (36)	121 (39)	124 (1)	127 (4)	129 (6)	132 (9)	134 (11)	136 (13)	138 (15)	140 (17)