41ed7/3

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41ed7/3

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Prime factorization	41 (prime)
Step size	35.7773¢
Octave	34\41ed7/3 (1216.43¢)
Twelfth	53\41ed7/3 (1896.2¢)
Consistency limit	2
Distinct consistency limit	2

41 equal divisions of 7/3 (abbreviated 41ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 41 equal parts of about 35.8⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/41, or the 41st root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	35.8
2	71.6	23/22, 26/25
3	107.3
4	143.1	25/23
5	178.9	21/19
6	214.7	17/15, 25/22, 26/23
7	250.4	15/13, 29/25
8	286.2	13/11
9	322	6/5
10	357.8
11	393.6
12	429.3	9/7, 23/18
13	465.1	17/13, 30/23
14	500.9
15	536.7	15/11
16	572.4	25/18
17	608.2	27/19
18	644
19	679.8
20	715.5
21	751.3	17/11
22	787.1	11/7
23	822.9	29/18
24	858.7	18/11, 23/14
25	894.4
26	930.2	29/17
27	966
28	1001.8	25/14
29	1037.5
30	1073.3	13/7
31	1109.1
32	1144.9	29/15
33	1180.7
34	1216.4
35	1252.2
36	1288	19/9
37	1323.8	15/7
38	1359.5	11/5
39	1395.3	29/13
40	1431.1
41	1466.9	7/3

Harmonics

Approximation of harmonics in 41ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+16.4	-5.8	-2.9	+4.3	+10.7	-5.8	+13.5	-11.5	-15.0	-1.1	-8.7
	Relative (%)	+45.9	-16.1	-8.2	+12.1	+29.8	-16.1	+37.8	-32.2	-42.0	-3.2	-24.2
Steps (reduced)		34 (34)	53 (12)	67 (26)	78 (37)	87 (5)	94 (12)	101 (19)	106 (24)	111 (29)	116 (34)	120 (38)

Approximation of harmonics in 41ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.1	+10.7	-1.4	-5.8	-3.5	+4.9	-17.1	+1.4	-11.5	+15.3	+9.9
	Relative (%)	-11.6	+29.8	-4.0	-16.3	-9.7	+13.7	-47.9	+3.9	-32.2	+42.7	+27.6
Steps (reduced)		124 (1)	128 (5)	131 (8)	134 (11)	137 (14)	140 (17)	142 (19)	145 (22)	147 (24)	150 (27)	152 (29)