41ed6

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41ed6

42ed6 →

Prime factorization	41 (prime)
Step size	75.6574¢
Octave	16\41ed6 (1210.52¢)
Twelfth	25\41ed6 (1891.44¢)
Consistency limit	5
Distinct consistency limit	5

41 equal divisions of the 6th harmonic (abbreviated 41ed6) is a nonoctave tuning system that divides the interval of 6/1 into 41 equal parts of about 75.7⁠ ⁠¢ each. Each step represents a frequency ratio of 6^1/41, or the 41st root of 6.

41ed6 is similar to 16edo, but has the 6/1 tuned just instead of the octave, which stretches the octave by 10.5 ¢. It can be used as a tuning for Mavila and also approximates Pelog tunings in Indonesian gamelan music.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	75.7	22/21, 23/22, 24/23, 25/24
2	151.3	12/11, 23/21, 25/23
3	227	8/7, 25/22
4	302.6	25/21
5	378.3
6	453.9	13/10, 30/23
7	529.6	23/17
8	605.3	17/12, 27/19
9	680.9
10	756.6	17/11
11	832.2	21/13, 29/18
12	907.9	22/13
13	983.5	23/13, 30/17
14	1059.2	24/13
15	1134.9	25/13, 29/15
16	1210.5
17	1286.2	21/10
18	1361.8	11/5
19	1437.5	16/7, 23/10
20	1513.1	12/5
21	1588.8	5/2
22	1664.5	21/8
23	1740.1	30/11
24	1815.8	20/7
25	1891.4
26	1967.1	25/8
27	2042.8	13/4
28	2118.4	17/5
29	2194.1
30	2269.7	26/7
31	2345.4
32	2421
33	2496.7
34	2572.4
35	2648	23/5
36	2723.7	29/6
37	2799.3
38	2875	21/4
39	2950.6	11/2
40	3026.3	23/4
41	3102	6/1

Harmonics

Approximation of harmonics in 41ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.5	-10.5	+21.0	+13.0	+0.0	+35.8	+31.6	-21.0	+23.5	+9.8	+10.5
	Relative (%)	+13.9	-13.9	+27.8	+17.2	+0.0	+47.3	+41.7	-27.8	+31.1	+13.0	+13.9
Steps (reduced)		16 (16)	25 (25)	32 (32)	37 (37)	41 (0)	45 (4)	48 (7)	50 (9)	53 (12)	55 (14)	57 (16)

Approximation of harmonics in 41ed6

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+23.3	-29.4	+2.5	-33.6	+12.8	-10.5	-28.5	+34.0	+25.2	+20.4	+19.1
	Relative (%)	+30.7	-38.8	+3.3	-44.4	+16.9	-13.9	-37.6	+45.0	+33.4	+26.9	+25.2
Steps (reduced)		59 (18)	60 (19)	62 (21)	63 (22)	65 (24)	66 (25)	67 (26)	69 (28)	70 (29)	71 (30)	72 (31)