41ed7/4

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41ed7/4

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Prime factorization	41 (prime)
Step size	23.6299¢
Octave	51\41ed7/4 (1205.12¢)
Twelfth	80\41ed7/4 (1890.39¢)
Consistency limit	2
Distinct consistency limit	2

41 equal divisions of 7/4 (abbreviated 41ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 41 equal parts of about 23.6 ¢ each. Each step represents a frequency ratio of (7/4)^1/41, or the 41st root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	23.63
2	47.26
3	70.89	23/22, 24/23, 25/24, 26/25
4	94.52	20/19
5	118.15
6	141.779	13/12, 25/23
7	165.409	11/10
8	189.039	19/17, 29/26
9	212.669	26/23
10	236.299	8/7, 23/20
11	259.929	22/19, 29/25
12	283.559	13/11, 20/17
13	307.189	25/21
14	330.819	17/14, 23/19, 29/24
15	354.449
16	378.078
17	401.708	24/19, 29/23
18	425.338
19	448.968	13/10, 22/17
20	472.598	25/19, 29/22
21	496.228
22	519.858	23/17
23	543.488	26/19
24	567.118
25	590.748	24/17
26	614.377	10/7
27	638.007	29/20
28	661.637	19/13, 25/17
29	685.267
30	708.897
31	732.527	26/17, 29/19
32	756.157	17/11
33	779.787	11/7
34	803.417
35	827.047	21/13
36	850.676
37	874.306
38	897.936
39	921.566	17/10, 29/17
40	945.196	19/11
41	968.826	7/4

Harmonics

Approximation of harmonics in 41ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.1	-11.6	+10.2	+2.0	-6.4	+10.2	-8.3	+0.5	+7.1	+7.5	-1.3
	Relative (%)	+21.7	-48.9	+43.4	+8.5	-27.2	+43.4	-34.9	+2.1	+30.2	+31.9	-5.6
Steps (reduced)		51 (10)	80 (39)	102 (20)	118 (36)	131 (8)	143 (20)	152 (29)	161 (38)	169 (5)	176 (12)	182 (18)

Approximation of harmonics in 41ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.9	-8.3	-9.5	-3.1	+10.1	+5.6	+6.5	-11.4	-1.3	-11.0	+6.6
	Relative (%)	+8.0	-34.9	-40.4	-13.2	+42.6	+23.8	+27.7	-48.1	-5.6	-46.4	+27.9
Steps (reduced)		188 (24)	193 (29)	198 (34)	203 (39)	208 (3)	212 (7)	216 (11)	219 (14)	223 (18)	226 (21)	230 (25)