41ed7/4

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 40ed7/4

41ed7/4

42ed7/4 →

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	23.6
2	47.3
3	70.9	23/22, 24/23, 25/24, 26/25
4	94.5	20/19
5	118.1
6	141.8	13/12, 25/23
7	165.4	11/10
8	189	19/17, 29/26
9	212.7	26/23
10	236.3	8/7, 23/20
11	259.9	22/19, 29/25
12	283.6	13/11, 20/17
13	307.2	25/21
14	330.8	17/14, 23/19, 29/24
15	354.4
16	378.1
17	401.7	24/19, 29/23
18	425.3
19	449	13/10, 22/17
20	472.6	25/19, 29/22
21	496.2
22	519.9	23/17
23	543.5	26/19
24	567.1
25	590.7	24/17
26	614.4	10/7
27	638	29/20
28	661.6	19/13, 25/17
29	685.3
30	708.9
31	732.5	26/17, 29/19
32	756.2	17/11
33	779.8	11/7
34	803.4
35	827	21/13
36	850.7
37	874.3
38	897.9
39	921.6	17/10, 29/17
40	945.2	19/11
41	968.8	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)