35ed7/4

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

← 34ed7/4

35ed7/4

36ed7/4 →

Prime factorization	5 × 7
Step size	27.6807¢
Octave	43\35ed7/4 (1190.27¢)
Twelfth	69\35ed7/4 (1909.97¢)
Consistency limit	2
Distinct consistency limit	2

35 equal divisions of 7/4 (abbreviated 35ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 35 equal parts of about 27.7 ¢ each. Each step represents a frequency ratio of (7/4)^1/35, or the 35th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	27.681
2	55.361
3	83.042	20/19, 23/22
4	110.723
5	138.404	13/12, 27/25
6	166.084	11/10
7	193.765	19/17
8	221.446
9	249.127	22/19, 23/20
10	276.807	20/17
11	304.488	25/21
12	332.169	17/14, 23/19, 28/23
13	359.85
14	387.53
15	415.211	14/11
16	442.892	9/7, 22/17
17	470.573	17/13
18	498.253
19	525.934	19/14, 23/17
20	553.615
21	581.296	7/5
22	608.976	17/12
23	636.657
24	664.338	19/13, 28/19
25	692.019
26	719.699
27	747.38	17/11, 20/13
28	775.061	11/7
29	802.741	19/12
30	830.422
31	858.103	18/11, 23/14, 28/17
32	885.784	5/3
33	913.464	17/10, 22/13
34	941.145	19/11
35	968.826

Harmonics

Approximation of harmonics in 35ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-9.7	+8.0	+8.2	+9.4	-1.7	+8.2	-1.5	-11.6	-0.3	+0.8	-11.4
	Relative (%)	-35.1	+29.0	+29.7	+34.1	-6.2	+29.7	-5.4	-42.1	-1.0	+2.9	-41.3
Steps (reduced)		43 (8)	69 (34)	87 (17)	101 (31)	112 (7)	122 (17)	130 (25)	137 (32)	144 (4)	150 (10)	155 (15)

Approximation of harmonics in 35ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.6	-1.5	-10.2	-11.2	-5.5	+6.3	-4.3	-10.0	-11.4	-8.9	-2.8
	Relative (%)	-41.9	-5.4	-36.9	-40.6	-19.7	+22.8	-15.4	-36.2	-41.3	-32.3	-10.3
Steps (reduced)		160 (20)	165 (25)	169 (29)	173 (33)	177 (2)	181 (6)	184 (9)	187 (12)	190 (15)	193 (18)	196 (21)