63ed7/3

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

← 62ed7/3

63ed7/3

64ed7/3 →

Prime factorization	32 × 7
Step size	23.2837¢
Octave	52\63ed7/3 (1210.75¢)
Twelfth	82\63ed7/3 (1909.26¢)
Consistency limit	3
Distinct consistency limit	3

63 equal divisions of 7/3 (abbreviated 63ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 63 equal parts of about 23.3⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/63, or the 63rd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	23.3
2	46.6	35/34
3	69.9	26/25
4	93.1
5	116.4	15/14, 31/29
6	139.7
7	163
8	186.3	10/9
9	209.6
10	232.8
11	256.1	22/19
12	279.4
13	302.7	25/21
14	326
15	349.3
16	372.5	26/21
17	395.8	34/27
18	419.1
19	442.4	22/17
20	465.7	17/13
21	489
22	512.2	35/26
23	535.5	34/25
24	558.8
25	582.1	7/5
26	605.4
27	628.7	33/23
28	651.9
29	675.2
30	698.5	3/2
31	721.8
32	745.1
33	768.4	14/9
34	791.6
35	814.9
36	838.2	34/21
37	861.5
38	884.8	5/3
39	908.1	22/13
40	931.3
41	954.6	26/15, 33/19
42	977.9
43	1001.2	25/14
44	1024.5
45	1047.8
46	1071	13/7
47	1094.3
48	1117.6
49	1140.9	27/14
50	1164.2
51	1187.5
52	1210.8
53	1234
54	1257.3
55	1280.6	21/10, 23/11
56	1303.9
57	1327.2
58	1350.5
59	1373.7
60	1397
61	1420.3	34/15
62	1443.6
63	1466.9	7/3

Harmonics

Approximation of harmonics in 63ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.8	+7.3	-1.8	+7.7	-5.2	+7.3	+9.0	-8.7	-4.8	-6.8	+5.5
	Relative (%)	+46.2	+31.4	-7.7	+33.2	-22.5	+31.4	+38.5	-37.2	-20.6	-29.3	+23.7
Steps (reduced)		52 (52)	82 (19)	103 (40)	120 (57)	133 (7)	145 (19)	155 (29)	163 (37)	171 (45)	178 (52)	185 (59)

Approximation of harmonics in 63ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.7	-5.2	-8.3	-3.6	+7.9	+2.1	+1.6	+5.9	-8.7	+3.9	-3.2
	Relative (%)	+28.6	-22.5	-35.4	-15.3	+33.9	+8.9	+6.9	+25.5	-37.2	+16.9	-13.7
Steps (reduced)		191 (2)	196 (7)	201 (12)	206 (17)	211 (22)	215 (26)	219 (30)	223 (34)	226 (37)	230 (41)	233 (44)