63ed4

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63 equal divisions of the 4th harmonic (abbreviated 63ed4) is a nonoctave tuning system that divides the interval of 4/1 into 63 equal parts of about 38.1 ¢ each. Each step represents a frequency ratio of 4^1/63, or the 63rd root of 4.

← 61ed4

63ed4

65ed4 →

Prime factorization	32 × 7
Step size	38.0952 ¢
Octave	32\63ed4 (1219.05 ¢)
Twelfth	50\63ed4 (1904.76 ¢)
Consistency limit	1
Distinct consistency limit	1

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	38.1
2	76.2
3	114.3	31/29
4	152.4
5	190.5	19/17
6	228.6
7	266.7
8	304.8	25/21
9	342.9
10	381
11	419	14/11
12	457.1	13/10
13	495.2
14	533.3	15/11
15	571.4
16	609.5	27/19
17	647.6
18	685.7
19	723.8	35/23
20	761.9	14/9
21	800	27/17
22	838.1
23	876.2
24	914.3	22/13
25	952.4	33/19
26	990.5
27	1028.6
28	1066.7
29	1104.8	17/9
30	1142.9	29/15
31	1181
32	1219
33	1257.1	29/14, 31/15
34	1295.2	19/9
35	1333.3
36	1371.4
37	1409.5
38	1447.6	30/13
39	1485.7	33/14
40	1523.8
41	1561.9
42	1600
43	1638.1
44	1676.2	29/11
45	1714.3
46	1752.4
47	1790.5	31/11
48	1828.6
49	1866.7
50	1904.8	3/1
51	1942.9
52	1981
53	2019
54	2057.1	23/7
55	2095.2
56	2133.3
57	2171.4
58	2209.5
59	2247.6	11/3
60	2285.7
61	2323.8
62	2361.9
63	2400

Harmonics

Approximation of harmonics in 63ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+19.0	+2.8	+0.0	-5.4	-16.2	-16.4	+19.0	+5.6	+13.7	+1.1	+2.8
	Relative (%)	+50.0	+7.4	+0.0	-14.1	-42.6	-43.2	+50.0	+14.7	+35.9	+2.8	+7.4
Steps (reduced)		32 (32)	50 (50)	63 (0)	73 (10)	81 (18)	88 (25)	95 (32)	100 (37)	105 (42)	109 (46)	113 (50)

Approximation of harmonics in 63ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.6	+2.6	-2.6	+0.0	+9.3	-13.4	+7.2	-5.4	-13.6	-18.0	-18.8
	Relative (%)	+43.6	+6.8	-6.7	+0.0	+24.5	-35.3	+19.0	-14.1	-35.8	-47.2	-49.2
Steps (reduced)		117 (54)	120 (57)	123 (60)	126 (0)	129 (3)	131 (5)	134 (8)	136 (10)	138 (12)	140 (14)	142 (16)