63edt

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63edt

64edt →

Prime factorization	32 × 7
Step size	30.1898¢
Octave	40\63edt (1207.59¢)
Consistency limit	2
Distinct consistency limit	2

63 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 63edt or 63ed3), is a nonoctave tuning system that divides the interval of 3/1 into 63 equal parts of about 30.2 ¢ each. Each step represents a frequency ratio of 3^1/63, or the 63rd root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	30.19
2	60.38	30/29, 31/30
3	90.569	19/18, 20/19
4	120.759	29/27
5	150.949	12/11
6	181.139	10/9
7	211.328	26/23, 35/31
8	241.518	23/20, 31/27
9	271.708	34/29
10	301.898	31/26
11	332.087	23/19
12	362.277
13	392.467
14	422.657	23/18
15	452.846	13/10, 35/27
16	483.036
17	513.226	31/23, 35/26
18	543.416	26/19
19	573.605
20	603.795
21	633.985	13/9
22	664.175	25/17
23	694.365
24	724.554	35/23
25	754.744	31/20
26	784.934	11/7
27	815.124
28	845.313	31/19
29	875.503
30	905.693
31	935.883	12/7
32	966.072	7/4
33	996.262
34	1026.452
35	1056.642	35/19
36	1086.831
37	1117.021	21/11
38	1147.211	35/18
39	1177.401
40	1207.59
41	1237.78
42	1267.97	27/13
43	1298.16
44	1328.35
45	1358.539
46	1388.729	29/13
47	1418.919	34/15
48	1449.109	30/13
49	1479.298
50	1509.488
51	1539.678
52	1569.868
53	1600.057
54	1630.247
55	1660.437	34/13
56	1690.627
57	1720.816	27/10
58	1751.006	11/4
59	1781.196
60	1811.386
61	1841.575	29/10
62	1871.765
63	1901.955	3/1

Harmonics

Approximation of harmonics in 63edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+7.6	+0.0	-15.0	-8.9	+7.6	+12.4	-7.4	+0.0	-1.3	+14.9	-15.0
	Relative (%)	+25.1	+0.0	-49.7	-29.3	+25.1	+41.2	-24.6	+0.0	-4.2	+49.3	-49.7
Steps (reduced)		40 (40)	63 (0)	79 (16)	92 (29)	103 (40)	112 (49)	119 (56)	126 (0)	132 (6)	138 (12)	142 (16)

Approximation of harmonics in 63edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	-10.2	-8.9	+0.2	-14.2	+7.6	+4.6	+6.3	+12.4	-7.7	+5.9
	Relative (%)	-8.7	-33.7	-29.3	+0.6	-47.1	+25.1	+15.1	+21.0	+41.2	-25.6	+19.5
Steps (reduced)		147 (21)	151 (25)	155 (29)	159 (33)	162 (36)	166 (40)	169 (43)	172 (46)	175 (49)	177 (51)	180 (54)