63edt

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63edt

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Prime factorization	32 × 7
Step size	30.1898 ¢
Octave	40\63edt (1207.59 ¢)
Consistency limit	3
Distinct consistency limit	3

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	Hekts	Approximate ratios
0	0	0	1/1
1	30.2	20.6
2	60.4	41.3	30/29, 31/30
3	90.6	61.9	19/18, 20/19
4	120.8	82.5	29/27
5	150.9	103.2	12/11
6	181.1	123.8	10/9
7	211.3	144.4	26/23, 35/31
8	241.5	165.1	23/20, 31/27
9	271.7	185.7	34/29
10	301.9	206.3	31/26
11	332.1	227	23/19
12	362.3	247.6
13	392.5	268.3
14	422.7	288.9	23/18
15	452.8	309.5	13/10, 35/27
16	483	330.2
17	513.2	350.8	31/23, 35/26
18	543.4	371.4	26/19
19	573.6	392.1
20	603.8	412.7
21	634	433.3	13/9
22	664.2	454	25/17
23	694.4	474.6
24	724.6	495.2	35/23
25	754.7	515.9	31/20
26	784.9	536.5	11/7
27	815.1	557.1
28	845.3	577.8	31/19
29	875.5	598.4
30	905.7	619
31	935.9	639.7	12/7
32	966.1	660.3	7/4
33	996.3	681
34	1026.5	701.6
35	1056.6	722.2	35/19
36	1086.8	742.9
37	1117	763.5	21/11
38	1147.2	784.1	35/18
39	1177.4	804.8
40	1207.6	825.4
41	1237.8	846
42	1268	866.7	27/13
43	1298.2	887.3
44	1328.3	907.9
45	1358.5	928.6
46	1388.7	949.2	29/13
47	1418.9	969.8	34/15
48	1449.1	990.5	30/13
49	1479.3	1011.1
50	1509.5	1031.7
51	1539.7	1052.4
52	1569.9	1073
53	1600.1	1093.7
54	1630.2	1114.3
55	1660.4	1134.9	34/13
56	1690.6	1155.6
57	1720.8	1176.2	27/10
58	1751	1196.8	11/4
59	1781.2	1217.5
60	1811.4	1238.1
61	1841.6	1258.7	29/10
62	1871.8	1279.4
63	1902	1300	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)