47edt

← 46edt

47edt

48edt →

Prime factorization	47 (prime)
Step size	40.4671¢
Octave	30\47edt (1214.01¢)
Consistency limit	2
Distinct consistency limit	2

47 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 47edt or 47ed3), is a nonoctave tuning system that divides the interval of 3/1 into 47 equal parts of about 40.5 ¢ each. Each step represents a frequency ratio of 3^1/47, or the 47th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	40.467
2	80.934
3	121.401	15/14, 29/27, 31/29
4	161.869	11/10, 23/21
5	202.336
6	242.803	15/13, 31/27
7	283.27	13/11, 27/23
8	323.737
9	364.204	21/17
10	404.671	19/15, 29/23
11	445.138
12	485.606
13	526.073	19/14, 23/17
14	566.54	18/13, 25/18
15	607.007	27/19
16	647.474
17	687.941
18	728.408	29/19
19	768.875	14/9
20	809.343
21	849.81	18/11, 31/19
22	890.277	5/3
23	930.744
24	971.211
25	1011.678	9/5
26	1052.145	11/6
27	1092.612
28	1133.08	25/13, 27/14
29	1173.547
30	1214.014
31	1254.481	31/15
32	1294.948	19/9
33	1335.415	13/6
34	1375.882	31/14
35	1416.349	25/11
36	1456.817
37	1497.284
38	1537.751	17/7
39	1578.218
40	1618.685	23/9, 28/11
41	1659.152	13/5
42	1699.619
43	1740.086	30/11
44	1780.554	14/5
45	1821.021
46	1861.488
47	1901.955	3/1

Harmonics

Approximation of harmonics in 47edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+14.0	+0.0	-12.4	+5.9	+14.0	-10.1	+1.6	+0.0	+19.9	+16.8	-12.4
	Relative (%)	+34.6	+0.0	-30.7	+14.6	+34.6	-24.8	+3.9	+0.0	+49.3	+41.5	-30.7
Steps (reduced)		30 (30)	47 (0)	59 (12)	69 (22)	77 (30)	83 (36)	89 (42)	94 (0)	99 (5)	103 (9)	106 (12)

Approximation of harmonics in 47edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.9	+4.0	+5.9	+15.6	-8.4	+14.0	+1.3	-6.5	-10.1	-9.7	-5.7
	Relative (%)	+26.8	+9.8	+14.6	+38.5	-20.8	+34.6	+3.3	-16.1	-24.8	-23.9	-14.0
Steps (reduced)		110 (16)	113 (19)	116 (22)	119 (25)	121 (27)	124 (30)	126 (32)	128 (34)	130 (36)	132 (38)	134 (40)

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