47ed4

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47ed4

49ed4 →

Prime factorization	47 (prime)
Step size	51.0638¢
Octave	24\47ed4 (1225.53¢)
Twelfth	37\47ed4 (1889.36¢)
Consistency limit	1
Distinct consistency limit	1

47 equal divisions of the 4th harmonic (abbreviated 47ed4) is a nonoctave tuning system that divides the interval of 4/1 into 47 equal parts of about 51.1 ¢ each. Each step represents a frequency ratio of 4^1/47, or the 47th root of 4.

47ed4 does very well on the 4.7.10.13 subgroup, and is an excellent tuning of Nelindic temperament.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	51.1
2	102.1	18/17
3	153.2	23/21
4	204.3
5	255.3	22/19
6	306.4
7	357.4
8	408.5	19/15
9	459.6	17/13
10	510.6
11	561.7	18/13, 29/21
12	612.8
13	663.8	22/15
14	714.9
15	766
16	817
17	868.1
18	919.1	29/17
19	970.2
20	1021.3
21	1072.3	13/7
22	1123.4	21/11
23	1174.5
24	1225.5
25	1276.6	23/11, 25/12
26	1327.7
27	1378.7
28	1429.8
29	1480.9
30	1531.9	17/7
31	1583	5/2
32	1634	18/7
33	1685.1
34	1736.2
35	1787.2	14/5
36	1838.3
37	1889.4
38	1940.4
39	1991.5	19/6
40	2042.6
41	2093.6
42	2144.7	31/9
43	2195.7
44	2246.8	11/3
45	2297.9
46	2348.9
47	2400

Harmonics

Approximation of harmonics in 47ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+25.5	-12.6	+0.0	+22.2	+12.9	+1.4	+25.5	-25.2	-3.3	-15.1	-12.6
	Relative (%)	+50.0	-24.7	+0.0	+43.5	+25.3	+2.7	+50.0	-49.3	-6.5	-29.7	-24.7
Steps (reduced)		24 (24)	37 (37)	47 (0)	55 (8)	61 (14)	66 (19)	71 (24)	74 (27)	78 (31)	81 (34)	84 (37)

Approximation of harmonics in 47ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.0	-24.1	+9.6	+0.0	-2.8	+0.3	+8.9	+22.2	-11.2	+10.4	-15.5
	Relative (%)	+4.0	-47.3	+18.8	+0.0	-5.5	+0.7	+17.4	+43.5	-21.9	+20.3	-30.4
Steps (reduced)		87 (40)	89 (42)	92 (45)	94 (0)	96 (2)	98 (4)	100 (6)	102 (8)	103 (9)	105 (11)	106 (12)