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	51.064
2	102.128	18/17
3	153.191	23/21
4	204.255
5	255.319	22/19
6	306.383
7	357.447
8	408.511	19/15
9	459.574	17/13
10	510.638
11	561.702	18/13, 29/21
12	612.766
13	663.83	22/15
14	714.894
15	765.957
16	817.021
17	868.085
18	919.149	29/17
19	970.213
20	1021.277
21	1072.34	13/7
22	1123.404	21/11
23	1174.468
24	1225.532
25	1276.596	23/11, 25/12
26	1327.66
27	1378.723
28	1429.787
29	1480.851
30	1531.915	17/7
31	1582.979	5/2
32	1634.043	18/7
33	1685.106
34	1736.17
35	1787.234	14/5
36	1838.298
37	1889.362
38	1940.426
39	1991.489	19/6
40	2042.553
41	2093.617
42	2144.681	31/9
43	2195.745
44	2246.809	11/3
45	2297.872
46	2348.936
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)