47ed7/3

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47ed7/3

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Prime factorization	47 (prime)
Step size	31.21¢
Octave	38\47ed7/3 (1185.98¢)
Twelfth	61\47ed7/3 (1903.81¢)
Consistency limit	2
Distinct consistency limit	2

47 equal divisions of 7/3 (abbreviated 47ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 47 equal parts of about 31.2⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/47, or the 47th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	31.2
2	62.4	26/25, 31/30
3	93.6	18/17, 19/18
4	124.8	14/13, 15/14, 29/27
5	156.1	23/21
6	187.3	19/17
7	218.5	17/15, 25/22
8	249.7	15/13, 22/19
9	280.9	27/23
10	312.1	6/5
11	343.3	11/9
12	374.5	31/25
13	405.7	19/15, 29/23
14	436.9	9/7
15	468.2	17/13
16	499.4
17	530.6	19/14
18	561.8	18/13, 29/21
19	593	31/22
20	624.2
21	655.4	19/13
22	686.6
23	717.8
24	749	17/11
25	780.3	11/7
26	811.5
27	842.7	31/19
28	873.9
29	905.1	22/13
30	936.3	31/18
31	967.5
32	998.7	25/14
33	1029.9
34	1061.1
35	1092.4
36	1123.6	21/11
37	1154.8
38	1186
39	1217.2
40	1248.4
41	1279.6	23/11
42	1310.8
43	1342	13/6
44	1373.2	31/14
45	1404.5
46	1435.7
47	1466.9	7/3

Harmonics

Approximation of harmonics in 47ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-14.0	+1.9	+3.2	-8.6	-12.2	+1.9	-10.8	+3.7	+8.6	-0.4	+5.0
	Relative (%)	-44.9	+5.9	+10.2	-27.6	-39.0	+5.9	-34.8	+11.9	+27.5	-1.2	+16.1
Steps (reduced)		38 (38)	61 (14)	77 (30)	89 (42)	99 (5)	108 (14)	115 (21)	122 (28)	128 (34)	133 (39)	138 (44)

Approximation of harmonics in 47ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.7	-12.2	-6.8	+6.3	-5.0	-10.3	-10.3	-5.5	+3.7	-14.4	+2.3
	Relative (%)	-27.9	-39.0	-21.7	+20.3	-16.0	-33.0	-32.9	-17.5	+11.9	-46.2	+7.3
Steps (reduced)		142 (1)	146 (5)	150 (9)	154 (13)	157 (16)	160 (19)	163 (22)	166 (25)	169 (28)	171 (30)	174 (33)