47ed11/5

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47ed11/5

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Prime factorization	47 (prime)
Step size	29.0426¢
Octave	41\47ed11/5 (1190.75¢)
Twelfth	65\47ed11/5 (1887.77¢)
Consistency limit	3
Distinct consistency limit	3

47 equal divisions of 11/5 (abbreviated 47ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 47 equal parts of about 29⁠ ⁠¢ each. Each step represents a frequency ratio of (11/5)^1/47, or the 47th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	29
2	58.1
3	87.1	21/20
4	116.2	15/14, 31/29
5	145.2	25/23
6	174.3
7	203.3	9/8
8	232.3
9	261.4	29/25
10	290.4	13/11
11	319.5
12	348.5
13	377.6	31/25
14	406.6	29/23
15	435.6
16	464.7	17/13
17	493.7	4/3
18	522.8	23/17
19	551.8
20	580.9	7/5
21	609.9
22	638.9
23	668	22/15, 25/17
24	697	3/2
25	726.1
26	755.1	17/11
27	784.2	11/7
28	813.2
29	842.2	31/19
30	871.3
31	900.3	27/16
32	929.4	29/17
33	958.4
34	987.4	23/13
35	1016.5
36	1045.5	31/17
37	1074.6	13/7, 28/15
38	1103.6
39	1132.7	25/13
40	1161.7
41	1190.7
42	1219.8
43	1248.8
44	1277.9	23/11
45	1306.9
46	1336
47	1365	11/5

Harmonics

Approximation of harmonics in 47ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-9.3	-14.2	+10.5	+1.8	+5.6	+0.1	+1.3	+0.7	-7.5	+1.8	-3.6
	Relative (%)	-31.9	-48.8	+36.3	+6.1	+19.3	+0.4	+4.4	+2.3	-25.7	+6.1	-12.5
Steps (reduced)		41 (41)	65 (18)	83 (36)	96 (2)	107 (13)	116 (22)	124 (30)	131 (37)	137 (43)	143 (2)	148 (7)

Approximation of harmonics in 47ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.0	-9.1	-12.4	-8.0	+3.3	-8.6	+14.0	+12.3	-14.1	-7.5	+2.7
	Relative (%)	+10.3	-31.4	-42.7	-27.4	+11.2	-29.5	+48.2	+42.4	-48.4	-25.7	+9.3
Steps (reduced)		153 (12)	157 (16)	161 (20)	165 (24)	169 (28)	172 (31)	176 (35)	179 (38)	181 (40)	184 (43)	187 (46)