46ed11/5

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46ed11/5

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Prime factorization	2 × 23
Step size	29.674¢
Octave	40\46ed11/5 (1186.96¢) (→20\23ed11/5)
Twelfth	64\46ed11/5 (1899.14¢) (→32\23ed11/5)
Consistency limit	3
Distinct consistency limit	3

46 equal divisions of 11/5 (abbreviated 46ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 46 equal parts of about 29.7⁠ ⁠¢ each. Each step represents a frequency ratio of (11/5)^1/46, or the 46th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	29.7
2	59.3	27/26, 28/27, 29/28, 30/29, 31/30
3	89
4	118.7	15/14, 29/27, 31/29
5	148.4	25/23
6	178	10/9, 21/19, 31/28
7	207.7	26/23
8	237.4	31/27
9	267.1
10	296.7	25/21
11	326.4	23/19
12	356.1	27/22
13	385.8
14	415.4	14/11
15	445.1	22/17
16	474.8	25/19, 29/22
17	504.5
18	534.1	15/11, 19/14
19	563.8
20	593.5	31/22
21	623.2
22	652.8	19/13
23	682.5
24	712.2
25	741.9	23/15
26	771.5
27	801.2	27/17
28	830.9	21/13, 29/18
29	860.5	23/14, 28/17
30	890.2	5/3
31	919.9	17/10, 29/17
32	949.6	19/11, 26/15
33	979.2	30/17
34	1008.9	25/14
35	1038.6	31/17
36	1068.3	13/7
37	1097.9	17/9
38	1127.6	25/13
39	1157.3
40	1187
41	1216.6
42	1246.3
43	1276	23/11
44	1305.7
45	1335.3
46	1365	11/5

Harmonics

Approximation of harmonics in 46ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-13.0	-2.8	+3.6	+3.0	+13.8	+14.0	-9.4	-5.6	-10.0	+3.0	+0.8
	Relative (%)	-43.9	-9.5	+12.1	+10.3	+46.6	+47.2	-31.8	-19.0	-33.7	+10.3	+2.6
Steps (reduced)		40 (40)	64 (18)	81 (35)	94 (2)	105 (13)	114 (22)	121 (29)	128 (36)	134 (42)	140 (2)	145 (7)

Approximation of harmonics in 46ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.6	+1.0	+0.2	+7.2	-8.7	+11.0	+6.4	+6.6	+11.2	-10.0	+2.1
	Relative (%)	+35.6	+3.3	+0.8	+24.2	-29.5	+37.1	+21.6	+22.4	+37.7	-33.7	+7.0
Steps (reduced)		150 (12)	154 (16)	158 (20)	162 (24)	165 (27)	169 (31)	172 (34)	175 (37)	178 (40)	180 (42)	183 (45)