45ed11/5

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45ed11/5

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Prime factorization	32 × 5
Step size	30.3334¢
Octave	40\45ed11/5 (1213.34¢) (→8\9ed11/5)
Twelfth	63\45ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit	3
Distinct consistency limit	3

45 equal divisions of 11/5 (abbreviated 45ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 45 equal parts of about 30.3⁠ ⁠¢ each. Each step represents a frequency ratio of (11/5)^1/45, or the 45th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	30.3
2	60.7	28/27
3	91
4	121.3	15/14, 31/29
5	151.7	23/21
6	182	10/9
7	212.3	17/15, 26/23
8	242.7
9	273
10	303.3	25/21, 31/26
11	333.7	17/14, 23/19
12	364	21/17, 26/21
13	394.3
14	424.7
15	455
16	485.3
17	515.7	27/20, 31/23
18	546	26/19
19	576.3	7/5
20	606.7
21	637
22	667.3	22/15, 25/17
23	697.7	3/2
24	728	29/19
25	758.3	17/11
26	788.7	11/7
27	819
28	849.3	31/19
29	879.7	5/3
30	910
31	940.3	19/11
32	970.7
33	1001	25/14
34	1031.3
35	1061.7
36	1092
37	1122.3	21/11
38	1152.7
39	1183
40	1213.3
41	1243.7
42	1274	23/11
43	1304.3
44	1334.7
45	1365	11/5

Harmonics

Approximation of harmonics in 45ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.3	+9.1	-3.7	+4.4	-7.9	-1.8	+9.7	-12.2	-12.6	+4.4	+5.4
	Relative (%)	+44.0	+29.8	-12.1	+14.4	-26.2	-6.0	+31.9	-40.3	-41.7	+14.4	+17.8
Steps (reduced)		40 (40)	63 (18)	79 (34)	92 (2)	102 (12)	111 (21)	119 (29)	125 (35)	131 (41)	137 (2)	142 (7)

Approximation of harmonics in 45ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.8	+11.5	+13.4	-7.3	+9.1	+1.1	-1.5	+0.7	+7.2	-12.6	+1.4
	Relative (%)	-39.1	+38.0	+44.2	-24.1	+29.9	+3.6	-4.9	+2.3	+23.9	-41.7	+4.6
Steps (reduced)		146 (11)	151 (16)	155 (20)	158 (23)	162 (27)	165 (30)	168 (33)	171 (36)	174 (39)	176 (41)	179 (44)