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	30.333
2	60.667	28/27
3	91
4	121.334	15/14, 31/29
5	151.667	23/21
6	182.001	10/9
7	212.334	17/15, 26/23
8	242.667
9	273.001
10	303.334	25/21, 31/26
11	333.668	17/14, 23/19
12	364.001	21/17, 26/21
13	394.335
14	424.668
15	455.001
16	485.335
17	515.668	27/20, 31/23
18	546.002	26/19
19	576.335	7/5
20	606.669
21	637.002
22	667.335	22/15, 25/17
23	697.669	3/2
24	728.002	29/19
25	758.336	17/11
26	788.669	11/7
27	819.003
28	849.336	31/19
29	879.669	5/3
30	910.003
31	940.336	19/11
32	970.67
33	1001.003	25/14
34	1031.337
35	1061.67
36	1092.003
37	1122.337	21/11
38	1152.67
39	1183.004
40	1213.337
41	1243.671
42	1274.004	23/11
43	1304.337
44	1334.671
45	1365.004	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)