45ed7/3

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45ed7/3

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Prime factorization	32 × 5
Step size	32.5971¢
Octave	37\45ed7/3 (1206.09¢)
Twelfth	58\45ed7/3 (1890.63¢)
Consistency limit	2
Distinct consistency limit	2

45 equal divisions of 7/3 (abbreviated 45ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 45 equal parts of about 32.6⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/45, or the 45th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	32.6
2	65.2	29/28
3	97.8	18/17, 19/18
4	130.4	14/13, 27/25
5	163	11/10
6	195.6	19/17
7	228.2
8	260.8	7/6
9	293.4	13/11
10	326	29/24
11	358.6
12	391.2
13	423.8	14/11
14	456.4	13/10
15	489
16	521.6
17	554.2
18	586.7	7/5
19	619.3	10/7
20	651.9	19/13
21	684.5
22	717.1
23	749.7	17/11, 20/13
24	782.3	11/7
25	814.9
26	847.5	18/11, 31/19
27	880.1	5/3
28	912.7	17/10, 22/13
29	945.3	19/11, 31/18
30	977.9	30/17
31	1010.5
32	1043.1	11/6, 31/17
33	1075.7	13/7
34	1108.3	19/10
35	1140.9
36	1173.5
37	1206.1	2/1
38	1238.7
39	1271.3
40	1303.9
41	1336.5	13/6
42	1369.1	11/5
43	1401.7
44	1434.3
45	1466.9	7/3

Harmonics

Approximation of harmonics in 45ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.1	-11.3	+12.2	-15.6	-5.2	-11.3	-14.3	+10.0	-9.5	-11.5	+0.9
	Relative (%)	+18.7	-34.7	+37.4	-47.7	-16.0	-34.7	-43.9	+30.5	-29.0	-35.2	+2.7
Steps (reduced)		37 (37)	58 (13)	74 (29)	85 (40)	95 (5)	103 (13)	110 (20)	117 (27)	122 (32)	127 (37)	132 (42)

Approximation of harmonics in 45ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-7.3	-5.2	+5.7	-8.2	-15.4	+16.0	-12.4	-3.4	+10.0	-5.4	+15.4
	Relative (%)	-22.4	-16.0	+17.5	-25.2	-47.2	+49.2	-37.9	-10.3	+30.5	-16.5	+47.4
Steps (reduced)		136 (1)	140 (5)	144 (9)	147 (12)	150 (15)	154 (19)	156 (21)	159 (24)	162 (27)	164 (29)	167 (32)