46ed7/3

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46ed7/3

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Prime factorization	2 × 23
Step size	31.8885¢
Octave	38\46ed7/3 (1211.76¢) (→19\23ed7/3)
Twelfth	60\46ed7/3 (1913.31¢) (→30\23ed7/3)
Consistency limit	3
Distinct consistency limit	3

46 equal divisions of 7/3 (abbreviated 46ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 46 equal parts of about 31.9 ¢ each. Each step represents a frequency ratio of (7/3)^1/46, or the 46th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	31.9
2	63.8	28/27, 30/29
3	95.7
4	127.6
5	159.4	11/10
6	191.3	19/17, 29/26
7	223.2
8	255.1	22/19
9	287	13/11, 20/17
10	318.9
11	350.8
12	382.7
13	414.6	19/15
14	446.4	22/17
15	478.3	29/22
16	510.2
17	542.1	15/11, 26/19
18	574
19	605.9
20	637.8	29/20
21	669.7
22	701.5	3/2
23	733.4	26/17, 29/19
24	765.3	14/9
25	797.2
26	829.1
27	861
28	892.9
29	924.8	17/10, 29/17
30	956.7	26/15
31	988.5	23/13, 30/17
32	1020.4
33	1052.3
34	1084.2
35	1116.1	19/10
36	1148
37	1179.9
38	1211.8
39	1243.7
40	1275.5	23/11
41	1307.4
42	1339.3
43	1371.2
44	1403.1	9/4
45	1435
46	1466.9	7/3

Harmonics

Approximation of harmonics in 46ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.8	+11.4	-8.4	-12.0	-8.8	+11.4	+3.4	-9.2	-0.3	-5.8	+3.0
	Relative (%)	+36.9	+35.6	-26.2	-37.7	-27.5	+35.6	+10.7	-28.8	-0.8	-18.2	+9.4
Steps (reduced)		38 (38)	60 (14)	75 (29)	87 (41)	97 (5)	106 (14)	113 (21)	119 (27)	125 (33)	130 (38)	135 (43)

Approximation of harmonics in 46ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.0	-8.8	-0.7	+15.2	+5.9	+2.6	+4.6	+11.5	-9.2	+5.9	-7.2
	Relative (%)	-25.2	-27.5	-2.1	+47.6	+18.4	+8.1	+14.6	+36.1	-28.8	+18.7	-22.7
Steps (reduced)		139 (1)	143 (5)	147 (9)	151 (13)	154 (16)	157 (19)	160 (22)	163 (25)	165 (27)	168 (30)	170 (32)