42ed7/3

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42ed7/3

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Prime factorization	2 × 3 × 7
Step size	34.9255¢
Octave	34\42ed7/3 (1187.47¢) (→17\21ed7/3)
Twelfth	54\42ed7/3 (1885.98¢) (→9\7ed7/3)
Consistency limit	3
Distinct consistency limit	3

42 equal divisions of 7/3 (abbreviated 42ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 42 equal parts of about 34.9 ¢ each. Each step represents a frequency ratio of (7/3)^1/42, or the 42nd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	34.9
2	69.9
3	104.8
4	139.7
5	174.6
6	209.6	9/8, 26/23
7	244.5	15/13, 23/20
8	279.4	20/17
9	314.3
10	349.3
11	384.2
12	419.1
13	454	13/10, 30/23
14	489
15	523.9	23/17
16	558.8
17	593.7
18	628.7
19	663.6	19/13, 22/15
20	698.5	3/2
21	733.4	23/15, 26/17, 29/19
22	768.4	14/9
23	803.3
24	838.2
25	873.1
26	908.1	22/13, 27/16
27	943	19/11
28	977.9	30/17
29	1012.8
30	1047.8
31	1082.7
32	1117.6	19/10
33	1152.5
34	1187.5
35	1222.4
36	1257.3
37	1292.2
38	1327.2
39	1362.1	11/5
40	1397
41	1431.9
42	1466.9	7/3

Harmonics

Approximation of harmonics in 42ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-12.5	-16.0	+9.9	+7.7	+6.4	-16.0	-2.7	+3.0	-4.8	+4.8	-6.1
	Relative (%)	-35.9	-45.7	+28.2	+22.1	+18.4	-45.7	-7.7	+8.5	-13.8	+13.8	-17.5
Steps (reduced)		34 (34)	54 (12)	69 (27)	80 (38)	89 (5)	96 (12)	103 (19)	109 (25)	114 (30)	119 (35)	123 (39)

Approximation of harmonics in 42ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.0	+6.4	-8.3	-15.2	-15.4	-9.6	+1.6	-17.3	+3.0	-7.7	-14.8
	Relative (%)	-14.3	+18.4	-23.6	-43.5	-44.1	-27.4	+4.6	-49.6	+8.5	-22.1	-42.4
Steps (reduced)		127 (1)	131 (5)	134 (8)	137 (11)	140 (14)	143 (17)	146 (20)	148 (22)	151 (25)	153 (27)	155 (29)