43ed7/3

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43ed7/3

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Prime factorization	43 (prime)
Step size	34.1133¢
Octave	35\43ed7/3 (1193.96¢)
Twelfth	56\43ed7/3 (1910.34¢)
Consistency limit	3
Distinct consistency limit	3

43 equal divisions of 7/3 (abbreviated 43ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 43 equal parts of about 34.1 ¢ each. Each step represents a frequency ratio of (7/3)^1/43, or the 43rd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	34.113
2	68.227	24/23
3	102.34	18/17
4	136.453	13/12, 27/25
5	170.566	11/10
6	204.68
7	238.793	23/20
8	272.906	7/6
9	307.019	25/21
10	341.133	11/9, 17/14, 28/23
11	375.246
12	409.359	24/19
13	443.473	22/17
14	477.586	29/22
15	511.699
16	545.812	26/19
17	579.926	7/5
18	614.039	10/7
19	648.152	29/20
20	682.266
21	716.379
22	750.492	17/11, 20/13
23	784.605	11/7
24	818.719
25	852.832	18/11, 23/14
26	886.945	5/3
27	921.058	17/10, 29/17
28	955.172
29	989.285	23/13, 30/17
30	1023.398	9/5
31	1057.512	24/13
32	1091.625
33	1125.738	21/11, 23/12
34	1159.851
35	1193.965	2/1
36	1228.078
37	1262.191	29/14
38	1296.305
39	1330.418	28/13
40	1364.531	11/5
41	1398.644
42	1432.758
43	1466.871	7/3

Harmonics

Approximation of harmonics in 43ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.0	+8.4	-12.1	+11.0	+2.4	+8.4	+16.0	+16.8	+4.9	+10.5	-3.7
	Relative (%)	-17.7	+24.6	-35.4	+32.2	+6.9	+24.6	+46.9	+49.2	+14.5	+30.8	-10.8
Steps (reduced)		35 (35)	56 (13)	70 (27)	82 (39)	91 (5)	99 (13)	106 (20)	112 (26)	117 (31)	122 (36)	126 (40)

Approximation of harmonics in 43ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.8	+2.4	-14.7	+10.0	+7.4	+10.7	-14.6	-1.1	+16.8	+4.5	-4.3
	Relative (%)	-17.0	+6.9	-43.2	+29.2	+21.6	+31.5	-42.9	-3.2	+49.2	+13.1	-12.5
Steps (reduced)		130 (1)	134 (5)	137 (8)	141 (12)	144 (15)	147 (18)	149 (20)	152 (23)	155 (26)	157 (28)	159 (30)