43ed5

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43ed5

44ed5 →

Prime factorization	43 (prime)
Step size	64.798 ¢
Octave	19\43ed5 (1231.16 ¢)
Twelfth	29\43ed5 (1879.14 ¢)
Consistency limit	2
Distinct consistency limit	2

43 equal divisions of the 5th harmonic (abbreviated 43ed5) is a nonoctave tuning system that divides the interval of 5/1 into 43 equal parts of about 64.8 ¢ each. Each step represents a frequency ratio of 5^1/43, or the 43rd root of 5.

Theory

43ed5 misses 2/1 and cannot be considered equal to 18edo or 19edo. It is actually similar to 37ed4 (18.5edo).

In terms of no-2's no-3's subgroups, 43ed5 excels in the 5.7.11 subgroup. It supports the pentadacus temperament and is a nearly-optimal tuning of it. Unfortunately, it completely misses the 13th harmonic and has mediocre approximations for the 17th and 19th harmonics.

Prime harmonics

Approximation of prime harmonics in 43ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+31.2	-22.8	+0.0	+0.7	-4.2	+30.5	+19.7	+21.5	+14.8	+2.2	+16.4
	Relative (%)	+48.1	-35.2	+0.0	+1.0	-6.6	+47.1	+30.4	+33.2	+22.8	+3.5	+25.3
Steps (reduced)		19 (19)	29 (29)	43 (0)	52 (9)	64 (21)	69 (26)	76 (33)	79 (36)	84 (41)	90 (4)	92 (6)

Interval table

Steps	Cents	Approximate ratios
0	0	1/1
1	64.8	30/29
2	129.6	14/13
3	194.4	19/17
4	259.2	22/19, 29/25
5	324
6	388.8
7	453.6	13/10, 30/23
8	518.4	23/17
9	583.2	7/5
10	648
11	712.8
12	777.6	11/7
13	842.4
14	907.2	22/13
15	972
16	1036.8
17	1101.6
18	1166.4
19	1231.2
20	1296
21	1360.8	11/5
22	1425.6	25/11
23	1490.4
24	1555.2
25	1619.9
26	1684.7	29/11
27	1749.5
28	1814.3
29	1879.1
30	1943.9
31	2008.7
32	2073.5
33	2138.3
34	2203.1	25/7
35	2267.9
36	2332.7	23/6
37	2397.5
38	2462.3	29/7
39	2527.1
40	2591.9
41	2656.7
42	2721.5	29/6
43	2786.3	5/1