40ed5

← 39ed5

40ed5

41ed5 →

Prime factorization	23 × 5
Step size	69.6578 ¢
Octave	17\40ed5 (1184.18 ¢)
Twelfth	27\40ed5 (1880.76 ¢)
Consistency limit	5
Distinct consistency limit	5

40 equal divisions of the 5th harmonic (abbreviated 40ed5) is a nonoctave tuning system that divides the interval of 5/1 into 40 equal parts of about 69.7 ¢ each. Each step represents a frequency ratio of 5^1/40, or the 40th root of 5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	69.7	26/25, 28/27
2	139.3	25/23
3	209	9/8, 26/23
4	278.6	20/17
5	348.3
6	417.9
7	487.6
8	557.3
9	626.9
10	696.6	3/2
11	766.2	14/9
12	835.9
13	905.6	22/13, 27/16
14	975.2	7/4
15	1044.9
16	1114.5	19/10
17	1184.2
18	1253.8
19	1323.5	15/7
20	1393.2	29/13
21	1462.8	7/3
22	1532.5	17/7
23	1602.1
24	1671.8	21/8, 29/11
25	1741.4
26	1811.1	20/7
27	1880.8
28	1950.4
29	2020.1
30	2089.7	10/3
31	2159.4
32	2229.1
33	2298.7
34	2368.4
35	2438
36	2507.7	17/4
37	2577.3
38	2647	23/5
39	2716.7
40	2786.3	5/1

Harmonics

Approximation of harmonics in 40ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-15.8	-21.2	-31.6	+0.0	+32.6	-25.2	+22.2	+27.3	-15.8	+28.2	+16.8
	Relative (%)	-22.7	-30.4	-45.4	+0.0	+46.9	-36.2	+31.9	+39.2	-22.7	+40.4	+24.2
Steps (reduced)		17 (17)	27 (27)	34 (34)	40 (0)	45 (5)	48 (8)	52 (12)	55 (15)	57 (17)	60 (20)	62 (22)

Music

• escape yourself - Merct (2025)

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