40edt

← 39edt

40edt

41edt →

Prime factorization	23 × 5
Step size	47.5489¢
Octave	25\40edt (1188.72¢) (→5\8edt)
Consistency limit	4
Distinct consistency limit	4

40EDT is the equal division of the third harmonic into 40 parts of 47.5489 cents each, corresponding to 25.2372 edo. It is related to the regular temperament which tempers out |440 -219 -40> in the 5-limit, which is supported by 101, 429, 530, 959, 1388, 1817, 2246 and 2347 EDOs.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	47.549
2	95.098	18/17, 19/18, 20/19
3	142.647	13/12
4	190.196	19/17
5	237.744	23/20
6	285.293	13/11, 20/17
7	332.842	17/14, 23/19
8	380.391
9	427.94	9/7, 23/18
10	475.489
11	523.038	19/14, 23/17, 27/20
12	570.587	18/13
13	618.135	10/7
14	665.684	28/19
15	713.233
16	760.782	14/9, 17/11
17	808.331
18	855.88	18/11, 23/14
19	903.429
20	950.978	19/11
21	998.526
22	1046.075	11/6
23	1093.624
24	1141.173	27/14, 29/15
25	1188.722
26	1236.271
27	1283.82	21/10, 23/11
28	1331.369	13/6, 28/13
29	1378.917	20/9
30	1426.466
31	1474.015	7/3
32	1521.564
33	1569.113
34	1616.662	28/11
35	1664.211
36	1711.76
37	1759.308
38	1806.857	17/6
39	1854.406
40	1901.955	3/1

Harmonics

Approximation of prime harmonics in 40edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-11.3	+0.0	+19.1	+7.1	-14.6	-18.5	-7.4	-9.8	-7.7	+18.9	-1.4
	Relative (%)	-23.7	+0.0	+40.1	+15.0	-30.6	-38.9	-15.6	-20.6	-16.2	+39.8	-3.0
Steps (reduced)		25 (25)	40 (0)	59 (19)	71 (31)	87 (7)	93 (13)	103 (23)	107 (27)	114 (34)	123 (3)	125 (5)

Approximation of prime harmonics in 40edt

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-22.4	-10.0	+2.7	-8.7	+21.1	-21.9	+15.4	-4.3	-9.6	-10.2	-4.3
	Relative (%)	-47.2	-21.0	+5.6	-18.2	+44.3	-46.1	+32.5	-9.1	-20.2	-21.4	-9.0
Steps (reduced)		131 (11)	135 (15)	137 (17)	140 (20)	145 (25)	148 (28)	150 (30)	153 (33)	155 (35)	156 (36)	159 (39)

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