40ed7/4

From Xenharmonic Wiki
Jump to navigation Jump to search
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 39ed7/4 40ed7/4 41ed7/4 →
Prime factorization 23 × 5
Step size 24.2206¢ 
Octave 50\40ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth 79\40ed7/4 (1913.43¢)
Consistency limit 3
Distinct consistency limit 3

40 equal divisions of 7/4 (abbreviated 40ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 40 equal parts of about 24.2⁠ ⁠¢ each. Each step represents a frequency ratio of (7/4)1/40, or the 40th root of 7/4. It has an accurate approximation to the 4:5:6:7 tetrad, and is close to 29edf, 99ed4, and is related to the sengagen temperament.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 24.2
2 48.4
3 72.7 23/22, 26/25
4 96.9
5 121.1 15/14
6 145.3 25/23
7 169.5
8 193.8 29/26
9 218 17/15, 25/22, 26/23
10 242.2
11 266.4
12 290.6 13/11
13 314.9
14 339.1 17/14
15 363.3 21/17, 26/21
16 387.5
17 411.8
18 436
19 460.2
20 484.4 29/22
21 508.6
22 532.9
23 557.1 29/21
24 581.3 7/5
25 605.5
26 629.7
27 654 19/13
28 678.2
29 702.4 3/2
30 726.6
31 750.8
32 775.1
33 799.3
34 823.5
35 847.7
36 871.9
37 896.2
38 920.4 17/10, 29/17
39 944.6 19/11
40 968.8

Harmonics

Approximation of harmonics in 40ed7/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +11.0 +11.5 -2.2 -0.9 -1.7 -2.2 +8.9 -1.3 +10.1 -9.6 +9.3
Relative (%) +45.5 +47.4 -8.9 -3.9 -7.1 -8.9 +36.6 -5.2 +41.7 -39.6 +38.5
Steps
(reduced)
50
(10)
79
(39)
99
(19)
115
(35)
128
(8)
139
(19)
149
(29)
157
(37)
165
(5)
171
(11)
178
(18)
Approximation of harmonics in 40ed7/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -8.1 +8.9 +10.5 -4.3 +11.8 +9.8 -11.2 -3.1 +9.3 +1.4 -2.8
Relative (%) -33.6 +36.6 +43.5 -17.8 +48.9 +40.3 -46.1 -12.8 +38.5 +6.0 -11.8
Steps
(reduced)
183
(23)
189
(29)
194
(34)
198
(38)
203
(3)
207
(7)
210
(10)
214
(14)
218
(18)
221
(21)
224
(24)