29ed5/4

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← 28ed5/4 29ed5/4 30ed5/4 →
Prime factorization 29 (prime)
Step size 13.3212¢ 
Octave 90\29ed5/4 (1198.9¢)
Twelfth 143\29ed5/4 (1904.93¢)
Consistency limit 8
Distinct consistency limit 6

29 equal divisions of 5/4 (abbreviated 29ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 29 equal parts of about 13.3 ¢ each. Each step represents a frequency ratio of (5/4)1/29, or the 29th root of 5/4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 13.3
2 26.6
3 40
4 53.3
5 66.6 23/22, 25/24, 26/25
6 79.9 20/19, 22/21, 24/23
7 93.2 19/18, 21/20
8 106.6 16/15, 17/16, 18/17
9 119.9 15/14
10 133.2 13/12, 14/13
11 146.5 12/11, 25/23
12 159.9
13 173.2 10/9, 11/10, 21/19
14 186.5
15 199.8 19/17
16 213.1 9/8, 17/15, 25/22, 26/23
17 226.5 8/7
18 239.8 23/20
19 253.1 15/13, 22/19
20 266.4 7/6
21 279.7 13/11, 20/17
22 293.1 25/21
23 306.4 19/16
24 319.7 6/5
25 333 17/14
26 346.4 11/9
27 359.7 16/13, 26/21, 27/22
28 373 21/17
29 386.3 5/4

Harmonics

Approximation of harmonics in 29ed5/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -1.10 +2.97 -2.19 -2.19 +1.88 +1.43 -3.29 +5.94 -3.29 +4.88 +0.78
Relative (%) -8.2 +22.3 -16.4 -16.4 +14.1 +10.7 -24.7 +44.6 -24.7 +36.7 +5.9
Steps
(reduced)
90
(3)
143
(27)
180
(6)
209
(6)
233
(1)
253
(21)
270
(9)
286
(25)
299
(9)
312
(22)
323
(4)
Approximation of harmonics in 29ed5/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -4.58 +0.33 +0.78 -4.38 -2.77 +4.85 +4.49 -4.38 +4.40 +3.79 -6.56
Relative (%) -34.4 +2.5 +5.9 -32.9 -20.8 +36.4 +33.7 -32.9 +33.0 +28.4 -49.3
Steps
(reduced)
333
(14)
343
(24)
352
(4)
360
(12)
368
(20)
376
(28)
383
(6)
389
(12)
396
(19)
402
(25)
407
(1)