14ed5/4

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← 13ed5/414ed5/415ed5/4 →
Prime factorization 2 × 7
Step size 27.5938¢ 
Octave 43\14ed5/4 (1186.53¢)
Twelfth 69\14ed5/4 (1903.97¢)
(semiconvergent)
Consistency limit 2
Distinct consistency limit 2

14 equal divisions of 5/4 (abbreviated 14ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 14 equal parts of about 27.6 ¢ each. Each step represents a frequency ratio of (5/4)1/14, or the 14th root of 5/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 27.594
2 55.188
3 82.782 18/17
4 110.375 14/13, 19/18
5 137.969 12/11, 15/14
6 165.563 10/9, 11/10, 21/19, 23/21
7 193.157 19/17
8 220.751 17/15
9 248.345 15/13
10 275.938 7/6
11 303.532 6/5, 13/11
12 331.126 11/9, 23/19
13 358.72 17/14, 21/17
14 386.314

Harmonics

Approximation of harmonics in 14ed5/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -13.5 +2.0 +0.7 +0.7 -11.4 -2.4 -12.8 +4.0 -12.8 -12.2 +2.7
Relative (%) -48.8 +7.3 +2.4 +2.4 -41.5 -8.6 -46.4 +14.6 -46.4 -44.4 +9.7
Steps
(reduced)
43
(1)
69
(13)
87
(3)
101
(3)
112
(0)
122
(10)
130
(4)
138
(12)
144
(4)
150
(10)
156
(2)
Approximation of harmonics in 14ed5/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +2.1 +11.8 +2.7 +1.3 +6.7 -9.4 +7.3 +1.3 -0.4 +1.9 +7.7
Relative (%) +7.5 +42.6 +9.7 +4.8 +24.5 -34.2 +26.6 +4.8 -1.3 +6.8 +27.9
Steps
(reduced)
161
(7)
166
(12)
170
(2)
174
(6)
178
(10)
181
(13)
185
(3)
188
(6)
191
(9)
194
(12)
197
(1)