10ed5/4

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← 9ed5/410ed5/411ed5/4 →
Prime factorization 2 × 5
Step size 38.6314¢ 
Octave 31\10ed5/4 (1197.57¢)
(semiconvergent)
Twelfth 49\10ed5/4 (1892.94¢)
(semiconvergent)
Consistency limit 12
Distinct consistency limit 2

Division of the just major third into 10 equal parts (10ED5/4) is related to 31 edo, but with the 5/4 rather than the 2/1 being just. The octave is about 2.43 cents compressed and the step size is 38.63 cents.

Lookalikes: 31edo, 49edt, 72ed5, 18edf

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 38.631
2 77.263 18/17, 20/19, 21/20, 22/21
3 115.894 14/13, 15/14, 16/15, 17/16, 19/18
4 154.525 11/10, 12/11, 13/12, 21/19
5 193.157 9/8, 10/9, 19/17
6 231.788 8/7, 15/13, 17/15, 22/19
7 270.42 7/6, 20/17
8 309.051 6/5, 13/11, 19/16
9 347.682 11/9, 16/13, 17/14, 21/17
10 386.314 5/4

Harmonics

Approximation of harmonics in 10ed5/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.4 -9.0 -4.9 -4.9 -11.4 -7.9 -7.3 -18.0 -7.3 -17.8 -13.9
Relative (%) -6.3 -23.3 -12.6 -12.6 -29.6 -20.4 -18.9 -46.7 -18.9 -46.0 -35.9
Steps
(reduced)
31
(1)
49
(9)
62
(2)
72
(2)
80
(0)
87
(7)
93
(3)
98
(8)
103
(3)
107
(7)
111
(1)
Approximation of harmonics in 10ed5/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +2.1 -10.3 -13.9 -9.7 +1.2 +18.2 +1.8 -9.7 -16.9 +18.4 +18.7
Relative (%) +5.4 -26.7 -35.9 -25.1 +3.2 +47.0 +4.7 -25.1 -43.8 +47.7 +48.5
Steps
(reduced)
115
(5)
118
(8)
121
(1)
124
(4)
127
(7)
130
(0)
132
(2)
134
(4)
136
(6)
139
(9)
141
(1)