10ed5/4: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''[[Ed5/4|Division of the just major third]] into 10 equal parts''' (10ED5/4) is related to [[31edo|31 edo]], but with the 5/4 rather than the 2/1 being just. The octave is about 2.43 cents stretched and the step size is 38.63 cents.
'''[[Ed5/4|Division of the just major third]] into 10 equal parts''' (10ED5/4) is related to [[31edo|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]]
Lookalikes: [[31edo]], [[49edt]], [[72ed5]], [[18edf]]

Revision as of 00:52, 15 September 2024

← 9ed5/4 10ed5/4 11ed5/4 →
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 9

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

Harmonics

Approximation of harmonics in 10ed5/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) -2.43 -9.02 -4.85 -4.85 -11.45 -7.90 -7.28 -18.04 -7.28 -17.76 -13.87 +2.08 -10.32 -13.87 -9.71
Relative (%) -6.3 -23.3 -12.6 -12.6 -29.6 -20.4 -18.9 -46.7 -18.9 -46.0 -35.9 +5.4 -26.7 -35.9 -25.1
Steps
(reduced)
31
(1)
49
(9)
62
(2)
72
(2)
80
(0)
87
(7)
93
(3)
98
(8)
103
(3)
107
(7)
111
(1)
115
(5)
118
(8)
121
(1)
124
(4)