7ed5

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← 6ed57ed58ed5 →
Prime factorization 7 (prime)
Step size 398.045¢ 
Octave 3\7ed5 (1194.13¢)
(convergent)
Twelfth 5\7ed5 (1990.22¢)
(semiconvergent)
Consistency limit 6
Distinct consistency limit 2

Division of the 5th harmonic into 7 equal parts (7ed5) is related to 3 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is related to the regular temperaments which temper out 441/440 and 244515348/244140625 in the 11-limit, which is supported by 3, 12, 15, 175, 190, 202, and/or 217 EDOs.

Harmonics

Approximation of harmonics in 7ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6 +88 -12 +0 +82 -184 -18 +177 -6 -171 +77
Relative (%) -1.5 +22.2 -2.9 +0.0 +20.7 -46.3 -4.4 +44.4 -1.5 -42.9 +19.2
Steps
(reduced)
3
(3)
5
(5)
6
(6)
7
(0)
8
(1)
8
(1)
9
(2)
10
(3)
10
(3)
10
(3)
11
(4)

Intervals

degree cents value corresponding
JI intervals
comments
0 0.0000 exact 1/1
1 398.0448 34/27 pseudo-5/4
2 796.0896 19/12
3 1194.1344 255/128 pseudo-octave
4 1592.1793 128/51 pseudo-5/2
5 1990.2241 60/19
6 2388.2689 135/34 pseudo-4/1
7 2786.3137 exact 5/1 just major third plus two octaves