Direct approximation

A direct approximation of an interval in a given edo is the number of edosteps that most closely approximates it, found by rounding to the nearest integer the edo number times the binary logarithm of the interval:

[math]\operatorname {round} (n\log_2(i))[/math]

for ratio i in n-edo.

Examples of direct approximations

Interval, ratio	12edo	17edo	19edo	26edo
Perfect fifth, 3/2	7	10	11	15
Just major third, 5/4	4	5	6	8
Just minor third, 6/5	3	4	5	7
Harmonic seventh, 7/4	10	14	15	21

Of these intervals, the fifth plays an important role for characterizing edo systems (as it defines the size of M2, m2, A1). Also, a simple test can show if circle-of-fifths notation can be applied to a given edo system, because for this the sizes of fifth and octave must be relatively prime.