Direct approximation
A direct approximation of an interval in a given EDO is the number of EDO steps that most closely approximates it, found by rounding to the nearest integer the EDO number times the binary logarithm of the interval: [math]\displaystyle{ ⌈n_{\text{edo}}·\log_2(i)⌋ }[/math].
Examples of direct approximations
| Interval, ratio | 12edo | 17edo | 19edo | 26edo |
|---|---|---|---|---|
| Just perfect fifth, 3/2 | 7 | 10 | 11 | 15 |
| Just classic major third, 5/4 | 4 | 5 | 6 | 8 |
| Just classic 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.