The following table provides frequency ratios for intervals up to an octave:
|
ASCENDING
|
INTERVALS |
DESCENDING
|
INTERVALS | |
| Interval | Frequency Ratio | Interval | Frequency Ratio | |
| unison | 1 : 1 | unison | 1 : 1 | |
| m2 | 1 : 1.059 | m2 | 1 : .943 | |
| M2 | 1 : 1.122 | M2 | 1 : .8909 | |
| m3 | 1 : 1.189 | m3 | 1 : .84 | |
| M3 | 1 : 1.26 | M3 | 1 : .7937 | |
| P4 | 1 : 1.334 | P4 | 1 : .749 | |
| aug4/dim5 | 1 : 1.4142 | aug4/dim5 | 1 : .707 | |
| P5 | 1 : 1.498 | P5 | 1 : .667 | |
| m6 | 1 : 1.587 | m6 | 1 : .63 | |
| M6 | 1 : 1.682 | M6 | 1 : .595 | |
| m7 | 1 : 1.7818 | m7 | 1 : .561 | |
| M7 | 1 : 1.887 | M7 | 1 : .530 | |
| Octave | 1 : 2 | Octave | 1 : .5 |
For ascending intervals greater than an octave, multiply the INTEGER portion of the Frequency ratio by 2 for each successive octave (1, 2, 4, 8, etc.)
Examples:
a minor tenth up = 2.189
2 octaves + a tritone up = 4.4142
For descending intervals greater than an octave, divide the Freq. ratio by 2 (if between 1 and 2 octaves), by 4 (if between 2 & 3 octaves), and so on.
Examples:
an octave plus a perfect 4th down = .3745 ( .749/2 )
2 octaves plus a minor 3rd down = .21 ( .84/4 )