| Ascending | Intervals | Descending | Intervals |
| Interval | Frequency Ratio | Interval | Frequency Ratio |
| unison | 1 : 1 | unison | 1 : 1 |
| m2 | 1 : 1.059 | minor 2nd | 1 : 0.943 |
| M2 | 1 : 1.122 | Major 2nd | 1 : 0.8909 |
| m3 | 1 : 1.189 | minor 3rd | 1 : 0.84 |
| M3 | 1 : 1.26 | Major 3rd | 1 : 0.7937 |
| P4 | 1 : 1.334 | Perfect 4th | 1 : 0.749 |
| aug4/dim5 | 1 : 1.4142 | augm 4th/dim 5th | 1 : 0.707 |
| P5 | 1 : 1.498 | Perfect 5th | 1 : 0.667 |
| m6 | 1 : 1.587 | minor 6th | 1 : 0.63 |
| M6 | 1 : 1.682 | Major 6th | 1 : 0.595 |
| m7 | 1 : 1.7818 | minor 7th | 1 : 0.561 |
| M7 | 1 : 1.887 | Major 7th | 1 : 0.530 |
| Octave | 1 : 2 | Octave | 1 : 0.5 |
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 = 0.3745 ( 0.749/2 )
– 2 octaves plus a minor 3rd down = 0.21 ( 0.84/4 )