Pitch Ratios

The following table provides frequency ratios for intervals up to an octave:

AscendingIntervalsDescendingIntervals
IntervalFrequency RatioIntervalFrequency Ratio
unison 1 : 1 unison 1 : 1
m21 : 1.059 m21 : 0.943
M21 : 1.122 M2 1 : 0.8909
m31 : 1.189 m31 : 0.84
M3 1 : 1.26 M3 1 : 0.7937
P41 : 1.334 P41 : 0.749
aug4/dim51 : 1.4142aug4/dim5 1 : 0.707
P51 : 1.498 P51 : 0.667
m6 1 : 1.587 m61 : 0.63
M61 : 1.682 M61 : 0.595
m71 : 1.7818 m71 : 0.561
M71 : 1.887 M71 : 0.530
Octave 1 : 2 Octave1 : 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 )