MIDI Note Number to Frequency Conversion

 

The standard tuning pitch is A4 (A above middle C) 440 Hertz(Hz). When the octave is divided into 12 equally spaced pitches, then each interval between these pitches when they are arranged within the same octave in an ascending sequence is the equal-tempered semitone:

 

  2^1/12 =  1.059463094 . . .

 

 

The frequencies of equal-tempered pitches are easily calculated from any reference frequency according to :

 

                                 f = 2 ^n/12 f_ref

 

where n is the number of semitones between the reference frequency (f_ref), and the desired frequency, f .  

 

For example, the frequency of the equal-tempered pitch located a major third up (+4 semitones) from A440 is 440(2^4/12) = 554.365... Hz, while middle C, a major sixth down ( -9 semitones), has a frequency of 440(2^-9/12) = 261.6255...Hz.