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Pitch and Frequency

Pitch and frequency are two ways to communicate how high or low a note sounds. Pitch is how humans perceive change in how high or low a sound is (e.g., MIDI pitch 0 to 127, with A4 = 69). Frequency is a physical measurement of how fast a sound wave vibrates.

NOTE: MIDI pitch A4 (69) corresponds to 440 Hertz in frequency.

The relationship between pitch and frequency is logarithmic / exponential.

NOTE: One octave change in pitch (e.g., A4 to A5), corresponds to a doubling (or halving) of frequency. For example:

  • A4 is 69 in pitch, and 440.0 Hz in frequency
  • A5 is 81 (69 + 12) in pitch, and 880.0 Hz (440.0 * 2) in frequency
  • A3 is 57 (69 – 12) in pitch, and 220.0 Hz (440.0 / 2) in frequency

Conversion between Pitch and Frequency

The music library provides two functions to convert between pitch (0-127) and frequency (in Hertz):

Function Description
pitchToFrequency(pitch) Converts MIDI pitch (0-127) to frequency (in Hertz).
frequencyToPitch(frequency) Converts frequency (in Hertz) to MIDI pitch (0-127) 
# convert MIDI pitches to frequencies
>>> pitchToFrequency(A4)
440.0
>>> pitchToFrequency(C4)
261.6255653005986
>>> pitchToFrequency(E4)
329.6275569128699

# convert frequencies to MIDI pitches
>>> frequencyToPitch(440.0)
(69, 0)
>>> frequencyToPitch(443.5)
(69, 562)
>>> frequencyToPitch(438.5)
(69, -242)

# capture values in variables
>>> pitch, pitchBend = frequencyToPitch(438.5)   
>>> pitch
69
>>> pitchBend
-242

This returns the closest MIDI pitch (0-127), and the remaining pitch bend for finer (microtonal) control. Pitch bend corresponds to +/- 2 half tones, and ranges from -8191 to +8192 (0 means no pitch bend).

NOTE: Note objects may be generated with either pitch or frequency values.