Pitch and Frequency

Listeners usually compare tones on the basis of the musical interval separating them: m3, P5, P8 etc.

An octave (P8) corresponds to a doubling of frequency.

There is a nonlinear relationship between pitch perception and frequency in Hz:

• an octave above 220 Hz is an increase of 220 Hz;
• an octave above 440 Hz is an increase of 440 Hz.

In equal-tempered tuning, there are 12 evenly spaced tones in an octave, called semi-tones:

• The frequency $n$ semitones above A440 is
  $$440 \times 2^{n/12}$$    Hz$$.$$

• The frequency $n$ semitones below A440 is
  $$440 \times 2^{-n/12}$$    Hz$$.$$

pitchFreq.pd