Pitch and Frequency

There is a nonlinear relationship between pitch perception and frequency.

• e.g., the pitch interval of an octave corresponds to a frequency ratio of 2:1.
• thus octaves in higher registers span more frequencies

We will often encounter a pitch notation wich designates a pitch with an octave: C4 is middle C.

The pitch A4 or ``A440'' is often used as a reference, and is an A at 440 Hz.

What is the frequency one octave below A440?

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$$.$$