Sine Waves for Musical Scales

The most common tuning system in Western music is the twelve-tone equal temperament scale. In this example, notation is used assuming octaves on a standard piano keyboard with 88 keys, numbered from the left end of the keyboard. Then middle C, for example, is the 40th key. The 49th key, A, is the reference pitch with a frequency of 440 Hz. The frequencies of the other keys in the octave come from this formula:

,

where is the frequency of the key.

We can model the tones using a sinusoidal wave, , with .