Why Sine Wave?

In this post we will understand what it means to say “this song has a lot of high frequencies”, then hunt and capture the waveform that allows us to say this! Some Python code will be used, but understanding it is not necessary. Footnotes are more technically advanced.

The x coordinate of the circle… is frequency?!

A simple sine wave
A sine wave

Sine waves are widely agreed to be the “most basic wave” when doing anything involving periodic signals – whether radio circuit analysis or music synthesis. Indeed, the sine wave is pretty simple as far as waves go, and quite smooth to boot, but I’ve always asked myself: why the sine? There are many other simple, basic waves that could be used as a basis for a theory of frequencies.

A square wave, a triangle wave, a sine wave and a sine wave
A square wave, a triangle wave, a sine wave and a sine wave “fattened” by taking its square root

… and yet mathematicians and engineers, even musicians, always choose the sine[1]. What makes the sine so special? Could a theory of frequency analysis be built around a different waveform, and how different would it be? How different would music sound if we used another simple waveform as our basis? Continue reading