Like the title says, I'm curious why sine waves are often referred to as "natural" or "pure" oscillations. Why not some other oscillating function? As an example of the type of idea I'm referring to, the wikipedia "Sine Wave" article says: To me, the argument that it sounds pure because it's a single frequency with no harmonics is a little weak. Doesn't it only lack harmonics because we've defined the notion of harmonics using sine waves? I do understand that orthogonality means there's a certain mathematical convenience associated with sine waves as opposed to, e.g. triangle waves, but the claim seems to be that sine waves are more than just a mathematical convenience; they're somehow "natural" feeling. So is there a physical reason to define everything based on sine waves, or is it purely mathematical convenience?