The sine wave thing is technically true, but if you try it in practice, as I did extensively in a college acoustics course, you’ll find that making even a decen

The sine wave thing is technically true, but if you try it in practice, as I did extensively in a college acoustics course, you’ll find that making even a decent approximation of a square or a saw wave requires sine waves at many multiples of the upper threshold of human hearing. You need those insanely high overtones to produce sharp “corners” in the wave form.