June 2021
I have a decent understanding of physics and a love of music, but music theory has always mystified me. In this series, I'd like to document my notes on the topic as I try to learn it from scratch. I'm sure this will be far from comprehensive or rigorous, so I welcome suggestions and corrections.
Why are sine waves used to describe basic musical sounds? This might seem obvious, but it isn't, and the question is often glossed over. The sound of a plucked string, for example, isn't a pure sine wave. Pure sine waves actually sound harsh.
Yes, we can use a Fourier transform to represent any sound as the sum of sine waves, but that begs the question. Why not use some other waveform as the basis for music theory? I think there are two main reasons:
Sine waves describe simple harmonic motion, in which a restoring force is proportional to displacement (Hooke's law). This is the simplest of all vibrating systems, and can be used to model the vibrations of musical instruments.^{1}
Adding two sine waves of the same frequency, but with any phase and magnitude, produces another sine wave of the same frequency. This unique property is what makes sine waves a good basis for Fourier analysis.
The use of “simplest” here actually continues to beg the question, though. Why isn't a square wave considered simpler? Maybe someone else can provide a better explanation.↩