Why are sine waves considered "pure" tones? Why do we consider sinusoids the building blocks of periodic functions?
When analyzing physical, electronic, and acoustic/musical phenomena, it's often handy to view things in the frequency domain. I understand the basic idea of Fourier Analysis
, namely breaking apart periodic functions in to the sums of sinusoids of given frequency and phase.
What I don't get is why or how sinusoids are "special". I know in the real world a great number of objects are essentially complicated dampened spring oscillators, so sinusoids are common in nature. Is that the end of it, or is there some deeper reason this function is good at representing periodic phenomena?
Isn't it possible to do a fourier analysis that breaks an arbitrary periodic function in to the sum of any other periodic function? Why not square waves, or a sawtooth?
While sine waves sound "pure" to me, it seems highly subjective. Is there something more than convention at work here? Some property of the ear?
The wikipedia page for sine waves
The human ear can recognize single sine waves because sounds with such a waveform sound "clean" or "clear" to humans; some sounds that approximate a pure sine wave are whistling, a crystal glass set to vibrate by running a wet finger around its rim, and the sound made by a tuning fork.
This seems arbitrary though.
We say that the timbre of a violin is complex because it has many different harmonics. But the very idea of harmonic content assumes some basis function, right? Could we just as easily say a sine wave is complex by choosing square waves as our basis of spectral analysis?
So is this just a convention, and if so, where do we get it?