So if an A is 440hz, why does a piano playing an A sound different than a violin, a guitar, or someone’s voice making that same A 440 note? It’s obvious that the pitch is the same on each instrument but each instrument has a distinct sound. I’ve never heard an A on a piano and thought, is that a piano or a cello. Why can we distinguish between instruments?
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When you play a note on an instrument, the instrument will produce the fundamental frequency, for A, this is 440Hz. But the instrument also produces harmonics. Harmonics are integer multiples of the fundamental frequency. For an A, the 2nd harmonic is 880Hz, 3rd is 1320Hz, etc…
You might also get subharmonics (integer fractions), ie, 220Hz, 110Hz, and maybe even harmonics of the subharmonics, so 660Hz, 1100Hz. Although these usually occur at much much lower amplitudes.
Essentially the relative amplitudes (and phase!) of all of the harmonics together create the specific timber or tonality of the instrument. This is why a violin will sound different from a piano.
Even laboratory sin wave generators cannot produce perfect sin waves, harmonics will always be present, although typically at *very* low amplitude compared to the fundamental.
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