Pluck a string or buzz a horn and you never get just one pitch — you get a whole stack of them at once, for free. Toggle harmonics 1–10 below to see (and hear) the stack build up.
Slowed way down so you can actually see it — a real string wiggles thousands of times a second. Higher harmonics wiggle proportionally faster, which is exactly why they sound higher.
A bugle has no valves at all. Every note in every bugle call is just a different harmonic of the same tube — the player's air and lips pick which one sounds, nothing else changes.
Touch the string lightly at one of these spots — don't press down — and everything mutes except the part that was already sitting still: the node. That's the bell-like harmonic tone (real guitarists call it a "natural harmonic").
Every instrument is playing roughly the same harmonic series — what makes them sound different is which harmonics are loud and which are quiet. Try a few mixtures:
Harmonic 1 (the fundamental) can't be switched off — it's the pitch you'd actually call "the note." Everything from 2 up is riding along on top of it, whether you can consciously hear it or not.