The harmonic series: where timbre comes from

When a string or air column vibrates, it doesn't just produce one frequency. It produces a fundamental plus a stack of overtones - integer multiples of the fundamental.

A note at 100 Hz on a guitar also contains energy at 200 Hz, 300 Hz, 400 Hz, etc. The relative loudness of those overtones is what makes a guitar sound different from a flute even when both play 100 Hz.

This stack is called the harmonic series. It's the same physics that makes pure water resonate in a glass and gives every musical instrument its character.