Why does a violin sound different from a flute playing the same note?

A violin and a flute sound different on the same note because a musical note is never a single frequency. When an orchestra plays its tuning A, the sound is a combination of 440, 880, 1,320 and 1,760 hertz and so on: whole-number multiples called harmonics. The lowest, the fundamental, gives the note its name. Every instrument produces a different mix of those frequencies, and the relative strength of each harmonic is the main ingredient of what musicians call timbre, or tone colour. Same note, different recipe.

The recipe comes from how the instrument vibrates. A bowed violin string is driven into a repeating but non-smooth motion that throws off a whole series of harmonics. In a transverse flute, the strongest frequency you hear is actually double the fundamental. A clarinet's cylindrical tube weakens the even-numbered harmonics, which is the main reason for its distinctive sound, while the conical saxophone lets them through.

The recipe isn't the whole story, though. The first instant of a note matters too: cut the attack off a piano or trumpet note and listeners struggle to tell which instrument it is.

The man who taught us to hear notes as mixtures was Hermann von Helmholtz. In his 1863 book On the Sensations of Tone, he called timbre Klangfarbe, tone colour, and described a resonator you could hold to your ear to pick a single frequency out of a complex sound.