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Explain overtones and timbre as you would to a capable student, in 3-4 sentences.

When you play a note on an instrument, you're not hearing just one pure frequency—you're hearing the fundamental pitch plus a series of higher frequencies called overtones that vibrate at whole-number multiples of that fundamental (2x, 3x, 4x, etc.). Timbre is the unique "color" or quality of a sound that lets you distinguish a violin from a trumpet playing the same note, and it's determined by which overtones are present and how loud each one is. Think of it like this: the fundamental frequency tells you what note is being played, while the pattern of overtones creates the instrument's sonic fingerprint. This is why the same melody sounds so different when played on different instruments—they each emphasize different combinations of overtones.