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Explain the overtone series as you would to a capable student, in 3-4 sentences.

When you play a single note on most instruments, you're actually hearing multiple frequencies at once: a fundamental pitch plus a series of higher "overtones" or "harmonics" that vibrate at whole-number multiples of that fundamental (2x, 3x, 4x, etc.). These overtones get progressively quieter and blend together to create the characteristic tone color, or timbre, that makes a trumpet sound different from a violin even when playing the same note. The overtone series follows a consistent pattern across all pitches—the intervals between successive overtones get smaller as you go higher, starting with an octave, then a fifth, then a fourth, and so on. Understanding this series helps explain why certain intervals sound consonant, how brass instruments produce different notes, and forms the basis for musical harmony itself.