Why do musical notes sound different on different instruments?

A musical pitch is a blend of many different frequencies beside the fundamental. Here’s a visualization of the different vibrational modes of an ideal string. The string’s movements are the sum of all these different modes simultaneously.

The top row shows the fundamental frequency, the one you hear as the pitch — say it’s a violin string playing A 440. The second row shows the first harmonic, the string vibrating in halves, producing A 880. The harmonic is quieter than the fundamental, so you aren’t necessarily conscious of it, but you can isolate it by lightly touching the string at its halfway point while playing. The other rows show other harmonics, vibrations of the string in integer ratios, each producing a pitch that’s an integer multiple of the fundamental frequency. The second harmonic is E 1320; the third is A 1760; the fourth is C# 2200.

In an ideal string, the harmonics would continue to get infinitely higher, beyond the range of your hearing. As the harmonics get higher, they also get quieter and subtler. Still, they all have an impact on the overall sound of the instrument. All musical instruments have overtones: winds, the human throat, speaker cones, even well-tuned drumheads.

Real instruments aren’t ideal, so they don’t produce all of the overtones pictured above equally. Different instruments will produce different overtones more or less prominently, and will mix in some non-harmonic overtones and noise. Also, real notes begin with a short burst of noise, and decay in characteristic ways. The precise blend of harmonic and inharmonic frequencies and noise in a note over time determines the timbre of the instrument.

Read more about how harmonics form the basis of western music theory.

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