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A musical tone is a complex blend of harmonic partials whose ratios are whole-number multiples of the fundamental

Concept L1Foundations A · Music theory & musicianshipB · Sound design & synthesis

When a string, pipe, or oscillator vibrates, it simultaneously vibrates along its fractional lengths (halves, thirds, quarters). Each fractional mode produces a partial at a whole-number multiple of the fundamental frequency. Partials with whole-number ratios are called harmonics; the resulting series is the harmonic series. The fundamental (first harmonic) determines perceived pitch; upper harmonics determine timbre. Instruments vary in which harmonics they emphasize: square waves emphasize odd harmonics; sawtooth waves are rich in all harmonics; sine waves contain only the fundamental. Inharmonic instruments (bells, gongs) have partials that are not whole-number multiples, producing indefinite pitch.

Examples

A1 at 110 Hz: harmonics at 220, 330, 440, 550, 660 Hz. The 4th harmonic (440 Hz) is A4 — two octaves up. The 5th harmonic (550 Hz) is approximately C#4.

Assessment

Given a fundamental of 220 Hz, list the first five harmonics. Explain why a sine wave sounds pure while a sawtooth sounds bright.

Prerequisites — understand these first

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Sources

“A succession of such partials—such as 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, and so on—is called aharmonic series.”
corpus · michael-hewitt-music-theory-for-computer-musicians · chunk 6

Taught in modules

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