Harmonic

A sinusoidal component whose frequency is an integer multiple of a fundamental frequency. The fundamental itself is the first harmonic; higher harmonics occur at whole-number multiples.

Fundamental frequency: The lowest frequency of a periodic signal, setting the spacing of its harmonics. Every harmonic’s frequency is measured as an integer multiple of this base frequency.
Timbre: The perceptual quality that distinguishes sounds with the same pitch and loudness. Different harmonic strengths give instruments distinct tone colors.
Overtone: A resonant frequency above a sound’s fundamental; overtones need not be integer multiples of it. The first overtone is often the second harmonic, but the terms are not interchangeable.
Piano string: A tensioned wire struck by a hammer to produce sound in a piano. Its stiffness shifts upper partials away from exact harmonic frequencies.
Fourier series: A representation of a periodic function as a sum of sinusoidal components at integer multiples of its fundamental frequency. It expresses periodic waveforms as sums of harmonics.
Musical acoustics: The study of how musical sounds are produced, transmitted, and perceived. Harmonic structure helps explain the pitch and tone of musical sounds.
Inharmonicity: The departure of a system’s partial frequencies from exact integer multiples of a fundamental. Inharmonic partials violate the defining frequency relationship of harmonics.
Clarinet acoustics: The sound-producing behavior of the clarinet’s cylindrical bore and reed. Its near-closed pipe behavior favors odd-numbered harmonics in the lower register.
Amplitude spectrum: A plot or representation of signal amplitude as a function of frequency. Its peaks show the strengths of a signal’s individual harmonics.
Resonance: The enhanced response of a system when driven near one of its natural frequencies. A resonator can selectively amplify harmonics near its natural modes.

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