armonic

Harmonic is an adjective and noun used across disciplines to denote relationships governed by harmony, periodicity, or a set of integer multiples of a base quantity. The term appears in music to describe tonal relations and overtone structure, in physics and signal processing to describe periodic motion and frequency content, and in mathematics to denote related functions and analyses.

In music, a harmonic refers to a partial sound frequency that is an integer multiple of a fundamental frequency. The collection of harmonics forms the harmonic series, shaping a tone's timbre. Players can produce harmonics on stringed instruments by lightly touching the string at nodal points (natural harmonics) or by combining stopping and touching to create artificial harmonics. The harmonic series also informs tuning and perceptions of consonance.

In physics, the harmonic oscillator models systems in which the restoring force is proportional to displacement, yielding simple sinusoidal motion. In wave phenomena and signal processing, any periodic waveform can be analyzed as a sum of harmonics via Fourier analysis; the relative amplitudes of these components determine waveform shape and timbre.

In mathematics, a harmonic function is a twice-differentiable function that satisfies Laplace's equation. Harmonic analysis studies functions and signals by decomposing them into harmonic components, using tools such as Fourier series and Fourier transforms. The term also appears in statistics as the harmonic mean, a specific type of average based on reciprocals.