Harmonic series (music)

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Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series (see harmonic series (mathematics)).

The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air column, or a higher harmonic chosen by the player. The musical timbre of a steady tone from such an instrument is determined by the relative strengths of each harmonic.

Contents

Terminology

Partial, harmonic, fundamental, inharmonicity, and overtone

Any complex tone "can be described as a combination of many simple periodic waves (i.e., sine waves) or partials, each with its own frequency of vibration, amplitude, and phase."[1]

A partial is any of the sine waves by which a complex tone is described.

A harmonic (or a harmonic partial) is any of a set of partials that are whole number multiples of a common fundamental frequency.[2] This set includes the fundamental, which is a whole number multiple of itself (1 times itself).

Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial.[3]

Typical pitched instruments are designed to have partials that are close to being harmonics, with very low inharmonicity; therefore, in music theory, and in instrument tuning, it is convenient to speak of the partials in those instruments' sounds as harmonics, even if they have some inharmonicity. Other pitched instruments, especially certain percussion instruments, such as marimba, vibraphone, tubular bells, and timpani, contain non-harmonic partials, yet give the ear a good sense of pitch. Non-pitched, or indefinite-pitched instruments, such as cymbals, gongs, or tam-tams make sounds rich in inharmonic partials.

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