Harmonic series (music)

Pitched musical instruments are usually based on a harmonic oscillator such as a string or a column of air. Both can and do oscillate at numerous frequencies simultaneously. Because of the self-filtering nature of resonance, these frequencies are mostly limited to integer multiples of the lowest possible frequency, and such multiples form the harmonic series.

Description of the harmonic series

The lowest possible frequency of a harmonic oscillator is called its fundamental frequency. This frequency determines the musical pitch or note that is created by vibration over the full length of the string or air column.

Related Topics:
Harmonic oscillator - Fundamental frequency - Pitch

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In nearly every musical instrument, the fundamental note is always accompanied by other, higher-frequency tones that are generally called overtones. In pitched (i.e., non-percussion) instruments, these shorter, faster waves are reflected between the two ends of the string or air column. As the reflected waves interact, frequencies whose wavelengths do not divide evenly into the length of the string or air column are suppressed, and the vibrations that persist are called harmonics. Their wavelengths are 1, 1/2, 1/3, 1/4, 1/5, 1/6, etc. of the length of the string or air column.

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Theoretically, these wavelengths produce vibrations at frequencies that are 2, 3, 4, 5, 6, etc. times the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator against which it vibrates often alter these frequencies. (See inharmonicity and stretched tuning for alterations specific to wire-stringed instruments and certain electric pianos.) However, those alterations are small, and except for precise, highly specialized tuning, it is reasonable to think of the frequencies of the harmonic series as integer multiples of the fundamental frequency.

Related Topics:
Inharmonicity - Stretched tuning

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The harmonic series is an arithmetic series (2xf, 3xf, 4xf, 5xf, ...). In terms of frequency (measured in cycles per second, or hertz (Hz)), the difference between consecutive harmonics is therefore constant. But because our ears respond to sound logarithmically, we perceive higher harmonics as "closer together" than lower ones. On the other hand, the octave series is a geometric progression (2×f, 4×f, 8×f, 16xf, ...), and we hear these distances as "the same" in all ranges. In terms of what we hear, each octave in the harmonic series is divided into increasingly "smaller" and more numerous intervals.

Related Topics:
Arithmetic series - Hertz - Logarithmically - Octave - Geometric progression

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The second harmonic, twice the frequency of the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a perfect fifth above the second. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a perfect fourth above the third (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher). The combined oscillation of a string with several of its lowest harmonics can be seen clearly in an interactive animation at Edward Zobel's "Zona Land".

Related Topics:
Octave - Perfect fifth - Perfect fourth

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For a fundamental of C1, the first 16 harmonics are notated as shown. If you have a player capable of reading Vorbis files (for example Winamp 3), you can listen to A2 (110 Hz) and 15 of its partials by . You can also hear a sweep of the first 20 harmonics of A1 (55 Hz) in Quicktime format by clicking here.

Related Topics:
Vorbis - Winamp

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