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harmonic.

1 Physical term describing the vibrationvibration,
in physics, commonly an oscillatory motion—a movement first in one direction and then back again in the opposite direction. It is exhibited, for example, by a swinging pendulum, by the prongs of a tuning fork that has been struck, or by the string of a musical
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 in segments of a sound-producing body (see soundsound,
any disturbance that travels through an elastic medium such as air, ground, or water to be heard by the human ear. When a body vibrates, or moves back and forth (see vibration), the oscillation causes a periodic disturbance of the surrounding air or other medium that
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). A string vibrates simultaneously in its whole length and in segments of halves, thirds, fourths, etc. These segments form what is known in algebra as a harmonic series or progression, since the rate of vibration of each segment is an integral multiple of the frequency of the whole string, i.e., each segment vibrates respectively twice, three times, four times, etc., as fast as the whole string. The vibration of the whole string produces the fundamental tone, and the segments produce weaker subsidiary tones. A similar phenomenon occurs in an air column in a pipe. At most the first 16 tones in such a series can be heard by the human ear; the character or timbre of a fundamental tone is determined by the number of its subsidiary tones heard and their relative intensity. The subsidiary tones have been loosely called harmonics (as a noun), but they are properly called partials, the fundamental tone being the first partial. They are also called overtones (a synonym for "upper partials"), although this term includes a number of sounds that do not fit in with the harmonic series, and are therefore not considered musical. 2 Term describing the silvery sound produced separately when the fundamental and possibly more partial tones are damped by touching a string at a nodal point. Similarly harmonics are produced separately in an air column by overblowing or in brass wind instruments by the use of valves.

Harmonic (periodic phenomena)

A sinusoidal quantity having a frequency that is an integral multiple of the frequency of a periodic quantity to which it is related. See Mode of vibration

A harmonic series of sounds is one in which the basic frequency of each sound is an integral multiple of some fundamental frequency. The name exists for historical reasons, even though according to the usual mathematical definition such frequencies form an arithmetic series. An ideal string (or air column) can vibrate as a whole or in a number of equal parts, and the respective periods of vibration are proportional to the lengths. These increasingly shorter lengths or periods form a harmonic series. The name came from the harmonious relation of such sounds, and the science of musical acoustics was once called harmonics. Nowadays, it is customary to deal with ratios of frequency rather than ratios of length and, because frequency is the reciprocal of period, the definition of harmonic in acoustics becomes that given here. See Musical acoustics

harmonic

[här′män·ik]
(acoustics)
One of a series of sounds, each of which has a frequency which is an integral multiple of some fundamental frequency.
(mathematics)
A solution of Laplace's equation which is separable in a specified coordinate system.
(physics)
A sinusoidal component of a periodic wave, having a frequency that is an integral multiple of the fundamental frequency. Also known as harmonic component.

harmonic

A component of a sound containing more than one frequency which is an integral multiple of the lowest frequency.

harmonic

A vibration whose frequency is an even multiple of another vibration or fundamental frequency. The first harmonic of a 200-Hz vibration has a frequency of 200 Hz. This is also its fundamental frequency. The second harmonic will have a frequency of 400 Hz, the third 800 Hz, the fourth 1600 Hz, and so on.

harmonic

1. Music of, relating to, or belonging to harmony
2. Maths
a. capable of expression in the form of sine and cosine functions
b. of or relating to numbers whose reciprocals form an arithmetic progression
3. Physics of or concerned with an oscillation that has a frequency that is an integral multiple of a fundamental frequency
4. Physics Music a component of a periodic quantity, such as a musical tone, with a frequency that is an integral multiple of the fundamental frequency. The first harmonic is the fundamental, the second harmonic (twice the fundamental frequency) is the first overtone, the third harmonic (three times the fundamental frequency) is the second overtone, etc.
5. Music (not in technical use) overtone: in this case, the first overtone is the first harmonic, etc.

harmonic

A multiple of a fundamental frequency occurring at the same time. For example, if the fundamental frequency is 1 kHz, the first harmonic is 1 kHz, the second harmonic is 2 kHz, and so on. Musical instruments oscillate at several frequencies, which are called "overtones." The first overtone is actually the second harmonic, and so on. See harmonic distortion.
References in periodicals archive ?
In the present paper, we study the Dirichlet problem for the time-fractional heat conduction equation in a half-line domain with the surface value of temperature varying harmonically in time.
The harmonically vibration amplitude is maximum at the middle of cylinder, and zero at the beginning of the it.
A quarter of a century later, Kristofferson has stepped into the studio to revisit his old songs, enlisting the help of some fellow musicians to sing a little harmony (with mixed results: Jackson Browne sounds completely disengaged from and hopelessly irrelevant to "Me and Bobby McGee," Steve Earle stays pretty well in the background but sounds natural in "Sunday Morning Coming Down," Matraca Berg adds a nice touch to "For the Good Times," Vince Gill seems completely miscast singing along with Kris in "Help Me Make It Through the Night," Marc Cohn adds some harmonically helpful vocal support to "Loving Her Was Easier (Than Anything I'll Ever Do Again)," Vince Gill and Alison Krauss sound right at home in "Why Me?
All at once, the East Village and SoHo's upper echelons had harmonically converged, and to a degree only hinted at by Keith Hating and Kenny Scharf's much-publicized defection from Fun Gallery to Tony Shafrazi two years before.
Meanwhile, singing groups like the Raging Grannies and the Frugalettes spread the word harmonically.
In the Harmonice mundi Kepler meant to show how mathematics, music, astrology, and astronomy fit harmonically into the divine plan of creation.
Much of the Taize repertoire (1) consists of short biblical or traditional texts set to simple melodies that are harmonically interesting and, therefore, enjoyable to repeat.
However, it required great compositional skill to prevent this idiom sounding merely bombastic, and the antiphonal sections harmonically repetitive and texturally predictable.
Alabama" is much more conservative, harmonically speaking, much less aurally demanding, than A Love Supreme, and its slow, majestic, sad harmonies are perfectly suited to the mood and scope of this scene.
Bebop, rhythmically as well as harmonically, upped the ante: Eighth notes became the common currency of riffs and solos, with triplets and dotted eighths appearing as frequent spikes to break up the rhythmic flow and prevent it from becoming too mechanical--although in the hands of the many Little Birds, it often did.
The densimeter is a U-shaped tube that vibrates harmonically as gas flows through it.
One of the most prolific and versatile composers of his day, Hindemith had a style that was neoclassical in flavor, harmonically advanced, but decidedly tonal (he was the most articulate opponent of Schoenberg 's atonal techniques).