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harmonic

(här-mŏn'ĭk) pronunciation

adj.

1. Of or relating to harmony.
2. Pleasing to the ear: harmonic orchestral effects.
3. Characterized by harmony: a harmonic liturgical chant.
Of or relating to harmonics.
Integrated in nature.

1. Any of a series of musical tones whose frequencies are integral multiples of the frequency of a fundamental tone.
2. A tone produced on a stringed instrument by lightly touching an open or stopped vibrating string at a given fraction of its length so that both segments vibrate. Also called overtone, partial; Also called partial tone.
harmonics (used with a sing. verb) The theory or study of the physical properties and characteristics of musical sound.
Physics. A wave whose frequency is a whole-number multiple of that of another.

[Latin harmonicus, from Greek harmonikos, from harmoniā, harmony. See harmony.]

harmonically har·mon'i·cal·ly adv.

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Sci-Tech Encyclopedia: Harmonic

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

A harmonic series of sounds is one in which the basic frequency of each sound is an integralmultiple 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 also Musical acoustics.

Computer Desktop Encyclopedia: 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.

Thesaurus: harmonic

adjective

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sounds/pleasant sounds/unpleasant sounds/neutral sounds or silence

Music Encyclopedia: Harmonics

The individual pure sounds normally present as part of an ordinary musical tone. They are present because a string or an air column can vibrate not only as a whole but also as two halves, three thirds etc simultaneously. The relative strength of each harmonic gives the tone quality to the note as heard. The first 16 harmonics of the note C are shown in ex.1. The richer the upper harmonics, the brighter the tone of an instrument; the oboe and the violin are instruments with many higher harmonics, whereas the flute and the recorder have a stronger fundamental and fewer and weaker harmonics. The ‘hollow’ sound of the clarinet is created by the predominance of odd-numbered harmonics. In some vibrating bodies, particularly bells, their irregular form will cause sounds that are not harmonic partials; this may give a confused or dubious perception of pitch.

Ex.1 (black notes are imperfectly tuned)

Harmonics are used in a variety of ways in musical instruments. Woodwind players can ‘overblow’ their instruments in the octave (oboe) or 12th (clarinet) and thus extend their compass; this may be done by lip pressure and/or by opening a nodal hole in the tube. On brass instruments, which have longer and narrower tubes, the player can choose the harmonic to be sounded by means of lip pressure; before valves were invented (c1815), only notes of the harmonic series (and in some circumstances their near neighbours) could be played. On string instruments, players can cause a string to vibrate only in sections by touching it lightly at the appropriate point; this can produce a note of a cool, silvery quality (sometimes called ‘flageolet notes’). These are ‘natural harmonics’, based on the open string; ‘artificial harmonics’ can be produced by fingering a note and touching lightly a 4th higher, thereby producing a note two octaves higher (these can be used to produce an effect of great virtuosity, for example in the finale of Sibelius's Violin Concerto). ex.2 shows how harmonics may be notated. On the harp, the use of the second harmonic (ex.3) can produce an effect of particular delicacy.

Ex. 2

Ex. 3

‘Harmonic’, applied to an organ stop, means one where the sounding note is a harmonic of the pipe's natural sounding length.

Architecture: harmonic

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

Columbia Encyclopedia: harmonic.

1 Physical term describing the vibration in segments of a sound-producing body (see sound). 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.

Electronics Dictionary: harmonic

Sine wave that is smaller in amplitude and some multiple of a fundamental frequency. Example: 880 Hz. is the second harmonic of 440 Hz., 880 Hz. is the third harmonic of 220 Hz.

Wikipedia: harmonic

This article is about the components of sound. For other uses, see Harmonic (disambiguation).

In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc. The harmonics have the property that they are all periodic at the signal frequency. Also, due to the properties of Fourier series, the sum of the signal and its harmonics is also periodic at that frequency.

Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and thus can be decomposed into harmonics.

Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at several frequencies known as overtones. When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the overtones are still integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Overtones whose frequency is not an integer multiple of the fundamental are called inharmonic and are often perceived as unpleasant.

The untrained human ear typically does not perceive harmonics as separate notes. Instead, they are perceived as the timbre of the tone. In a musical context, overtones that are not exactly integer multiples of the fundamental are known as inharmonics. Inharmonics that are not close to harmonics are known as partials. Bells have more clearly perceptible partials than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic overtones or multiphonics.

The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted:

1f	440 Hz	fundamental frequency	first harmonic
2f	880 Hz	first overtone	second harmonic
3f	1320 Hz	second overtone	third harmonic
4f	1760 Hz	third overtone	fourth harmonic

In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g. recorder) this has the effect of making the note go up in pitch by an octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found half way down the highest string of a cello produces the same pitch as lightly fingering the node 1/3 of the way down the second highest string. For the human voice see Overtone singing, which uses harmonics.

Harmonics may be either used or considered as the basis of just intonation systems. Composer Arnold Dreyblatt is able to bring out different harmonics on the single string of his modified double bass by slightly altering his unique bowing technique halfway between hitting and bowing the strings. Composer Lawrence Ball uses harmonics to generate music electronically.

The fundamental frequency is the reciprocal of the period of the periodic phenomenon.

This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain.

Harmonics on stringed instruments

playing a harmonic on a string (click to enlarge)

The following table displays the stop points on a stringed instrument, such as the guitar, at which gentle touching of a string will force it into a harmonic mode when vibrated.

harmonic	stop note	harmonic note	cents	reduced cents
2	octave	P8	1200.0	0.0
3	just perfect fifth	P8 + P5	1902.0	702.0
4	just perfect fourth	2P8	2400.0	0.0
5	just major third	2P8 + just M3	2786.3	386.3
6	just minor third	2P8 + P5	3102.0	702.0
7	septimal minor third	2P8 + septimal m7	3368.8	968.8
8	septimal major second	3P8	3600.0	0.0
9	Pythagorean major second	3P8 + pyth M2	3803.9	203.9
10	just minor whole tone	3P8 + just M3	3986.3	386.3
11	greater unidecimal neutral second	3P8 + just M3 + GUN2	4151.3	551.3
12	lesser unidecimal neutral second	3P8 + P5	4302.0	702.0
13	tridecimal 2/3-tone	3P8 + P5 + T23T	4440.5	840.5
14	2/3-tone	3P8 + P5 + septimal m3	4568.8	968.8
15	septimal (or major) diatonic semitone	3P8 + P5 + just M3	4688.3	1088.3
16	just (or minor) diatonic semitone	4P8	4800.0	0.0

		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved. Read more
		Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Read more
		Computer Desktop Encyclopedia. THIS COPYRIGHTED DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction is strictly prohibited without permission from the publisher. © 1981-2008 Computer Language Company Inc. All rights reserved. Read more
		Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved. Read more
		Music Encyclopedia. The Concise Grove Dictionary of Music. Copyright © 1994 by Oxford University Press, Inc.. All rights reserved. Read more
		Architecture. McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc. All rights reserved. Read more
		Columbia Encyclopedia. The Columbia Electronic Encyclopedia, Sixth Edition Copyright © 2003, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/ Read more
		Electronics Dictionary. Copyright 2001 by Twysted Pair. All rights reserved. Read more
		Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Harmonic". Read more
		Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved. Read more

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Harmonics on stringed instruments

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