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harmonic

 
Dictionary: har·mon·ic   (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.
  1. Of or relating to harmonics.
  2. Integrated in nature.
n.
    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.
  1. harmonics (used with a sing. verb) The theory or study of the physical properties and characteristics of musical sound.
  2. 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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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.


 

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.

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Music Encyclopedia: Harmonics
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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.

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


 
Columbia Encyclopedia: harmonic
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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.


 

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
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In acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is f, the harmonics have frequencies f, 2f, 3f, 4f, etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 25 Hz, 50 Hz, 75 Hz, 100 Hz, etc.

Contents

Characteristics

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 partials. When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the partials are practically integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Partials whose frequencies are not integer multiples of the fundamental are called inharmonic and are sometimes 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. Bells have more clearly perceptible partials than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic partials or multiphonics.

Harmonics and overtones

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 1,320 Hz second overtone third harmonic
4f 1,760 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 or flageolets 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 incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

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 noting Cents Reduced
cents
2 octave P8 1,200.0 0.0
3 just perfect fifth P8 + P5 1,902.0 702.0
4 just perfect fourth 2P8 2,400.0 0.0
5 just major third 2P8 + just M3 2,786.3 386.3
6 just minor third 2P8 + P5 3,102.0 702.0
7 septimal minor third 2P8 + septimal m7 3,368.8 968.8
8 septimal major second 3P8 3,600.0 0.0
9 Pythagorean major second 3P8 + pyth M2 3,803.9 203.9
10 just minor whole tone 3P8 + just M3 3,986.3 386.3
11 greater unidecimal neutral second 3P8 + just M3 + GUN2 4,151.3 551.3
12 lesser unidecimal neutral second 3P8 + P5 4,302.0 702.0
13 tridecimal 2/3-tone 3P8 + P5 + T23T 4,440.5 840.5
14 2/3-tone 3P8 + P5 + septimal m3 4,568.8 968.8
15 septimal (or major) diatonic semitone 3P8 + P5 + just M3 4,688.3 1,088.3
16 just (or minor) diatonic semitone 4P8 4,800.0 0.0

Table

Table of harmonics of a stringed instrument with colored dots indicating which positions can be lightly fingered to generate just intervals up to the 7th harmonic

See also


 
Translations: Harmonic
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Dansk (Danish)
adj. - harmonisk
n. - overtone

Nederlands (Dutch)
boventoon, deeltonen, elektrische voltage, harmonisch, passend

Français (French)
adj. - (Math, Mus) harmonique
n. - (Phys, Mus) harmonique

Deutsch (German)
n. - (mus.) Oberton
adj. - harmonisch

Ελληνική (Greek)
n. - αρμονικός (ήχος)
adj. - αρμονικός

Italiano (Italian)
armonia, armonioso

Português (Portuguese)
n. - som (m) harmônico
adj. - harmônico, musical

Русский (Russian)
гармоничный, мелодичный, обертон

Español (Spanish)
adj. - armónico
n. - armonía

Svenska (Swedish)
n. - (harmonisk) överton
adj. - harmonisk

中文(简体)(Chinese (Simplified))
调和的, 和声的, 音乐般的, 谐波, 谐函数, 和声

中文(繁體)(Chinese (Traditional))
adj. - 調和的, 和聲的, 音樂般的
n. - 諧波, 諧函數, 和聲

한국어 (Korean)
adj. - 조화적인, 화성의, 조화의
n. - 배음, 고조파, 조화

日本語 (Japanese)
adj. - 調和的, 和声の
n. - 倍音, 調波

العربيه (Arabic)
‏(الاسم) النغمه التوافقيه موسيقى (صفه) موسيقي, إيقاعي, تناغمي, تآلفي, متآلف, متناسق, مطرب, توافقي‏

עברית (Hebrew)
adj. - ‮הרמוני‬
n. - ‮צליל הרמוני‬


 
Best of the Web: harmonic
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Some good "harmonic" pages on the web:


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mathworld.wolfram.com
 
 
 

 

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