The nodes of a vibrating string are harmonics.

A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 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: 50 Hz, 75 Hz, 100 Hz etc.



Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and so composed of harmonics.

Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at not one, but several frequencies known as partials. When the oscillator is long and thin, such as a guitar string, or the column of air in a trumpet, many of the partials are integer multiples of the fundamental frequency; these are called harmonics. Sounds made by long, thin oscillators are for the most part arranged harmonically, and these sounds are generally considered to be musically pleasing. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic and are sometimes perceived as unpleasant.

The untrained human ear typically does not perceive harmonics as separate notes. Rather, a musical note composed of many harmonically related frequencies is perceived as one sound, the quality, or timbre of that sound being a result of the relative strengths of the individual harmonic frequencies. Bells have more clearly perceptible inharmonics 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:

Frequency Order Name 1 Name 2
1 · f =   440 Hz n = 1 fundamental tone 1st harmonic
2 · f =   880 Hz n = 2 1st overtone 2nd harmonic
3 · f = 1320 Hz n = 3 2nd overtone 3rd harmonic
4 · f = 1760 Hz n = 4 3rd overtone 4th harmonic

Harmonics are not overtones, when it comes to counting. Even numbered harmonics are odd numbered overtones and vice versa.
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.

While it is true that electronically produced periodic tones (e.g. square waves or other non-sinusoidal waves) have "harmonics" that are whole number multiples of the fundamental frequency, practical instruments do not all have this characteristic. For example higher "harmonics"' of piano notes are not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series. This is especially true of instruments other than stringed or brass/woodwind ones, e.g., xylophone, drums, bells etc., where not all the overtones have a simple whole number ratio with the fundamental frequency.

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 (guitar harmonics), at which gentle touching of a string will force it into a harmonic mode when vibrated. String harmonics are described as having a "flutelike, silvery quality that can be highly effective as a special color" when used and heard in orchestration.[1] It is unusual to encounter natural harmonics higher than the fifth partial on any stringed instrument except the double bass, on account of its much longer strings.[2]

Harmonic Stop note Sounded note relative to open string Cents above open string Cents reduced to one octave
2 octave octave (P8) 1,200.0 0.0
3 just perfect fifth P8 + just perfect fifth (P5) 1,902.0 702.0
4 second octave 2P8 2,400.0 0.0
5 just major third 2P8 + just major third (M3) 2,786.3 386.3
6 just minor third 2P8 + P5 3,102.0 702.0
7 septimal minor third 2P8 + septimal minor seventh (m7) 3,368.8 968.8
8 septimal major second 3P8 3,600.0 0.0
9 Pythagorean major second 3P8 + Pythagorean major second (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 + lesser undecimal tritone 4,151.3 551.3
12 lesser unidecimal neutral second 3P8 + P5 4,302.0 702.0
13 tridecimal 2/3-tone 3P8 + tridecimal neutral sixth (n6) 4,440.5 840.5
14 2/3-tone 3P8 + P5 + septimal minor third (m3) 4,568.8 968.8
15 septimal (or major) diatonic semitone 3P8 + just major seventh (M7) 4,688.3 1,088.3
16 just (or minor) diatonic semitone 4P8 4,800.0 0.0


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

Other information

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.

See also


  1. ^ Kennan, Kent and Grantham, Donald (2002/1952). The Technique of Orchestration, p.69. Sixth Edition. ISBN 0-13-040771-2.
  2. ^ Kennan & Grantham, ibid, p.71.

External links

Wikimedia Foundation. 2010.


См. также в других словарях:

  • Harmonic — Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of leather, horn …   The Collaborative International Dictionary of English

  • harmonic — [här män′ik] adj. [L harmonicus < Gr harmonikos < harmonia, HARMONY] 1. harmonious in feeling or effect; agreeing 2. Math. designating or of a harmonic progression 3. Music a) of or pertaining to harmony rather than to melody or rhythm b) …   English World dictionary

  • harmonic — 1560s, relating to music; earlier (c.1500) armonical tuneful, harmonious, from L. harmonicus, from Gk. harmonikos harmonic, musical, skilled in music, from harmonia (see HARMONY (Cf. harmony)). Meaning relating to harmony is from 1660s. The noun …   Etymology dictionary

  • harmonic — ► ADJECTIVE 1) relating to or characterized by harmony. 2) Music relating to or denoting a harmonic or harmonics. ► NOUN Music ▪ an overtone accompanying a fundamental tone at a fixed interval, produced by vibration of a string, column of air,… …   English terms dictionary

  • Harmonic — Har*mon ic (h[aum]r*m[o^]n [i^]k), n. (Mus.) A musical note produced by a number of vibrations which is a multiple of the number producing some other; an overtone. See {Harmonics}. [1913 Webster] …   The Collaborative International Dictionary of English

  • harmonic — англ. [хамо/ник] harmonique фр. [армони/к] harmonisch нем. [хармо/ниш] гармонический, гармоничный ◊ harmonie tone англ. [хамо/ник то/ун] обертон, флажолет …   Словарь иностранных музыкальных терминов

  • harmonic — [hα: mɒnɪk] adjective 1》 relating to or characterized by harmony: a four chord harmonic sequence. 2》 Music relating to or denoting a harmonic or harmonics. 3》 Mathematics relating to a harmonic progression.     ↘Physics of or denoting components… …   English new terms dictionary

  • harmonic — adj. & n. adj. 1 of or characterized by harmony; harmonious. 2 Mus. a of or relating to harmony. b (of a tone) produced by vibration of a string etc. in an exact fraction of its length. 3 Math. of or relating to quantities whose reciprocals are… …   Useful english dictionary

  • harmonic — [[t]hɑː(r)mɒ̱nɪk[/t]] harmonics 1) ADJ: usu ADJ n Harmonic means composed, played, or sung using two or more notes which sound right and pleasing together. I had been looking for ways to combine harmonic and rhythmic structures. 2) N COUNT: usu… …   English dictionary

  • 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… …   Aviation dictionary

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