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 a sine wave, it is an integer multiple of the frequency of the wave. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc.

In musical terms, harmonics are component pitches of a harmonic tone which sound at whole number multiples above, or "within", the named note being played on a musical instrument. Non-integer multiples are called partials or inharmonic overtones. It is the amplitude and placement of harmonics and partials which give different instruments different timbre (despite not usually being detected separately by the untrained human ear), and the separate trajectories of the overtones of two instruments playing in unison is what allows one to perceive them as separate. Bells have more clearly perceptible partials than most instruments.

Sample for a harmonic series:

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

Amplitudes are varying.

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 which are located on the nodes of the strings. Harmonics may be used to check at a unison the tuning of strings which 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 used as the basis of just intonation systems or considered as the basis of all 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.

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

Harmonics on Stringed Instruments

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

harmonic	stop note	harmonic note	cents	reduced cents
2	octave	P8	1200	0
3	just perfect fifth	P8 + P5	1901.95500	701.95500
4	just perfect fourth	2P8	2400	0
5	just major third	2P8 + just M3	2786.31371	386.31371
6	just minor third	2P8 + P5	3101.95500	701.95500
7	septimal minor third	2P8 + septimal m7	3368.82591	968.82591
8	septimal major second	3P8	3600	0
9	Pythagorean major second	3P8 + pyth M2	3803.91000	203.91000
10	just minor whole tone	3P8 + just M3	3986.31371	386.31371
11	greater unidecimal neutral second	3P8 + just M3 + GUN2	4151.31794	551.31794
12	lesser unidecimal neutral second	3P8 + P5	4301.95500	701.955
13	tridecimal 2/3-tone	3P8 + P5 + T23T	4440.52766	840.52766
14	2/3-tone	3P8 + P5 + septimal m3	4568.82591	968.82591
15	septimal (or major) diatonic semitone	3P8 + P5 + just M3	4688.26871	1088.26871
16	just (or minor) diatonic semitone	4P8	4800	0

Harmonic: Encyclopedia BETA

Contents

Harmonic

Harmonics on Stringed Instruments

See also

External links