Harmonic

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In

The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz.

An n^th characteristic mode, for n > 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at ${\displaystyle {\tfrac {1}{3}}}$L and ${\displaystyle {\tfrac {2}{3}}}$L, where L is the length of the string. In fact, each n^th characteristic mode, for n not a multiple of 3, will not have nodes at these points. These other characteristic modes will be vibrating at the positions ${\displaystyle {\tfrac {1}{3}}}$L and ${\displaystyle {\tfrac {2}{3}}}$L. If the player gently touches one of these positions, then these other characteristic modes will be suppressed. The tonal harmonics from these other characteristic modes will then also be suppressed. Consequently, the tonal harmonics from the n^th characteristic modes, where n is a multiple of 3, will be made relatively more prominent.^[1]

In music, harmonics are used on string instruments and wind instruments as a way of producing sound on the instrument, particularly to play higher notes and, with strings, obtain notes that have a unique sound quality or "tone colour". On strings, bowed harmonics have a "glassy", pure tone. On stringed instruments, harmonics are played by touching (but not fully pressing down the string) at an exact point on the string while sounding the string (plucking, bowing, etc.); this allows the harmonic to sound, a pitch which is always higher than the fundamental frequency of the string.

Terminology

Harmonics may be called "overtones", "partials", or "upper partials", and in some music contexts, the terms "harmonic", "overtone" and "partial" are used fairly interchangeably. But more precisely, the term "harmonic" includes all pitches in a harmonic series (including the fundamental frequency) while the term "overtone" only includes pitches above the fundamental.

Characteristics

A whizzing, whistling tonal character, distinguishes all the harmonics both natural and artificial from the firmly stopped intervals; therefore their application in connection with the latter must always be carefully considered.^{[citation needed]}

— Richard Scholz (c. 1888-1912)^[2]

Most acoustic instruments emit complex tones containing many individual partials (component simple tones or sinusoidal waves), but the untrained human ear typically does not perceive those partials as separate phenomena. Rather, a musical note is perceived as one sound, the quality or

Oscillators that produce harmonic partials behave somewhat like one-dimensional resonators, and are often long and thin, such as a guitar string or a column of air open at both ends (as with the metallic modern orchestral transverse flute). Wind instruments whose air column is open at only one end, such as trumpets and clarinets, also produce partials resembling harmonics. However they only produce partials matching the odd harmonics – at least in theory. In practical use, no real acoustic instrument behaves as perfectly as the simplified physical models predict; for example, instruments made of non-linearly elastic wood, instead of metal, or strung with gut instead of brass or steel strings, tend to have not-quite-integer partials.

Partials whose frequencies are not integer multiples of the fundamental are referred to as

Building on of

Partials, overtones, and harmonics

An

pitched percussion

instruments), it is also convenient to call the component partials "harmonics", but not strictly correct, because harmonics are numbered the same even when missing, while partials and overtones are only counted when present. This chart demonstrates how the three types of names (partial, overtone, and harmonic) are counted (assuming that the harmonics are present):

Frequency	Order (n)	Name 1	Name 2	Name 3	Standing wave representation	Longitudinal wave representation
1 × f = 0440 Hz	n = 1	1st partial	fundamental tone	1st harmonic
2 × f = 0880 Hz	n = 2	2nd partial	1st overtone	2nd harmonic
3 × f = 1320 Hz	n = 3	3rd partial	2nd overtone	3rd harmonic
4 × f = 1760 Hz	n = 4	4th partial	3rd overtone	4th harmonic

In many

Harmonics may be singly produced [on stringed instruments] (1) by varying the point of contact with the bow, or (2) by slightly pressing the string at the nodes, or divisions of its aliquot parts (${\displaystyle {\tfrac {\ 1\ }{2}}}$, ${\displaystyle {\tfrac {\ 1\ }{3}}}$, ${\displaystyle {\tfrac {\ 1\ }{4}}}$, etc.). (1) In the first case, advancing the bow from the usual place where the fundamental note is produced, towards the bridge, the whole scale of harmonics may be produced in succession, on an old and highly resonant instrument. The employment of this means produces the effect called '

Grove's Dictionary of Music and Musicians (1879)^[11]