Editing Harmonic (section)

==Partials, overtones, and harmonics==
<!-- [[Flageolet (disambiguation)]] links to this section -->

An [[overtone]] is any partial higher than the lowest partial in a compound tone. The relative strengths and frequency relationships of the component partials determine the timbre of an instrument. The similarity between the terms overtone and partial sometimes leads to their being loosely used interchangeably in a [[music]]al context, but they are counted differently, leading to some possible confusion. In the special case of instrumental timbres whose component partials closely match a harmonic series (such as with most strings and winds) rather than being inharmonic partials (such as with most [[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):

{| class="wikitable"
|- class="hintergrundfarbe5"
! Frequency
! Order<br/>({{mvar|n}})
! Name&nbsp;1
! Name&nbsp;2
! Name&nbsp;3
! [[Standing wave]] representation
! [[Longitudinal wave]] representation
|-
| 1 × {{mvar|f}} = {{0}}440&nbsp;Hz
| {{mvar|n}} = 1
| 1st partial
| [[fundamental tone]]
| 1st harmonic
| [[File:Pipe001.gif|220px]]
| [[File:Molecule1.gif|220px]]
|-
| 2 × {{mvar|f}} = {{0}}880&nbsp;Hz
| {{mvar|n}} = 2
| 2nd partial
| 1st overtone
| 2nd harmonic
| [[File:Pipe002.gif|220px]]
| [[File:Molecule2.gif|220px]]
|-
| 3 × {{mvar|f}} = 1320&nbsp;Hz
| {{mvar|n}} = 3
| 3rd partial
| 2nd overtone
| 3rd harmonic
| [[File:Pipe003.gif|220px]]
| [[File:Molecule3.gif|220px]]
|-
| 4 × {{mvar|f}} = 1760&nbsp;Hz
| {{mvar|n}} = 4
| 4th partial
| 3rd overtone
| 4th harmonic
| [[File:Pipe004.gif|220px]]
| [[File:Molecule4.gif|220px]]
|}

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 (musical instrument)|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 [[multiphonic]]s also produces harmonics. On [[string instruments]] it is possible to produce very pure sounding notes, called [[string harmonic|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 halfway down the highest string of a [[cello]] produces the same pitch as lightly fingering the node {{sfrac| 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 (music)|harmonic series]]. This is especially true of instruments other than [[stringed instrument|strings]], [[brass instrument|brass]], or [[woodwinds]]. Examples of these "other" instruments are xylophones, drums, bells, chimes, etc.; not all of their overtone frequencies make a simple whole number ratio with the fundamental frequency. (The [[fundamental frequency]] is the [[reciprocal (mathematics)|reciprocal]] of the longest [[period (physics)|time period]] of the collection of vibrations in some single periodic phenomenon.<ref>{{FS1037C}}</ref>)