Editing Harmonic (section)

==Characteristics==
{{Quote|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.{{cn|date=January 2024}} {{right|— Richard Scholz ({{circa|1888–1912}})<ref>{{cite web |title=Category:Scholz, Richard |type=site sub-index & mini-bio for Scholz |website=Petrucci Music Library / International Music Score Library Project (IMSLP) (imslp.org) |place=Canada |url=https://imslp.org/wiki/Category:Scholz,_Richard |access-date=2020-12-21}}</ref>}} }}

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 [[timbre]] of that sound being a result of the relative strengths of the individual partials. Many acoustic [[oscillator]]s, such as the [[human voice]] or a [[bow (music)|bowed]] [[violin]] string, produce complex tones that are more or less [[Periodic function|periodic]], and thus are composed of partials that are nearly matched to the integer multiples of fundamental frequency and therefore resemble the ideal harmonics and are called "harmonic partials" or simply "harmonics" for convenience (although it's not strictly accurate to call a &thinsp;''partial''&thinsp; a &thinsp;''harmonic'',&thinsp; the first being actual and the second being theoretical).

Oscillators that produce harmonic partials behave somewhat like one-dimensional [[resonator]]s, 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 [[trumpet]]s and [[clarinet]]s, 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 [[nonlinear acoustics|non-linearly]] [[elasticity (physics)|elastic]] wood, instead of metal, or strung with [[catgut|gut]] instead of [[string (music)#string_core_anchor|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 [[Inharmonicity|inharmonic partials]]. Some acoustic instruments emit a mix of harmonic and inharmonic partials but still produce an effect on the ear of having a definite fundamental pitch, such as [[piano]]s, strings plucked [[pizzicato]], vibraphones, marimbas, and certain pure-sounding bells or chimes. Antique [[singing bowl]]s are known for producing multiple harmonic partials or [[multiphonics]].
<ref>
{{cite press release
 |first1=Alexander |last1=Galembo
 |first2=Lola L. |last2=Cuddly
 |date=2 December 1997
 |title=Large grand and small upright pianos
 |publisher=[[Acoustical Society of America]]
 |website=acoustics.org |url=http://www.acoustics.org/press/134th/galembo.htm
 |url-status=dead |access-date=13 January 2024
 |archive-url=https://web.archive.org/web/20120209050929/http://www.acoustics.org/press/134th/galembo.htm
 |archive-date=2012-02-09
 |quote=There are many ways to make matters worse, but very few to improve.
}} — Minimally technical summary of string acoustics research given at conference; discusses listeners' perceptions of pianos' inharmonic partials.
</ref><ref>
{{cite journal
 |first=Sophie R.A. |last=Court
 |date=April 1927
 |title=''Golo und Genovefa'' {{grey|[by]}} Hanna Rademacher
 |type=book review
 |journal=Books Abroad
 |volume=1 |issue=2 |pages=34–36
 |doi=10.2307/40043442 |jstor=40043442 |issn=0006-7431
}}
</ref>
Other oscillators, such as [[cymbals]], drum heads, and most percussion instruments, naturally produce an abundance of inharmonic partials and do not imply any particular pitch, and therefore cannot be used melodically or harmonically in the same way other instruments can.

Building on of [[William Sethares|Sethares]] (2004),<ref name=TTSS>
{{cite book
 |last=Sethares |first=W.A. |author-link=William Sethares
 |year=2004
 |title=Tuning, Timbre, Spectrum, Scale
 |publisher=Springer
 |isbn=978-1852337971
 |url=https://books.google.com/books?id=KChoKKhjOb0C |via=Google books
}}
</ref> [[dynamic tonality]] introduces the notion of pseudo-harmonic partials, in which the frequency of each partial is aligned to match the pitch of a corresponding note in a pseudo-just tuning, thereby maximizing the [[consonance]] of that pseudo-harmonic timbre with notes of that pseudo-just tuning.<ref name=Spectral_Tools>
{{cite journal
 | last1=Sethares | first1=W.A. | author1-link=William Sethares
 | last2=Milne    | first2=A.       | last3=Tiedje    | first3=S.
 | last4=Prechtl  | first4=A.       | last5=Plamondon | first5=J. 
 | year = 2009
 | title = Spectral tools for dynamic tonality and audio morphing
 | journal = [[Computer Music Journal]]
 | volume = 33  | issue = 2  | pages = 71–84
 | s2cid = 216636537  | doi = 10.1162/comj.2009.33.2.71  |doi-access=free
 }}</ref><ref name=Continua>
{{cite journal
 |first1=Andrew  |last1=Milne
 |first2=William |last2=Sethares  | author2-link=William Sethares
 |first3=James   |last3=Plamondon
 |date=29 August 2008
 |title=Tuning continua and keyboard layouts
 |journal=[[Journal of Mathematics and Music]]
 |volume=2  |issue=1  |pages=1–19
 |doi=10.1080/17459730701828677 |s2cid=1549755
 |url=http://oro.open.ac.uk/21504/1/tuningcontinua.pdf
 |url-status=live
 |archive-url=https://ghostarchive.org/archive/20221009/http://oro.open.ac.uk/21504/1/tuningcontinua.pdf
 |archive-date=2022-10-09
}} {{cite web
 |title=Alt URL
 |series=[[William Sethares|Sethares]] pers. academic site
 |publisher=[[University of Wisconsin]]
 |url=http://sethares.engr.wisc.edu/paperspdf/tuningcontinua.pdf
}}
</ref><ref name=Fingering>
{{cite journal
 |first1=A.   |last1=Milne
 |first2=W.A. |last2=Sethares  | author2-link=William Sethares
 |first3=J.   |last3=Plamondon
 |date=Winter 2007
 |title=Invariant fingerings across a tuning continuum
 |journal=[[Computer Music Journal]]
 |volume=31  |issue=4  |pages=15–32
 |doi=10.1162/comj.2007.31.4.15
 |s2cid=27906745
 |url=http://oro.open.ac.uk/21503/1/comj.2007.31.4.15
 |doi-access=free
}}</ref><ref name=X_System>
{{cite report
 |first1=A.   |last1=Milne
 |first2=W.A. |last2=Sethares  | author2-link=William Sethares
 |first3=J.   |last3=Plamondon
 | year = 2006
 | title = X System
 | publisher = Thumtronics Inc.
 | type = technical report
 | url = http://oro.open.ac.uk/21510/1/X_System.pdf
 | access-date = 2020-05-02
}}
</ref>