Editing Harmonic series (music) (section)

== Terminology {{anchor|Partial}} ==

===Partial, harmonic, fundamental, inharmonicity, and overtone===
A "complex tone" (the sound of a note with a timbre particular to the instrument playing the note) "can be described as a combination of many simple [[Wave|periodic waves]] (i.e., [[sine wave]]s) or ''partials,'' each with its own frequency of [[vibration]], [[amplitude]], and [[Phase (waves)|phase]]".<ref>{{cite book|title=Music, Thought, and Feeling: Understanding the Psychology of Music|author=[[William Forde Thompson]]|isbn=978-0-19-537707-1|page=46|year=2008|publisher=Oxford University Press |url=http://www.oup.com/us/catalog/general/subject/Psychology/CognitivePsychology/?view=usa&ci=9780195377071}}</ref> (See also, [[Fourier analysis]].)

A '''partial''' is any of the [[sine wave]]s (or "simple tones", as [[Alexander John Ellis|Ellis]] calls them<ref>{{cite book
 | title = On the Sensations of Tone as a Physiological Basis for the Theory of Music
 | edition = 2nd
 | author = [[Hermann von Helmholtz]]|translator=[[Alexander John Ellis]]
 | publisher = Longmans, Green
 | year = 1885
 | page = 23
 | url = https://books.google.com/books?id=GwE6AAAAIAAJ&q=%22musical+tone%22+simple+compound&pg=PA23
 }}</ref> when translating [[Hermann von Helmholtz|Helmholtz]]) of which a complex tone is composed, not necessarily with an integer multiple of the lowest harmonic.

A '''harmonic''' is any member of the harmonic series, an ideal set of [[Frequency|frequencies]] that are [[Natural number|positive integer]] multiples of a common [[fundamental frequency]]. The '''fundamental''' is a [[harmonic]] because it is one times itself. A '''harmonic partial''' is any real partial component of a complex tone that matches (or nearly matches) an ideal harmonic.<ref>{{cite book | title = Music, Cognition, and Computerized Sound | author = [[John R. Pierce]] | chapter = Consonance and Scales | editor = Perry R. Cook | publisher = MIT Press | year = 2001 | isbn = 978-0-262-53190-0 | chapter-url = https://books.google.com/books?id=L04W8ADtpQ4C&q=musical+tone+harmonic+partial+fundamental+integer&pg=PA169}}</ref>

An '''inharmonic partial''' is any partial that does not match an ideal harmonic. ''[[Inharmonicity]]'' is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in [[cent (music)|cents]] for each partial.<ref>{{cite book | title = The Historical Harpsichord Volume Two: The Metallurgy of 17th- and 18th- Century Music Wire | author = [[Martha Goodway]] and Jay Scott Odell | publisher = Pendragon Press | year = 1987 | isbn = 978-0-918728-54-8 | url = https://books.google.com/books?id=sE1mk8ed1dkC&q=inharmonicity+defined+partial+frequencies&pg=PA93}}</ref>

Many [[Definite pitch|pitched]] [[Acoustic music|acoustic instruments]] are designed to have partials that are close to being whole-number ratios with very low inharmonicity; therefore, in [[music theory]], and in instrument design, it is convenient, although not strictly accurate, to speak of the partials in those instruments' sounds as "harmonics", even though they may have some degree of inharmonicity. The [[piano]], one of the most important instruments of western tradition, contains a certain degree of inharmonicity among the frequencies generated by each string. Other pitched instruments, especially certain [[percussion]] instruments, such as [[marimba]], [[vibraphone]], [[tubular bell]]s, [[timpani]], and [[singing bowl]]s contain mostly inharmonic partials, yet may give the ear a good sense of pitch because of a few strong partials that resemble harmonics. Unpitched, or indefinite-pitched instruments, such as [[cymbal]]s and [[Gong#Chau gong (tam-tam)|tam-tams]] make sounds (produce spectra) that are rich in inharmonic partials and may give no impression of implying any particular pitch.

An '''[[overtone]]''' is any partial above the lowest partial. The term overtone does not imply harmonicity or inharmonicity and has no other special meaning other than to exclude the fundamental. It is mostly the relative strength of the different overtones that give an instrument its particular [[timbre]], tone color, or character. When writing or speaking of overtones and partials numerically, care must be taken to designate each correctly to avoid any confusion of one for the other, so the second overtone may not be the third partial, because it is the second sound in a series.<ref>{{harvnb|Riemann|1896|p=143}}: "let it be understood, the second overtone is not the third tone of the series, but the second"</ref>
 
Some [[Electronic musical instrument|electronic instruments]], such as [[synthesizer]]s, can play a pure frequency with no [[overtone]]s (a [[sine wave]]). Synthesizers can also combine pure frequencies into more complex tones, such as to simulate other instruments. Certain flutes and ocarinas are very nearly without overtones.