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The '''harmonic series''' is a sequence of [[Pitch|tone]]s generated by whole-number frequency [[ratio]]s over a fundamental: [[1/1]], [[2/1]], [[3/1]], [[4/1]], [[5/1]], [[6/1]], [[7/1]]… ad infinitum. Each member of this series is a [[harmonic]] (which is short for "harmonic partial").
English Wikipedia has an article on:


Note that the terms ''overtone'' and '''overtone series''' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage is also attested. Technically speaking, ''overtone series'' excludes the starting fundamental, so the 2nd harmonic is the 1st overtone. Because of that distinction, the math of the "overtone series" is off by one. So, "harmonic series" is arguably the preferred standard.
'''Harmonic series (music)'''
==Prerequisite Knowledge==
[[Hertz]], basic 12EDO Intervals, basic understanding of linear vs. exponential relationships
==Overview==
[[File:Harmonic series intervals.png|alt=|thumb|600x600px|Harmonic Series|link=https://en.xen.wiki/w/File:Harmonic_series_intervals.png]]The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. This phenomenon can be observed in most sounds.


In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance.  
The '''fundamental''' is the lowest frequency (or '''partial''') in a given harmonic series. While the fundamental is generally the main audible pitch of a given sound, the harmonic series contains an infinitely proliferating sequence of higher partials called '''overtones'''. With practice, one can learn to hear and identify specific overtones:


The [[subharmonic series]] (or undertone series) is the inversion of the harmonic series: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.
[https://www.youtube.com/watch?v=hDLhe-NkH2A&ab_channel=mannfishh Learn to hear Harmonics!! (Intros to Just Intonation) by Mannfish]


== Music based on the harmonic series ==
The approach of creating music based on intervallic relationships derived from the harmonic series relationships is called [[Just intonation|Just Intonation]].
The [[chord of nature]] is the name sometimes given to the harmonic series, or the series up to a certain stopping point, regarded as a chord.


Steps between adjacent members of the harmonic series are called "[[superparticular]]," and they appear in the form (''n''+1)/''n'' (e.g. [[4/3]], [[28/27]], [[33/32]]).
<small>(For a diagram of the harmonic series up to the 49th partial, see [https://heji.plainsound.org/ The Helmholtz-Ellis JI Pitch Notation Legend and Series])</small>
=== The Harmonic Series In Real Life ===
[[File:Cello natural harmonics.png|left|thumb|Cello Natural Harmonics|alt=|200x200px|link=https://en.xen.wiki/w/File:Cello_natural_harmonics.png]]
====Musical Instruments====
Many musicians are already familiar with the harmonic series, even if they may not realize it. For example: the natural harmonics of a string instrument (bowed or strummed) and the open notes on a French horn are two manifestations of the harmonic series. Using the cello as an example, the low, open C string acts as the fundamental of its harmonic series. In this case, the first available natural harmonic is C one octave up, then G, C, E, G etc. To play these harmonics, one effectively shortens the length of the string, at ratios that match those in the harmonic series.[[File:(a) (e) (i) (o) (u) Video.mov|Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced|alt=|thumb|left|link=https://en.xen.wiki/w/File:(a)_(e)_(i)_(o)_(u)_Video.mov]]
====Timbre====
The harmonic series is also responsible for timbre: one can easily identify the sound of a trumpet, violin, or electric guitar, even if they play the same pitch. This is because while the same set of frequencies is (mostly) present in all these sounds, some partials will be more prominent than others depending on the sound source. This also applies to speech and singing, as different vowel [[formants]] are distinguished by their unique harmonic identity.


One might compose with the harmonic series by, for instance:
In this video, individual harmonic partials are gradually re-introduced to a recording of a singer alternating between different vowels. A psychoacoustic illusion is created where at a certain point, the the individual frequencies are suddenly interpreted by the brain as one, timbrally unique and recognizable sound: the human voice. Also note how the intensity of each partial varies depending on the vowel being sung.


* Tuning to the first several harmonics over one fundamental;
<small>This audio was created using [https://www.klingbeil.com/spear/ Spear]: a free, downloadable spectral analysis software allowing users to explore and edit individual frequencies within recorded sounds.</small>
* Tuning to an octave-repeating slice of the harmonic series for use as a scale (for instance harmonics 8 though 16, [[otones12-24|12 through 24]], [[otones20-40|20 through 40]]... see [[overtone scales]]);
==Mathematical Formula and Ratio Notation ==
* Tuning to the overtones of the overtones & the undertones of the undertones. (This can produce complex scales such as [[Harry Partch]]'s 43-tone Monophonic; this kind of thing is more often called "just intonation" than "overtone music".)
The mathematical formula for the harmonic series is simple: each positive-integer multiple of the fundamental frequency represents one overtone. For example, if the fundamental frequency is 100Hz, the partials, in ascending order, will be 100Hz, 200Hz, 300Hz, 400Hz, etc...


== Music ==
Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. With a new partial at every interval of 100Hz, the number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].
; [[Richard Burdick]]
===Musical Intervals As Ratios===
* [http://www.i-ching-music.com/FREE102.html ''Planetary Ripples'']{{dead link}}
Beginning with the seventh partial, intervals in the harmonic series begin to deviate significantly from those used in 12EDO. 12EDO interval nomenclature (minor third, perfect fifth, etc.) fails to accurately represent these relationships because, for instance, the harmonic series contains an infinite number of ''different'' minor thirds. Therefore, it is standard in [[Just intonation|Just Intonation]] to use ratios (such as 6:5) to refer to a specific ''type'' of minor third. There are two main ways in which one might think of these ratios:
*6:5 represents the 6th and 5th partials of the harmonic series
*6:5 is the mathematical ratio of the two pitches' frequencies (600Hz and 500Hz, for example).
These two frames of reference are fundamentally the same.


; [[Folkart Slovakia]] ([http://www.fujara.sk/audio_samples.htm site])
* Various played with Fujara (slovak overtone flute)


; {{w|Georg Friedrich Haas}}
Interestingly, if one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see [[Psychoacoustics|psychoacoustics.]]
* Various<sup>[''which?'']</sup>
===Terminology===
Note that the terms ''overtone'' and ''overtone series'' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage is also attested. Technically speaking, ''overtone series'' excludes the starting fundamental, so the 2nd harmonic is the 1st overtone. Because of that distinction, the math of the "overtone series" is off by one. So, "harmonic series" is arguably the preferred standard. Likewise, the standard way to refer to frequencies in the harmonic series is by using numbered '''partials''' (beginning with the fundamental as the first partial), not overtones.


; [[Dave Hill]]
Also note that interval ratios are always notated with the greater number first. In order to change the order of the two pitches, one must use the ratio's '''reciprocal.''' For example, to represent a major sixth instead of a minor third, one must notate the interval as 10:6, not 5:6.
* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm ''Chord Progression on the Harmonic Overtone Series'']{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3 play]{{dead link}}


; [[Norbert Oldani]]
The [[subharmonic series]] (or undertone series) is the inversion of the harmonic series: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum. The words otonal (referring to overtones) and utonal (referring to undertones) are used to refer to the harmonic and subharmonic series, respectively.
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/DroneInsideAnHarmonicSeries.mp3 Drone Inside An Harmonic Series]''{{dead link}}
==Advanced Concepts==
 
===The Harmonic Series As A Fractal===
; [[Dave Seidel]]
The harmonic series contains an infinite number of harmonic series within it. By isolating every numbered partial with a given factor, one finds that an entire harmonic series manifests within this smaller subset of the original harmonic series.
* [http://mysterybear.net/article/18/threnody ''Threnody'']{{dead link}} [https://web.archive.org/web/20201127015923/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Threnody.mp3 play]
===Prime Partials===
* [http://mysterybear.net/article/22/owllight ''Owllight'']{{dead link}} [https://web.archive.org/web/20201127012201/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Owllight.mp3 play]
Prime-numbered partials are sometime referred to simply as "primes". These partials are of interest because each new prime produces a unique interval not present in any of the lower partials. For more information on this, see: [[Prime interval]]
* [http://mysterybear.net/article/23/palimpsest ''Palimsest'']{{dead link}} [https://web.archive.org/web/20201127012920/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Seidel/Palimpsest.mp3 play]
==Further Reading==
 
{| class="wikitable"
; [[William Sethares]]
|+
* ''Immanent Sphere'' – [https://sethares.engr.wisc.edu/mp3s/immanent.html detail] | [https://web.archive.org/web/20201127013148/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/ImmanentSphere.mp3 play]
!Title
 
!Author
; [[SoundWell]] ([http://www.soundwell.com/en/music site])
|-
* Various ("Snake" overtone flute)
|The Arithmetic Of Listening
 
|Gann, Kyle
; [[Spectral Voices]] ([http://www.spectralvoices.com/ site])
|-
* Various (meditative new age with overtone singing)
|Harmonic Experience: Tonal Harmony From Its Natural Origins to Its Modern Expression
 
|Mathieu, W. A.
; [[Stimmhorn]] ([http://www.stimmhorn.ch/ site])
|-
* Various (experimental alphorn and yodeling combined with overtone singing)
|An Introduction To the Harmonic Series And Logarithmic Integrals-For High School Students Up To Researchers
 
|Olaikhan, Ali
; {{w|Karlheinz Stockhausen}}
|}
* {{w|Stimmung|''Stimmung''}} (1968)
==See also[edit | edit source]==
* {{w|Sternklang|''Sternklang''}} (1971)
 
; [[Cam Taylor]]
* [https://www.youtube.com/watch?v=ECLEbVXoTvA Harmonic series 4-8, 8-16 and 16-32 on the Lumatone] (2022)
 
; [[Chris Vaisvil]]
* ''Rock Trio in Harmonic Series'' (2016) – [http://chrisvaisvil.com/rock-trio-in-harmonic-series/ blog] | [http://micro.soonlabel.com/harmonic_series/Nevadatite20160226_harmonic_band.mp3 play]
 
; {{w|Glenn Branca}} ([http://www.glennbranca.com/ site])
* ''Symphony No. 3 "Gloria"'' (1983)
 
== See also ==
*[[Subharmonic series]]
*[[Subharmonic series]]
* [[Gallery of just intervals]]
*[[Gallery of just intervals]]
* [[Isoharmonic chords]]
*[[Isoharmonic chords]]
* [[First Five Octaves of the Harmonic Series]]
*[[First Five Octaves of the Harmonic Series]]
* [[Overtone scales]]
*[[Overtone scales]]
* [[List of octave-reduced harmonics]]
*[[List of octave-reduced harmonics]]
* [[Prime harmonic series]]
*[[Prime harmonic series]]
* [[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]
*[[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]
* [[8th Octave Overtone Tuning]]
*[[8th Octave Overtone Tuning]]
 
===External links[edit | edit source]===
== External links ==
*Spectral music article on Wikipedia
 
*www.naturton-musik.de <sup>[<nowiki/>[[:Category:Pages containing dead links|''dead link'']]]</sup> - web site dedicated to overtone music (by Austrian composer Johannes Kotschy) - a lot of theory material and practical guides to write music based on the overtone series<sup><nowiki/></sup>
* [https://en.wikipedia.org/wiki/Spectral_music Spectral music article on Wikipedia]
*Overtone music network - a portal for overtone music.
* [http://www.naturton-musik.de/ www.naturton-musik.de]{{dead link}} - web site dedicated to overtone music (by Austrian composer Johannes Kotschy) - a lot of theory material and practical guides to write music based on the overtone series
*Oberton-Netzwerk (Xing) <sup>[<nowiki/>[[:Category:Pages containing dead links|''dead link'']]]</sup> - German-speaking group dedicated to overtone music on the social network platform Xing. Microtonal music in general is welcome, too.
* [http://www.overtone.cc Overtone music network] - a portal for overtone music.
* [https://www.xing.com/net/overtonenetwork Oberton-Netzwerk (Xing)]{{dead link}} - German-speaking group dedicated to overtone music on the social network platform [http://www.xing.com Xing]. Microtonal music in general is welcome, too.
     
[[Category:Harmonic]]
[[Category:Harmonic]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Terms]]
[[Category:Terms]]
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