Harmonic series: Difference between revisions

=Harmonic series=

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[[Hertz]], basic 12EDO Intervals, basic understanding of linear vs. exponential relationships

[[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.

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:

[https://www.youtube.com/watch?v=hDLhe-NkH2A&ab_channel=mannfishh Learn to hear Harmonics!! (Intros to Just Intonation) by Mannfish]

The approach of creating music based on intervallic relationships derived from the harmonic series relationships is called [[Just intonation|Just Intonation]].

<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>

[[File:Cello natural harmonics.png|left|thumb|Cello Natural Harmonics|alt=|200x200px|link=https://en.xen.wiki/w/File:Cello_natural_harmonics.png]]

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]]

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.

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.

<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>

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...

===Musical Intervals As Ratios===

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:

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.]]

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.

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.

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.

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.

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]]

{| class="wikitable"

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|The Arithmetic Of Listening

|Harmonic Experience: Tonal Harmony From Its Natural Origins to Its Modern Expression

|Mathieu, W. A.

|An Introduction To the Harmonic Series And Logarithmic Integrals-For High School Students Up To Researchers

|}

==See also[edit | edit source]==

*[[Subharmonic series]]

*[[Gallery of just intervals]]

*[[Isoharmonic chords]]

*[[First Five Octaves of the Harmonic Series]]

*[[Overtone scales]]

*[[List of octave-reduced harmonics]]

*[[Prime harmonic series]]

*[[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]

*[[8th Octave Overtone Tuning]]

===External links[edit | edit source]===

*Spectral music article on Wikipedia

*www.naturton-musik.de ^{[<nowiki/>[[:Category:Pages containing dead links|''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^<nowiki/>

*Overtone music network - a portal for overtone music.

*Oberton-Netzwerk (Xing) ^{[<nowiki/>[[:Category:Pages containing dead links|''dead link'']]]} - German-speaking group dedicated to overtone music on the social network platform Xing. Microtonal music in general is welcome, too.