Harmonic series: Difference between revisions
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{{Wikipedia|Harmonic series (music)}} | {{Wikipedia|Harmonic series (music)}} | ||
The '''harmonic series''' is a sequence of [[pitch|tones]] 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"). | The '''harmonic series''' is a sequence of [[pitch|tones]] 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"). | ||
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 | 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. | ||
In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance. | In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance. | ||
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 | 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. | ||
[[File:HEJI harmonics 1-16.png|thumb|center|650px|Harmonic series on A, partials 1 to 16, notated in [[HEJI]].]] | [[File:HEJI harmonics 1-16.png|thumb|center|650px|Harmonic series on A, partials 1 to 16, notated in [[HEJI]].]] | ||
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Treated as a [[chord]], the harmonic series is sometimes called the '''chord of nature'''; in German this has been called the '''Klang'''. | Treated as a [[chord]], the harmonic series is sometimes called the '''chord of nature'''; in German this has been called the '''Klang'''. | ||
The ''q''-limit chord of nature is 1:2:3:4: | The ''q''-limit chord of nature is 1:2:3:4:…:''q'' up to some odd number ''q'', and is the basic ''q''-[[limit]] [[Otonality and utonality|otonality]] which can be equated via [[Octave reduction|octave equivalence]] to other versions of the complete ''q''-limit otonal chord. | ||
== Segments == | |||
A ''segment'' of the harmonic series is a run of consecutive harmonics. It is written ''a''::''b'' for the harmonics ''a'' through ''b''. For example, 4::8 consists of the harmonics 4, 5, 6, 7 and 8, which as a chord is 4:5:6:7:8. Relative to its lowest member, the segment ''a''::''b'' has the frequency ratios ''a''/''a'', (''a''+1)/''a'', …, ''b''/''a''; the steps between its members are [[superparticular]] ratios. | |||
A segment whose last harmonic is twice its first, ''n''::2''n'', spans one octave and can be repeated at the octave to form a scale. These are the [[overtone scale]]s. Several have their own pages, for example [[Harmonics 8–16|8::16]], [[Harmonics 12–24|12::24]] and [[Harmonics 16–32|16::32]]. Used as a scale, the segment ''n''::2''n'' is also called mode ''n'' of the harmonic series. | |||
== Music based on the harmonic series == | == Music based on the harmonic series == | ||
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One might compose with the harmonic series by, for instance: | One might compose with the harmonic series by, for instance: | ||
* Tuning to the first several harmonics over one fundamental; | * Tuning to the first several harmonics over one fundamental; | ||
* Tuning to an octave-repeating | * Tuning to an octave-repeating segment of the harmonic series for use as a scale. For instance: [[Harmonics 8–16|8::16]], [[Harmonics 12–24|12::24]], [[Harmonics 20–40|20::40]], ... See [[overtone scale]]. | ||
* 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".) | * 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".) | ||
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* Various played with Fujara (slovak overtone flute) | * Various played with Fujara (slovak overtone flute) | ||
; {{ | ; {{W|Georg Friedrich Haas}} | ||
* String Quartet No.2, mm. 1~57 | * String Quartet No.2, mm. 1~57 | ||
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* Various (experimental alphorn and yodeling combined with overtone singing) | * Various (experimental alphorn and yodeling combined with overtone singing) | ||
; {{ | ; {{W|Karlheinz Stockhausen}} | ||
* {{ | * {{W|Stimmung|''Stimmung''}} (1968) | ||
* {{ | * {{W|Sternklang|''Sternklang''}} (1971) | ||
; [[Cam Taylor]] | ; [[Cam Taylor]] | ||
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* ''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] | * ''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) | * ''Symphony No. 3 "Gloria"'' (1983) | ||
== See also == | == See also == | ||
* [[ | * [[Overtone scales]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Isoharmonic chords]] | * [[Isoharmonic chords]] | ||
* [[List of octave-reduced harmonics]] | * [[List of octave-reduced harmonics]] | ||
* [[Prime harmonic series]] | * [[Prime harmonic series]] | ||
* [[Kite's thoughts on the V-I cadence in higher prime limits]] | * [[Kite's thoughts on the V-I cadence in higher prime limits]] | ||
* [[ | * [[Harmonics 128–256|8th octave overtone tuning]] | ||
== External links == | == External links == | ||
* [[Wikipedia: Spectral 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 | * [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 | ||
* [http://www.overtone.cc Overtone music network] - a portal for overtone music. | * [http://www.overtone.cc Overtone music network] - a portal for overtone music. | ||