Editing Octatonic scale (section)

==History==

===Early examples===
[[Joseph Schillinger]] suggests that the scale was formulated already by [[Persian traditional music]] in the 7th century AD, where it was called "Zar ef Kend", meaning "string of pearls", the idea being that the two different sizes of intervals were like two different sizes of pearls.{{sfn|Schillinger|1946|loc={{Page needed|date=December 2014}}}}

Octatonic scales first occurred in Western music as byproducts of a series of minor-third transpositions. While [[Nikolai Rimsky-Korsakov]] claimed he was conscious of the octatonic collection "as a cohesive frame of reference" in his autobiography ''My Musical Life'',{{sfn|Rimsky-Korsakov|1935}}{{sfn|Van den Toorn|1983|loc=329, 493n5}} instances can be found in music of previous centuries. Eytan Agmon{{sfn|Agmon|1990|loc=1–8}} locates one in [[Domenico Scarlatti]]'s Sonata K. 319. In the following passage, according to [[Richard Taruskin]],{{sfn|Taruskin|1996|loc=266}} "its descending whole-step/half-step bass progression is complete and continuous".
[[File:Scarlatti Sonasta K319, bars 62-80.wav|thumb|Scarlatti Sonata K319, bars 62–80]]
[[File:Scarlatti Sonata K319, bars 62-80.png|thumb|center|500px|Scarlatti's Sonata K. 319, bars 62–80]]

Taruskin{{sfn|Taruskin|1996|loc=269}} also cites the following bars from [[J. S. Bach]]'s [[English Suites (Bach)|English Suite No. 3]] as octatonic:
[[File:Octatonic bars from Sarabande from English Suite No 3.wav|thumb|Octatonic bars from Sarabande from English Suite No 3]]
[[File:Sarabande from J.S.Bach's English Suite No.3, bars 17-19.png|thumb|center|500px|Sarabande from J. S. Bach's English Suite No. 3, bars 17–19]]

[[Honoré Langlé]]'s 1797 harmony treatise contains a sequential progression with a descending octatonic bass, supporting harmonies that use all and only the notes of an octatonic scale.{{sfn|Langlé|1797|loc=72, ex. 25.2}}

===19th century===
In 1800, Beethoven composed his [[Piano Sonata No. 11 (Beethoven)|Piano Sonata No. 11 in B]]{{music|flat}}[[Piano Sonata No. 11 (Beethoven)|, Op. 22]]. The slow movement of this work contains a passage of what was, for its time, highly dissonant harmony. In a lecture (2005),{{sfn|Schiff|2005}} pianist [[András Schiff]] describes the harmony of this passage as "really extraordinary". The chord progressions at the beginning of the second and third bars of this passage are octatonic:[[File:Beethoven Piano Sonata Op 22, 2nd movement, bars 30-32.wav|thumb|Adagio (2nd movement) from Beethoven's Piano Sonata No. 11, bars 31–33.]]
[[File:Adagio (2nd movement) from Beethoven's Piano Sonata Op.22, bars 31-33.png|thumb|center|500px|Adagio (2nd movement) from Beethoven's Piano Sonata No. 11, bars 31–33.]]

Octatonic scales can be found in Chopin's Mazurka, Op. 50, No. 3 and in several Liszt piano works: the closing measures of the third ''Étude de Concert'', "Un Sospiro," for example, where (mm. 66–70) the bass contains a complete falling octatonic scale from D-flat to D-flat, in the opening piano cadenzas of [[Totentanz]], in the lower notes between the alternating hands, and in the First Mephisto Waltz, in which a short cadenza (m. 525) makes use of it by harmonizing it with a B-flat Diminished Seventh chord. Later in the 19th century, the notes in the chords of the coronation bells from the opening scene of [[Modest Mussorgsky]]'s opera ''[[Boris Godunov (opera)|Boris Godunov]]'', which consist of "two dominant seventh chords with roots a tritone apart" according to Taruskin,{{sfn|Taruskin|1996|loc=283}} are entirely derived from an octatonic scale.
[[File:Coronation scene from Boris Godunov.wav|thumb|Coronation scene from ''Boris Godunov'']]
[[File:Coronation scene from Boris Godunov.png|thumb|center|500px|Coronation scene from ''Boris Godunov''. {{YouTube|1=UEBq-gsdI58|2=Link to passage}}]]
Taruskin continues: "Thanks to the reinforcement the lesson has received in some equally famous pieces like ''[[Scheherazade (Rimsky-Korsakov)|Scheherazade]]'', the progression is often thought of as being peculiarly Russian."{{sfn|Taruskin|1996|loc=283}}

[[Tchaikovsky]] was also influenced by the harmonic and coloristic potential of octatonicism. As Mark DeVoto{{sfn|DeVoto|2007|loc=144}} points out, the cascading arpeggios played on the celesta in the "Sugar Plum Fairy" from ''[[The Nutcracker]]'' ballet are made up of dominant seventh chords a minor third apart. [[File:Cascading arpeggios on celesta from Sugar Plum Fairy.wav|thumb|Cascading arpeggios on celesta from Sugar Plum Fairy]][[File:Cascading arpeggios on celesta from the Dance of the Sugar Plum Fairy.png|thumb|center|500px|Cascading arpeggios on celesta from the Dance of the Sugar Plum Fairy.]] "Hagens Watch", one of the darkest and most sinister scenes in [[Richard Wagner]]'s opera ''[[Götterdämmerung]]'' features chromatic harmonies using eleven of the twelve chromatic notes, within which the eight notes of the octatonic scale may be found in bars 9–10 below:
[[File:Wagner, "Hagen's Watch" from Gotterdamerung.png|thumb|center|500px|Wagner, "Hagen's Watch" from ''Götterdämmerung'', act 1<ref>[https://www.youtube.com/watch?v=JNkJoZuGJe8 "Hagen's Watch"]</ref>]]

===Late 19th and 20th century===
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    \relative c' {
        \set Score.currentBarNumber = #5
        \key d\major
        \time 4/4
        \tempo Modéré
        \override DynamicLineSpanner.staff-padding = #2
        r4 r8 \tuplet 3/2 { cis!16\p\< d e } f2~
        f4\> e2 d4\!
        cis4 b b2~
        b1
    }
}
</score>|width=425|caption=The cor anglais melody from "Nuages", the first movement of [[Debussy]]'s ''[[Nocturnes (Debussy)|Nocturnes]]'', bars 5–8. [https://www.youtube.com/watch?v=spXwXLqFLvs&t=25s Link to passage]}}
[[File:Istrian scale Schubert Symphony No. 8 in B minor (1922), 1st mvt., bars 13-20.png|thumb|upright=1.8|[[Istrian scale]] in Schubert's Symphony No. 8 in B minor (1822), 1st mvt., bars 13–20; flat fifth marked with asterisk{{sfn|van der Merwe|2005|loc=228}}[[File:Istrian scale Schubert Symphony No. 8 in B minor (1922), 1st mvt., bars 13-20.mid]]]]

The scale is also found in the music of [[Claude Debussy]] and [[Maurice Ravel]]. Melodic phrases that move by alternating tones and semitones frequently appear in the works of both these composers. [[Allen Forte]]{{sfn|Forte|1991|loc=144–145}} identifies a five-note segment in the [[cor anglais]] melody heard near the start of Debussy's "Nuages" from his orchestral suite ''[[Nocturnes (Debussy)|Nocturnes]]'' as octatonic. Mark DeVoto{{sfn|DeVoto|2003|loc=183}} describes "Nuages" as "arguably [Debussy's] boldest single leap into the musical unknown. 'Nuages' defines a kind of tonality never heard before, based on the centricity of a diminished tonic triad (B-D-F natural)." According to Stephen Walsh, the [[cor anglais]] theme "hangs in the texture like some motionless object, always the same and always at the same pitch".{{sfn|Walsh|2018|loc=137}} There is a particularly striking and effective use of the octatonic scale in the opening bars of [[Liszt]]'s late piece ''[[Bagatelle sans tonalité]]'' from 1885.{{Citation needed|date=April 2020}}

The scale was extensively used by Rimsky-Korsakov's student [[Igor Stravinsky]], particularly in his Russian-period works such as ''[[Petrushka (ballet)|Petrushka]]'' (1911), ''[[The Rite of Spring]]'' (1913), up to the ''[[Symphonies of Wind Instruments]]'' (1920). Passages using this scale are unmistakable as early as the ''[[Scherzo fantastique]]'', ''[[Fireworks (Stravinsky)|Fireworks]]'' (both from 1908), and ''[[The Firebird]]'' (1910). It also appears in later works by Stravinsky, such as the ''[[Symphony of Psalms]]'' (1930), the ''[[Symphony in Three Movements]]'' (1945), most of the neoclassical works from the [[Octet (Stravinsky)|Octet]] (1923) to ''[[Agon (ballet)|Agon]]'' (1957), and even in some of the later [[Serialism|serial]] compositions such as the ''[[Canticum Sacrum]]'' (1955) and ''[[Threni (Stravinsky)|Threni]]'' (1958). In fact, "few if any composers have been known to employ relations available to the collection as extensively or in as varied a manner as Stravinsky".{{sfn|Van den Toorn|1983|loc=42}}

The second movement of Stravinsky's Octet<ref>[https://www.youtube.com/watch?v=EgMOX57Copk Stravinsky's Octet]</ref> for wind instruments opens with what Stephen Walsh{{sfn|Walsh|1988|loc=127}} calls "a broad melody completely in the octatonic scale". Jonathan Cross{{sfn|Cross|2015|loc=144}} describes a highly rhythmic passage<ref>Archived at [https://ghostarchive.org/varchive/youtube/20211205/n9oY_cikDl0 Ghostarchive]{{cbignore}} and the [https://web.archive.org/web/20150720102019/https://www.youtube.com/watch?v=n9oY_cikDl0 Wayback Machine]{{cbignore}}: {{cite web| url = https://www.youtube.com/watch?v=n9oY_cikDl0&t=0m44s| title = Igor Stravinsky - Symphony in Three Movements | website=[[YouTube]]| date = 15 March 2014 }}{{cbignore}}</ref> in the first movement of the ''Symphony in Three Movements'' as "gloriously octatonic, not an unfamiliar situation in jazz, where this mode is known as the 'diminished scale', but Stravinsky of course knew it from Rimsky. The '[[rumba]]' passage... alternates chords of E-flat7 and C7, over and over, distantly recalling the coronation scene from Mussorgsky's ''Boris Godunov''. In celebrating America, the émigré looked back once again to Russia." Van den Toorn{{sfn|Van den Toorn|1983}} catalogues many other octatonic moments in Stravinsky's music.

The scale also may be found in music of [[Alexander Scriabin]] and [[Béla Bartók]]. In Bartók's ''Bagatelles'', [[String Quartet No. 4 (Bartók)|Fourth Quartet]], ''[[Cantata Profana]]'', and ''[[Eight Improvisations on Hungarian Peasant Songs|Improvisations]]'', the octatonic is used with the diatonic, whole tone, and other "abstract pitch formations" all "entwined... in a very complex mixture".{{sfn|Antokoletz|1984|loc={{Page needed|date=December 2014}}}} ''[[Mikrokosmos (Bartók)|Mikrokosmos]]'' Nos. 99, 101, and 109 are octatonic pieces, as is No. 33 of the ''[[44 Duos for Two Violins]]''. "In each piece, changes of motive and phrase correspond to changes from one of the three octatonic scales to another, and one can easily select a single central and referential form of 8–28 in the context of each complete piece." However, even his larger pieces also feature "sections that are intelligible as 'octatonic music{{'"}}.{{sfn|Wilson|1992|loc=26–27}}

[[Olivier Messiaen]] made frequent use of the octatonic scale throughout his career as a composer, and indeed in his seven [[modes of limited transposition]], the octatonic scale is Mode 2. Peter Hill{{sfn|Hill|1995|loc=73}} writes in detail about "La Colombe" (The Dove),<ref>[https://www.youtube.com/watch?v=z2pwTP7g7xE "La Colombe" (The Dove)]</ref> the first of a set of ''[[Preludes (Messiaen)|Preludes]]'' for piano that Messiaen completed in 1929, at the age of 20. Hill speaks of a characteristic "merging of tonality (E major) with the octatonic mode" in this short piece.

Other twentieth-century composers who used octatonic collections include [[Samuel Barber]], [[Ernest Bloch]], [[Benjamin Britten]], [[Julian Cochran]], [[George Crumb]], [[Irving Fine]], [[Ross Lee Finney]], [[Alberto Ginastera]], [[John Harbison]], [[Jacques Hétu]], [[Aram Khachaturian]], [[Witold Lutosławski]], [[Darius Milhaud]], [[Henri Dutilleux]], [[Robert Morris (composer)|Robert Morris]], [[Carl Orff]], [[Jean Papineau-Couture]], [[Krzysztof Penderecki]], [[Francis Poulenc]], [[Sergei Prokofiev]], [[Alexander Scriabin]], [[Dmitri Shostakovich]], [[Toru Takemitsu]], [[Joan Tower]],{{sfn|Alegant|2010|loc=109}} [[Robert Xavier Rodriguez]], [[John Williams]]{{sfn|Durrand|2020|p={{page needed|date=April 2021}}}} and [[Frank Zappa]].{{sfn|Clement|2009|loc=214}} Other composers include [[Willem Pijper]],{{sfn|Chan|2005|loc=52}} who may have inferred the collection from Stravinsky's ''The Rite of Spring'', which he greatly admired, and composed at least one piece—his Piano Sonatina No. 2—entirely in the octatonic system.{{sfn|Van den Toorn|1983|loc=464n11}}

In the 1920s, [[Heinrich Schenker]] criticized the use of the octatonic scale, specifically Stravinsky's [[Concerto for Piano and Wind Instruments (Stravinsky)|Concerto for Piano and Wind Instruments]], for the oblique relation between the diatonic scale and the harmonic and melodic surface.{{sfn|Pople|1991|loc=2}}

===Jazz===
Both the half-whole diminished and its partner mode, the whole-half diminished (with a tone rather than a semitone beginning the pattern) are commonly used in jazz improvisation, frequently under different names. The whole-half diminished scale is commonly used in conjunction with diminished harmony (e.g., the E<sup>dim7</sup> chord) while the half-whole scale is used in dominant harmony (e.g., with an F<sup>{{music|13}}{{music|flat}}9</sup> chord).

Examples of octatonic jazz include Jaco Pastorius' composition "Opus Pocus"<ref>[https://www.youtube.com/watch?v=AybUd-GaUC4 "Opus Pocus"]</ref> from the album ''[[Jaco Pastorius (album)|Pastorius]]''{{sfn|Pastorius|1976}}{{Failed verification|date=April 2019|reason=No mention of scales of any sort on this website.}} and [[Herbie Hancock]]'s piano solo on "Freedom Jazz Dance"<ref>[https://www.youtube.com/watch?v=ZdMVVIXzxr4&t=4m50s Piano solo] on "Freedom Jazz Dance"</ref><ref>Tymoczko, D. (2017, bars 18-21, right hand part) Transcription of Piano solo from “Freedom Jazz dance” https://dmitri.mycpanel.princeton.edu/transcriptions.html accessed 24/11/2021.</ref> from the album ''[[Miles Smiles]]'' (1967). The [[John McLaughlin (musician)]] composition "The Dance of Maya" is structured around modes of the octatonic scale <ref>[https://www.youtube.com/watch?v=RV64F4jJsE4 Octatonic Basis of The Dance of Maya</ref>

=== Rock and pop ===
[[Jonny Greenwood]] of the English rock group [[Radiohead]] uses the octatonic scale extensively, such as in the song "[[Just (song)|Just]]" and his soundtrack for the film ''[[The Power of the Dog (film)|The Power of the Dog]]''.<ref name="Ross-2021">{{Cite magazine |last=Ross |first=Alex |author-link=Alex Ross (music critic) |date=2021-12-19 |title=How Jonny Greenwood wrote the year's best film score |url=https://www.newyorker.com/culture/the-new-yorker-interview/how-jonny-greenwood-wrote-the-years-best-film-score |access-date=2021-12-19 |magazine=[[The New Yorker]] |language=en-US}}</ref><ref>{{Cite magazine |last=Ross |first=Alex |author-link=Alex Ross (music critic) |date=August 12, 2001 |title=The Searchers |url=https://www.newyorker.com/magazine/2001/08/20/the-searchers |archive-url=https://web.archive.org/web/20080214053947/http://www.therestisnoise.com/2004/04/mahler_1.html |archive-date=14 February 2008 |access-date=2021-07-11 |magazine=[[The New Yorker]] |language=en-US}}</ref> He said "It's a slightly more grownup version of the pentatonic scales that we're all taught to do with xylophones and glockenspiels when you're a kid. It's not a major scale or a minor scale; it's something else. But all the notes work together and make a certain color that is its own thing."<ref name="Ross-2021" />

The scale is used in progressive [[Heavy metal music|heavy metal]] music such as that by [[Dream Theater]] and [[Opeth]], both of which strive for a dissonant and tonally ambiguous sound in their music. Examples include the instrumental break in Dream Theater's ''[[Octavarium (song)|Octavarium]]'' and Opeth's ''[[Deliverance (Opeth album)|Deliverance]]''. Earlier examples of the scale's use in [[progressive rock]] include [[King Crimson|King Crimson's]] ''[[Red (King Crimson album)|Red]]'' and [[Emerson Lake & Palmer|Emerson Lake & Palmer's]] ''[[Emerson, Lake & Palmer (album)|The Barbarian]]''.

Progressive keyboardist [[Derek Sherinian]] is also closely associated with the octatonic scale, which can be found in most of his works, both solo and as part of a band. Examples include [[Planet X (band)|Planet X's]] ''Desert Girl'' and [[Sons of Apollo|Sons of Apollo's]] ''King of Delusion''. The dissonances associated with the scale when used in conjunction with conventional tonality form an integral part of his signature sound which has influenced hundreds of keyboardists of the 21st century.