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Encyclopedia > Octatonic scale

In music, a diminished scale (set 8-28) is a scale in which the notes of the scale ascend in alternating intervals of a whole step and a half step. Because a scale constructed in such a way has eight tones (versus seven for conventional scales), it is sometimes called an eight-tone or octatonic scale (there are other possible eight-tone scales, but the diminished is by far the most common). The latter term ("octatonic pitch collection") was first introduced by Arthur Berger in 1963. The name diminished comes from the fact that the first, third, fifth, and seventh notes of a diminished scale for a key form the diminished chord for that key. Formulated already by Arab musicians in the 7th century A.D., the scale was called "Zer ef Kend," meaning "string of pearls," the idea being that the two different sizes of intervals were like two different sizes of pearls (see Joseph Schillinger, The Schillinger System of Musical Composition, Vol 1). The octatonic scale is, vertically, the complete alpha chord. Someone who performs, composes, or conducts music is a musician. ... Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... In music, a scale is a set of musical notes in order by pitch, either ascending or descending. ... In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... The musical interval of a major second — also called a whole-tone — is the relationship between the first note (the root or tonic) and the second note in a major scale (and also a minor scale). ... A half step is either: the interval of a minor second in music, or the half step (dance move) in dance. ... Arthur Berger (May 15, 1912 in New York, NY - Oct 7, 2003) was a composer who has been described as a New Mannerist. ... In music and music theory, a chord (from the Middle English cord) short for accord is three or more different notes or pitches sounding simultaneously, or nearly simultaneously, over a period of time. ... Arab music is the music of Arabic-speaking people or countries, especially those centered around the Arabian Peninsula. ... In music the alpha-chord collection is a vertically organized statement of the octatonic scale as two diminished seventh chords such as: C#-E-G-Bb-C-Eb-F#-A. (Wilson 1992, p. ...

Because of the half-whole symmetry, there are only three distinct diminished scales, and a given diminished scale has only two modes (one beginning its ascent with a whole step between its first two notes, while the other begins its ascent with a half step or semitone). In music, a mode is an ordered series of musical intervals, which, along with the key or tonic, define the pitches. ... The musical interval of a major second — also called a whole-tone — is the relationship between the first note (the root or tonic) and the second note in a major scale (and also a minor scale). ... A half step is either: the interval of a minor second in music, or the half step (dance move) in dance. ... A half step is either: the interval of a minor second in music, or the half step (dance move) in dance. ...

Each of the three distinct scales can form differently-named scales with the same sequence of tones by starting at a different point in the scale. With alternate starting points listed in parentheses, the three are:

• Db diminished (E, G, Bb diminished): Db, Eb, E, F#, G, A, Bb, C, Db
• D diminished (F, Ab, B diminished): D, E, F, G, Ab, Bb, B, C#, D
• Eb diminished (Gb, A, C diminished): Eb, F, F#, G#, A, B, C, D, Eb

Image File history File links Download high resolution version (959x219, 8 KB)Diminished scales on Db, D, and Eb. ...

The diminished scale may first have been used by Nikolai Rimsky-Korsakov, who describes his "discovery" in his My Musical Life, was extensively used by his student Igor Stravinsky, particularly in his famous piece The Rite of Spring, Alexander Scriabin and, most often as a source set with other source sets, Béla Bartók. In his Bagatelles, Improvisations, Fourth Quartet, Cantata Profana, and Improvisations the octatonic is used with the diatonic, whole tone, and other "abstract pitch formations" (Antokoletz 1984) all "entwined...in a very complex mixture. Bartók does use the octatonic collection exclusively in his "Diminished Fifth" (no.101, vol. 4, Mikrokosmos) and "Harvest Song" (no.33 of the Forty-Four Duos for two violins) and "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 intelligable as 'octatonic music'" (Wilson 1992, p.26-27) Nikolai Andreyevich Rimsky-Korsakov (Russian: , Nikolaj AndreeviÄ Rimskij-Korsakov), also Nikolay, Nicolai, and Rimsky-Korsakoff, (March 6/18, 1844â€“June 8/21, 1908) was a Russian composer and teacher of classical music particularly noted for his fine orchestration, which may have been influenced by his synaesthesia. ... Igor Fyodorovitch Stravinsky (Russian: ) (June 17, 1882 â€“ April 6, 1971) was a Russian-French-American composer of modern classical music. ... Le Sacre du printemps (English: The Rite of Spring; Russian: Ð’ÐµÑÐ½Ð° ÑÐ²ÑÑ‰ÐµÐ½Ð½Ð°Ñ) is a ballet with music by the Russian composer Igor Stravinsky. ... Alexander Nikolayevich Scriabin (Russian: ÐÐ»ÐµÐºÑÐ°ÌÐ½Ð´Ñ€ ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐµÐ²Ð¸Ñ‡ Ð¡ÐºÑ€ÑÌÐ±Ð¸Ð½, Aleksandr NikolaeviÄ Skrjabin; sometimes transliterated as Skryabin or Skrjabin) (6 January 1872â€“27 April 1915) was a Russian composer and pianist. ... BÃ©la Viktor JÃ¡nos BartÃ³k (March 25, 1881 â€“ September 26, 1945) was a composer, pianist and collector of Eastern European and Middle Eastern folk music. ...

## Contents

### In Jazz

Both the true diminished and its partner mode (with a semitone rather than a tone beginning the pattern) are commonly used in Jazz improvisation, frequently under different names. The diminished scale is commonly used in conjunction with diminished harmony (e.g. the "C dim" harmony) and its partner mode - more commonly known as a "half-tone whole-tone" scale- in dominant harmony (e.g. with a "G7b9" harmony.) In more advanced improvisation, the scale may be used in other circumstances, for example with a minor-major chord.

### The Petrushka chord

Igor Stravinsky's ballet Petrushka is characterized by the so-called "Petrushka chord," a recurring polytonic device based on two major triads a tritone apart (C major and F-sharp major) played at the same time and heralding the appearance of the main character. It has been suggested that this is another application of one of Stravinksky's favourite devices, the diminished or octatonic scale, as both the C major and F# major triads are obtainable from a single permutation of that scale. Igor Fyodorovitch Stravinsky (Russian: ) (June 17, 1882 â€“ April 6, 1971) was a Russian-French-American composer of modern classical music. ... The Waltz of the Snowflakes from Tchaikovskys The Nutcracker Ballet is the name given to a specific dance form and technique. ... PÃ¨troushka (English: Petrushka; Russian: Ð¿ÐµÑ‚Ñ€ÑƒÑˆÐºÐ°) is a ballet with music by the Russian composer Igor Stravinsky. ... The use of more than two keys simultaneously is known in music as polytonality. ... This article needs cleanup. ... The augmented fourth between C and F# forms a tritone. ...

### Bitonality

In both of the short works by Bartók mentioned above the octatonic collection is partitioned into two (symmetrical) four-note segments (4-10 or 0235) of the natural minor scales a tritone apart. Paul Wilson argues against viewing this as bitonality since "the larger octatonic collection embraces and supports both supposed tonalities." (ibid, p.27) The use of more than two keys simultaneously is known in music as polytonality. ...

As mentioned above, both the C major and F# major triads are obtainable from a single permutation of the diminshed scale. In fact eight major and minor triads can be obtained from a each permutation of the scale. If one takes the Db diminished scale as outlined above, one can produce the following triads:

• C Major (C E G)
• C Minor (C Eb G)
• Eb Major (Eb G Bb)
• Eb Minor (Eb Gb Bb)
• F# Major (F# A# C#)
• F# Minor (F# A C#)
• A Major (A C# E)
• A Minor (A C E)

This is of particular interest to Jazz musicians as it facilitates the creation of chord voicings, especially polychord and upper structure voicings, and triad-based melodic improvisation.

## Sources

• Berger, Arthur (1963). "Problems of Pitch Organization in Stravinsky". Perspectives of New Music II/I (Fall-Winter)
• Van den Toorn, Pieter (1983). The Music of Igor Stravinsky. New Haven: Yale University Press.
• Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0300051115.
• Antokoletz, Elliott (1984). The Music of Béla Bartók: A Study of Tonality and Progression in Twentieth-Century Music. Berkeley and Los Angeles: University of California Press. Cited in Wilson directly above.

• Taruskin, Richard (Spring 1985). "Chernomor to Kashchei: Harmonic Sorcery; or Stravinsky's 'Angle'", Journal of the American Musicological Society 38:1, p. 74-142.

Results from FactBites:

 The Classical Octatonic scale Dictonary Page on Classic Cat (940 words) Because a scale constructed in such a way has eight tones (versus seven for diatonic scales), it is sometimes called an eight-tone or octatonic scale (there are other possible eight-tone scales, but the diminished is by far the most common). The true diminished is often called the whole-half diminished scale, while its partner is known as the half-whole diminished scale, so named for the first two intervals in their construction. This is likely another application of one of Stravinsky's favorite devices, the diminished or octatonic scale, as both the C major and F♯ major triads chosen are obtainable from a single permutation of that scale.
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