The diminished scale is a musical scale the pitches of which ascend in alternating whole tones and semitones. It is called the diminished scale because it can be conceived as a combination of two interlocking diminished seventh chords, just as the augmented scale can be conceived as a combination of two interlocking augmented triads. In classical theory, in contradistinction to jazz theory, it is more commonly called the octatonic scale, although there are forty-two other non-enharmonically equivalent, non-transpositionally equivalent eight-tone sets possible. The term ("octatonic pitch collection") was introduced by Arthur Berger in 1963 (van den Toorn 1983). A hexatonic scale is a musical scale with six pitches or notes per octave. ... Arthur Berger (May 15, 1912 in New York City –- October 7, 2003 in Boston, Massachusetts) was a composer who has been described as a New Mannerist. ...

Because of the half-whole symmetry, there are only three distinct (non-transpositionally equivalent) 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). Thus Olivier Messiaen considered it one of the modes of limited transposition. This article is about modes as used in music. ... 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. ... Olivier Messiaen It has been suggested that List of students of Olivier Messiaen be merged into this article or section. ... The modes of limited transposition are musical modes discovered by the French composer Olivier Messiaen. ...

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:

• E♭ diminished (F♯/G♭, A, C diminished): E♭, F, F♯, G♯, A, B, C, D, E♭
• D diminished (F, A♭, B diminished): D, E, F, G, A♭, B♭, B, C♯, D
• D♭ diminished (E, G, B♭ diminished): D♭, E♭, E, F♯, G, A, B♭, C, D♭

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

History

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). Arabic music includes several genres and styles of music ranging from Arab classical to Arabic pop music and from secular to sacred music. ... Joseph Schillinger (1895-1943) was born in Kharkiv, Ukraine (at that time, part of Russia). ...

The diminished scales may first have been used in Western music by Franz Liszt in No. 5, "Feux Follets" of his Etudes d'execution transcendante (composed 1826, and twice revised) as a recurring theme found in the descending arpeggiated figures of bars 7 and 8, 10 and 11, 43, 45 through 48, 122, and 124 through 126. In turn, all three distinct octatonic scales are used, respectively containing all, and only, the notes of each of these scales. Liszt was boldly innovative in his use of fresh scales and harmonies. “Liszt” redirects here. ... The Transcendental Etudes (sometimes Études dexécution transcendante or Transcendental Studies) are a series of twelve compositions written for solo piano by Franz Liszt, begun in 1826 and finalized in 1851. ...

Liszt was to become an idol of the Russian school, and starting with Glinka's Ruslan and Lyudmila, the diminished scale was often used by Russian composers to evoke scenes of magic and exotic mystery. Still, Nikolai Rimsky-Korsakov claimed the diminished scale as "his discovery" in his My Musical Life (van den Toorn 1983). He certainly used the scale extensively in his opera Kashchey the Immortal, which premiered in 1902. Following that, the scale was extensively used by his student Igor Stravinsky, particularly in his major ballets Petrushka and The Rite of Spring. Other composers who experimented with the scale are Alexander Scriabin and, most often as a source set with other source sets, Béla Bartók. In Bartók's 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 makes use of the notes of one particular octatonic scale (E♭ diminished) exclusively in "Crossed Hands" (no. 99, vol. 4, Mikrokosmos); incidentally, this piece uses unusual, non-standard key signatures, which are different in each hand. Bartók also uses the entire octatonic collection to the exclusion of other scales 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 intelligible as 'octatonic music'" (Wilson 1992, p.26-27). Ruslan and Lyudmila (Russian: , transliteration: Ruslan i Lyudmila) is an opera in five acts (eight tableaux) composed by Mikhail Glinka between 1837 and 1842. ... Nikolai Andreyevich Rimsky-Korsakov Nikolai Andreyevich Rimsky-Korsakov (Russian: , Nikolaj Andreevič Rimskij-Korsakov), also Nikolay, Nicolai, and Rimsky-Korsakoff, (March 6 (N.S. March 18), 1844 – June 8 (N.S. June 21) 1908) was a Russian composer, one of five Russian composers known as The Five, and was later a... Kashchey the Deathless (Russian: , Kashchey bessmertnïy, Kashchey the Immortal) is a one-act opera (styled a little autumnal fairy tale) by Nikolay Rimsky-Korsakov. ... Igor Stravinsky. ... For other uses, see Ballet (disambiguation). ... Pétrouchka (English: Petrushka; Russian: петрушка) is a ballet with music by the Russian composer Igor Stravinsky. ... The Rite of Spring, commonly referred to by its original French title, Le Sacre du printemps (Russian: Весна священная, Vesna svjaščennaja) is a ballet with music by the Russian composer Igor Stravinsky, which was first performed in 1913. ... Alexander Nikolayevich Scriabin Alexander Nikolayevich Scriabin (Russian: Александр Николаевич Скрябин, Aleksandr Nikolajevič Skriabin; sometimes transliterated as Skryabin or Scriabine (6 January 1872 [O.S. 26 December 1871]—27 April 1915) was a Russian composer and pianist. ... Bartok redirects here. ... Béla Bartóks composition for piano Mikrokosmos (Sz. ... This key signature – A major or F# minor – consists of three sharps placed after the clef In musical notation, a key signature is a series of sharp symbols or flat symbols placed on the staff, designating notes that are to be consistently played one semitone higher or lower than the...

Harmonic implications

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 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. The whole-half diminished scale is commonly used in conjunction with diminished harmony (e.g. the "C dim" harmony) while the half-whole scale is used in dominant harmony (e.g. with a "G7♭9" 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. 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. Igor Stravinsky. ... For other uses, see Ballet (disambiguation). ... Pétrouchka (English: Petrushka; Russian: петрушка) is a ballet with music by the Russian composer Igor Stravinsky. ... The Petrushka chord is a recurring polytonic device used in Igor Stravinskys ballet Petrushka and in later music. ...

Bitonality

In both of the short works by Bartók mentioned above ("Diminished Fifth" and "Harvest Song") 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. ...

Triads

As mentioned above in the context of Stravinsky's Petrushka chord, both the C major and F♯ major triads are obtainable from a single permutation of the diminished scale. In fact eight major and minor triads can be obtained from each permutation of the scale. If one takes the D♭ diminished scale as outlined above, one can produce the following triads:

• C Major (C E G)
• C Minor (C E♭ G)
• E♭ Major (E♭ G B♭)
• E♭ Minor (E♭ G♭ B♭)
• 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.
• Wollner, Fritz (1924) "7 mysteries of Stravinsky in Progression" 1924 German international school of music study.
• Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0-300-05111-5.
• 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. ISBN 0-520-06747-9

Further reading

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