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Octatonic scale

An octatonic scale is an eight-note musical scale. Among the most famous of these is a scale in which the notes ascend in alternating intervals of a whole step and a half step. In classical theory, in contradistinction to jazz theory, this scale is commonly simply called the octatonic scale, although there are forty-two other non-enharmonically equivalent, non-transpositionally equivalent eight-tone sets possible. In jazz theory this scale is more particularly 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. The term octatonic pitch collection was first introduced by Arthur Berger in 1963 (van den Toorn 1983).

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.

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♭

It may also be represented as 0235689e or labeled as set 8-28.

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).

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 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 staff. 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).

Harmonic implications

Jazz

Both the half-whole diminished and its partner mode, the whole-half diminished (with a semitone rather than a tone 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 "C dim7" chord) while the half-whole scale is used in dominant harmony (e.g., with a "G7♭9" chord). The scale may be used in other circumstances as well, for example with a minor-major seventh chord.

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.

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)

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.

Alpha chord

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.7)

One of the most important subsets of the alpha collection, the alpha chord, E-G-C-Eb may be considered a mistuned major chord. (ibid, p.9)

Sources

  • 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.
  • 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.
  • Lendvai, Ernő Béla Bartók: An Analysis of his Music. London: Kahn & Averill. Cited in Wilson (1992).

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.

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