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 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♭
550px|Diminished scales on E♭, D, and D♭, ascending

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 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).

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==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.

thumb|72px|Bildliche Darstellung der verminderten Skala, 1. Form. ([[:Bild:Tonleiter_bildlich_schema.png|Erläuterung)]] 
thumb|72px|Bildliche Darstellung der verminderten Skala, 2. Form. ([[:Bild:Tonleiter_bildlich_schema.png|Erläuterung)]] 

Die '''verminderte Skala''' oder '''verminderte Tonleiter''' ist in der oktatonische Tonleiter. Sie besteht aus acht Tönen, der Abstand zwischen zwei Tönen ist dabei immer abwechselnd ein Ganzton und ein Halbton. Verminderte Skalen werden häufig im Jazz eingesetzt.

Die Bezeichnung ''vermindert'' kommt von der Tatsache, dass die erste, dritte, fünfte und siebte Note einer verminderten Skala den verminderten Terz, Tritonus und große Sexte).

Die vermindete Skala hat zwei Modi: einen, der mit einem Ganztonschritt beginnt (die '''Ganzton-Halbton-Leiter'''), und einen, der mit einem Halbtonschritt beginnt (die '''Halbton-Ganzton-Leiter''').

Aus Symmetriegründen gibt es in der gleichstufigen Stimmung nur drei verschiedene verminderte Skalen. Jeweils vier verminderte Tonarten verwenden dieselben Noten; sie beginnen dabei lediglich bei unterschiedlichen Startpunkten innerhalb der Skala (in Klammern angegeben).