Octatonic scale

However, the term most often refers to the ancohemitonic symmetric scale composed of alternating whole and half steps, as shown at right.

Across all conventional key signatures, at least two of the octatonic notes must share similar horizontal alignment on the staves, although the precise combination of accidentals and naturals varies.

[14] 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.

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.

Taruskin continues: "Thanks to the reinforcement the lesson has received in some equally famous pieces like Scheherazade, the progression is often thought of as being peculiarly Russian.

As Mark DeVoto[24] 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.

"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: The scale is also found in the music of Claude Debussy and Maurice Ravel.

Allen Forte[27] identifies a five-note segment in the cor anglais melody heard near the start of Debussy's "Nuages" from his orchestral suite Nocturnes as octatonic.

Mark DeVoto[28] 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".

[29] 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] The scale was extensively used by Rimsky-Korsakov's student Igor Stravinsky, particularly in his Russian-period works such as Petrushka (1911), The Rite of Spring (1913), up to the Symphonies of Wind Instruments (1920).

[30] The second movement of Stravinsky's Octet[31] for wind instruments opens with what Stephen Walsh[32] calls "a broad melody completely in the octatonic scale".

The 'rumba' passage... alternates chords of E-flat7 and C7, over and over, distantly recalling the coronation scene from Mussorgsky's Boris Godunov.

In Bartók's Bagatelles, Fourth Quartet, Cantata Profana, and Improvisations, the octatonic is used with the diatonic, whole tone, and other "abstract pitch formations" all "entwined... in a very complex mixture".

Peter Hill[38] writes in detail about "La Colombe" (The Dove),[39] the first of a set of 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, Carl Orff, Jean Papineau-Couture, Krzysztof Penderecki, Francis Poulenc, Sergei Prokofiev, Alexander Scriabin, Dmitri Shostakovich, Toru Takemitsu, Joan Tower,[40] Robert Xavier Rodriguez, John Williams[41] and Frank Zappa.

Jonny Greenwood of the English rock group Radiohead uses the octatonic scale extensively, such as in the song "Just" and his soundtrack for the film The Power of the Dog.

Earlier examples of the scale's use in progressive rock include King Crimson's Red and Emerson Lake & Palmer's 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.

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.

The chord can be built from the first, fourth, sixth and eighth degrees of the half-step/whole-step octatonic scale, and is transpositionally invariant about a tritone, a property somewhat contributing to its popularity.

In Béla Bartók's piano piece, "Diminished Fifth" from Mikrokosmos, octatonic collections form the basis of the pitch content.

From this, one can see that Bartók has partitioned the octatonic collection into two (symmetrical) four-note segments 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".

Other relevant features of the piece include the groups of three notes taken from the whole-half diminished scale in mm.

[59][clarification needed] The number of semitones in the interval array of the alpha chord corresponds to the Fibonacci sequence.