[Triad Pairs For Jazz By Gary Campbell 23.pdfl
Facunda Ganesh
An octatonic scale is any eight-note musical scale. However, the term most often refers to the ancohemitonic symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetrical scale is commonly called the octatonic scale (or the octatonic collection), although there are a total of 43 enharmonically inequivalent, transpositionally inequivalent eight-note sets.
The earliest systematic treatment of the octatonic scale was in Edmond de Polignac's unpublished treatise "tude sur les successions alternantes de tons et demi-tons (Et sur la gamme dite majeure-mineure)" (Study of the Succession of Alternating Whole Tones and Semitones (and of the so-called Major-Minor Scale)) from c. 1879,[1] which preceded Vito Frazzi's Scale alternate per pianoforte of 1930[2] by 50 years.[3]
In jazz theory, it is called the diminished scale[8] or symmetric diminished scale[9] 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 two modes are sometimes referred to as the half-step/whole step diminished scale and the whole step/half-step diminished scale.[10]
The twelve tones of the chromatic scale are covered by three disjoint diminished seventh chords. The notes from two such seventh-chords combination form an octatonic collection. Because there are three ways to select two from three, there are three octatonic scales in the twelve-tone system.
Each octatonic scale has exactly two modes: the first begins its ascent with a whole step, while the second begins its ascent with a half step (semitone). These modes are sometimes referred to as the whole step/half-step diminished scale and the half-step/whole step diminished scale, respectively.[10]
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 alternative starting points listed below in square brackets, and return to tonic in parentheses, the three are, ascending by semitones:
With one more scale tone than present in the western diatonic scale, it is not possible to notate music in the octatonic scale in any conventional occidental key signature, without the use of accidentals. In any conventional key signature, at least one of the semitone steps must be written as two notes with the same letter/on the same line or space on the staff. (That is, there must be at least one note that regularly appears with two different accidentals.) There are usually several equally succinct combinations of key signature and accidentals, and different composers have chosen to notate their music differently, sometimes ignoring the niceties of notation conventions designed to facilitate diatonic tonality.
Among the collection's remarkable features is that it is the only collection that can be disassembled into four transpositionally related pitch pairs in six different ways, each of which features a different interval class.[13] For example:
The scale "allows familiar harmonic and linear configurations such as triads and modal tetrachords to be juxtaposed unusually but within a rational framework" though the relation of the diatonic scale to the melodic and harmonic surface is thus generally oblique.[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.[15]
Octatonic scales first occurred in Western music as byproducts of a series of minor-third transpositions. While Nikolai Rimsky-Korsakov claimed he was conscious of the octatonic collection "as a cohesive frame of reference" in his autobiography My Musical Life,[16][17] instances can be found in music of previous centuries. Eytan Agmon[18] locates one in Domenico Scarlatti's Sonata K. 319. In the following passage, according to Richard Taruskin,[19] "its descending whole-step/half-step bass progression is complete and continuous".
Tchaikovsky was also influenced by the harmonic and coloristic potential of octatonicism. 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.
The scale is also found in the music of Claude Debussy and Maurice Ravel. Melodic phrases that move by alternating tones and semitones frequently appear in the works of both these composers. 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 tonalit from 1885.[citation needed]
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". Jonathan Cross[33] describes a highly rhythmic passage[34] in the first movement of the Symphony in Three Movements as "gloriously octatonic, not an unfamiliar situation in jazz, where this mode is known as the 'diminished scale', but Stravinsky of course knew it from Rimsky. The 'rumba' passage... alternates chords of E-flat7 and C7, over and over, distantly recalling the coronation scene from Mussorgsky's Boris Godunov. In celebrating America, the migr looked back once again to Russia." Van den Toorn[35] catalogues many other octatonic moments in Stravinsky's music.
Olivier Messiaen made frequent use of the octatonic scale throughout his career as a composer, and indeed in his seven modes of limited transposition, the octatonic scale is Mode 2. 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.
In the 1920s, Heinrich Schenker criticized the use of the octatonic scale, specifically Stravinsky's Concerto for Piano and Wind Instruments, for the oblique relation between the diatonic scale and the harmonic and melodic surface.[14]
Examples of octatonic jazz include Jaco Pastorius' composition "Opus Pocus"[45] from the album Pastorius[46][failed verification] and Herbie Hancock's piano solo on "Freedom Jazz Dance"[47] [48] from the album Miles Smiles (1967).
The scale can also be found in progressive heavy metal music such as that by Dream Theater and Opeth, both of which strive for a dissonant and tonally ambiguous sound in their music. Examples include the instrumental break in Dream Theater's Octavarium and Opeth's Deliverance. 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. Examples include Planet X's Desert Girl and Sons of Apollo's King of Delusion. 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.
While used functionally as a pre-dominant chord in the classical period, late romantic composers saw the French sixth used as a dissonant and unstable chord. 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. The octatonic collection contains two distinct French sixth chords a minor third apart, and since they share no notes, the scale can be thought of as the union of those two chords. For example, two French sixths based on G and E contain all the notes of an octatonic scale between them.
The octatonic scale is used very frequently for melodic material above a French sixth chord throughout the 19th and 20th centuries, particularly in Russia, in the music of Rimsky-Korsakov, Mussorgsky, Scriabin and Stravinsky, but also outside Russia in the works of Debussy and Ravel. Examples include Rimsky's Scheherezade,[52] Scriabin's Five Preludes, Op. 74,[53] Debussy's Nuages and Ravel's Scarbo.[54] All works are full of non-functional French sixths, and the octatonic scale is almost always the mode of choice.
By adding a major sixth above the root, from within the scale, and a major second, from outside the scale, the new chord is the Mystic chord found in some of Scriabin's late works. While no longer transpositionally invariant, Scriabin teases the tritone symmetry of the French sixth in his music by alternating transpositions of the Mystic chord a tritone apart, implying the notes of an octatonic scale.
From this, one can see that Bartk 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".[55]
795a8134c1