'Ode-to-Napoleon' hexachord - AbsoluteAstronomy.com

In music

Music

Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

, the 'Ode-to-Napoleon' hexachord (also magic hexachord and hexatonic collection or hexatonic set class) is the hexachord

Hexachord

In music, a hexachord is a collection of six pitch classes including six-note segments of a scale or tone row. The term was adopted in the Middle Ages and adapted in the twentieth-century in Milton Babbitt's serial theory.-Middle Ages:...

named after its use in the twelve-tone

Twelve-tone technique

Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...

piece Ode to Napoleon Buonaparte (1942) by Arnold Schoenberg

Arnold Schoenberg

Arnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...

(setting a text by Byron). Containing the pitch-classes 014589 (C, C, E, F, G, A) it is labeled 6-20 in Allen Forte

Allen Forte

Allen Forte is a music theorist and musicologist. He was born in Portland, Oregon and fought in the Navy at the close of World War II before moving to the East Coast. He is now Battell Professor of Music, Emeritus at Yale University...

's taxonomic system. The primary form of the tone row

Tone row

In music, a tone row or note row , also series and set, refers to a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.-History and usage:Tone rows are the basis of...

used in the Ode allows the triads

Triad (music)

In music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...

of G minor

Minor chord

In music theory, a minor chord is a chord having a root, a minor third, and a perfect fifth.When a chord has these three notes alone, it is called a minor triad....

, E minor, and B minor to easily appear.

The 'Ode-to-Napoleon' hexachord is the six-member set-class with the highest number of interval class

Interval class

In musical set theory, an interval class , also known as unordered pitch-class interval, interval distance, undirected interval, or interval mod...

es 3 and 4 yet lacks 2s and 6s. 6-20 maps onto itself under transposition three times (@0,4,8) and under inversion three times (@1,4,9) (six degrees of symmetry), allowing only four distinct forms, one form overlapping with another by way of an augmented triad

Augmented triad

In music, an augmented triad is a triad, or chord, consisting of two major thirds . The term augmented triad arises from an augmented triad being a three note chord, or triad, whose top note is raised, or augmented...

or not at all, and two augmented triads exhaust the set as do six minor and major triads with roots along the augmented triad. Its only five-note subset is 5-21 (0,1,4,5,8), the complement

Complement (music)

In music the term complement refers to two distinct concepts.In traditional music theory a complement is the interval which, when added to the original interval, spans an octave in total. For example, a major 3rd is the complement of a minor 6th. The complement of any interval is also known as its...

of which is 7-21 (0,1,2,4,5,8,9), the only superset of 6-20. The only more redundant hexchord is 6-35

Whole tone scale

In music, a whole tone scale is a scale in which each note is separated from its neighbors by the interval of a whole step. There are only two complementary whole tone scales, both six-note or hexatonic scales:...

. It is also Ernő Lendvaï

Erno Lendvai

Ernő Lendvai was one of the first theorists to write on the appearance of the golden section and Fibonacci series and how these are implemented in Bartók's music...

's "1:3 Model" scale

Distance model

In music a distance model is the alternation of two different intervals to create a non-diatonic musical mode such as the 1:3 distance model, the alternation of semitones and minor thirds: C-E-E-G-A-B-C...

and one of Milton Babbitt

Milton Babbitt

Milton Byron Babbitt was an American composer, music theorist, and teacher. He is particularly noted for his serial and electronic music.-Biography:...

's six all-combinatorial hexachord "source sets".

The hexachord has been used by composers including Bruno Maderna

Bruno Maderna

Bruno Maderna was an Italian conductor and composer. For the last ten years of his life he lived in Germany and eventually became a citizen of that country.-Biography:...

and Luigi Nono

Luigi Nono

Luigi Nono was an Italian avant-garde composer of classical music and remains one of the most prominent composers of the 20th century.- Early years :Born in Venice, he was a member of a wealthy artistic family, and his grandfather was a notable painter...

, such as in Nono's Variazioni canoniche sulla serie dell’op. 41 di Arnold Schönberg (1950), Webern

Anton Webern

Anton Webern was an Austrian composer and conductor. He was a member of the Second Viennese School. As a student and significant follower of Arnold Schoenberg, he became one of the best-known exponents of the twelve-tone technique; in addition, his innovations regarding schematic organization of...

's Concerto

Concerto (Webern)

Anton Webern's Concerto for Nine Instruments, Op. 24 is a twelve-tone concerto for nine instruments: flute, oboe, clarinet, horn, trumpet, trombone, violin, viola, and piano; containing three movements: I. Etwas lebhaft, II. Sehr langsam, and III...

Op. 24, Schoenberg's Suite Op. 29 (1926), Babbitt

Milton Babbitt

Milton Byron Babbitt was an American composer, music theorist, and teacher. He is particularly noted for his serial and electronic music.-Biography:...

's Composition for Twelve Instruments (1948) and Composition for Four Instruments

Composition for Four Instruments

Composition for Four Instruments is an early serial music composition written by American composer Milton Babbitt. It is Babbitt’s first published ensemble work, following shortly after his Three Compositions for Piano . In both these pieces, Babbitt expands upon the methods of twelve-tone...

(1948) third and fourth movements. The hexachord has also been used by Alexander Scriabin

Alexander Scriabin

Alexander Nikolayevich Scriabin was a Russian composer and pianist who initially developed a lyrical and idiosyncratic tonal language inspired by the music of Frédéric Chopin. Quite independent of the innovations of Arnold Schoenberg, Scriabin developed an increasingly atonal musical system,...

and Béla Bartók

Béla Bartók

Béla Viktor János Bartók was a Hungarian composer and pianist. He is considered one of the most important composers of the 20th century and is regarded, along with Liszt, as Hungary's greatest composer...

but is not featured in the music of Igor Stravinsky

Igor Stravinsky

Igor Fyodorovich Stravinsky ; 6 April 1971) was a Russian, later naturalized French, and then naturalized American composer, pianist, and conductor....

Further reading