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The BACH motif.

In music, the BACH motif is the sequence of notes B flat, A, C, B natural. Bach's use of this cruciform melody in reference to himself extended to its inversion, retrograde, retrograde-inversion, and all transpositions thereof.

This four-note motif has been used by a number of composers, usually as a homage to Johann Sebastian Bach. The first known example, however, is in a piece by Jan Pieterszoon Sweelinck in the 17th century—it is possible, though not certain, that he used it in homage to one of Johann Sebastian's ancestors, many of whom were themselves musicians.

BACH signature cross

The possibility of being able to spell the surname Bach in this way comes about because, in German, B indicates what in English is called B flat, while H indicates what in English is called B natural.

J. S. Bach himself used it as a fugue subject in the final part of Die Kunst der Fuge (BWV 1080), a work he did not complete before he died in 1750. It appears in passing in several of his other pieces, such as at the end of the fourth and fifth of the canonic variations on "Vom Himmel Hoch", BWV 769. Its appearance in the penultimate bar of the Kleines harmonisches Labyrinth, BWV 591, is not thought to be very significant and the work may even be spurious (Johann David Heinichen has been suggested as a possible composer). It shows up in the St Matthew Passion in the section where the chorus sings "This man was God's own son most truly." In many pieces, while the exact notes B-A-C-H are not played, a transposition of the motif is used (a note sequence with the same intervals: down a semitone, up a minor third, down a semitone). Many of the fugues in Bach's Well-Tempered Clavier, for example, employ the motive in transposed form.

A fugue for keyboard in F major by one of Bach's sons, probably either Johann Christian Bach or Carl Philipp Emanuel Bach, exists using the motif, but it was not until the 19th century when interest in Bach was revived that the motif began to be used with any regularity.

Perhaps because it was used by Bach himself in a fugue, the motif is often used by other composers in fugues or other complex contrapuntal writing.

Works which prominently feature the BACH motif include, in chronological order:

• 1845 - Robert Schumann: Six Fugues for organ, pedal piano or harmonium, Op. 60
• 1855 - Franz Liszt: Fantasia and Fugue on B-A-C-H, for organ (later arranged for piano)
• 1878 - Nikolai Rimsky-Korsakov: Variations on BACH, for piano
• 1900 - Max Reger: Fantasia and Fugue on B-A-C-H for organ
• 1910 - Ferruccio Busoni: Fantasia Contrappuntistica for piano (first version; later versions 1912 and 1922)
• 1911 - Carl Nielsen: Concerto for Violin and Orchestra (Op. 33/FS 61)
• 1932 - Alfredo Casella: Due Ricercari sul nome B-A-C-H, Op. 52
• 1932 - Arthur Honegger: Prélude, Arioso, Fughette for piano (later arranged for string orchestra)
• 1932 - Francis Poulenc: Valse-improvisation sur le nom Bach for piano
• 1937-38 - Anton Webern: String Quartet (the tone row is based on the BACH motif)
• 1952 - Jean Coulthard: Variations on BACH for piano
• 1952 - Luigi Dallapiccola: Quaderno musicale di Annalibera
• 1964 - Arvo Pärt: Collage over B-A-C-H for strings, oboe, harpsichord and piano
• 1974 - Rudolf Brucci: "Metamorfosis B-A-C-H" for strings
• 1976 - Milos Sokola: Passacaglia quasi Toccata on B-A-C-H for organ
• 1976 - Alfred Schnittke: Piano Quintet
• 1985 - Alfred Schnittke: Concerto Grosso No. 3
• 1990s - Ron Nelson: Passacaglia (Homage on B-A-C-H) for wind ensemble

The motif features in passing in a number of other works including Arnold Schoenberg's Variations for Orchestra (1926-28) and his String Quartet No. 3 (1927), Krzysztof Penderecki's St. Luke Passion, Johannes Brahms' cadenza for the first movement of Ludwig van Beethoven's Piano Concerto No. 4, Jason Bahr's Divergence for brass quintet (II. Fugue) and the fifth and final movement of Godowsky's Piano Sonata in E Minor (1910-11).

In a comprehensive study published in the catalogue for the 1985 exhibition "300 Jahre Johann Sebastian Bach" ("300 years of Johann Sebastian Bach") in Stuttgart, Germany Ulrich Prinz lists 409 works by 330 composers from the 17th to the 20th century using the BACH motif (ISBN 3-7952-0459-3).

In popular music, the BACH motif is found in the bass lines of the Radiohead songs "Optimistic" and "Go to Sleep," and in the bass line of the solo Thom Yorke song "Black Swan."

Note: These are possible because, in German, E-flat is "Es" sounding the same as 'S', and A-flat is "As"

Other signature motifs include:

• F, E flat, C, B natural for Franz Schubert (F. Schubert)
• E flat, C, B natural, B flat, E, G for Arnold Schoenberg (Schönberg)
• D, E flat, C, B natural for Dmitri Shostakovich (D. Schostakowitsch; see DSCH)
• B, E, B, A or B, A, B, E for Béla Bartók (Béla Bartók, the latter motif recognizing the Hungarian practice of placing the family name before the personal name, see eastern order)
• C, A, G, E for John Cage, used by Pauline Oliveros[1] and, in the composition "CAGE DEAD", by Simon Jeffes of the Penguin Cafe Orchestra.
• A, B flat, B natural, F for Alban Berg and Hanna Fuchs-Robettin (A. B. and H. F.), used in Berg's Lyric Suite
• A, B flat, E, G, G for Meta Abegg, the inspiration for Robert Schumann's Abegg Variations, Op. 1
• A, S, C, H and As, C, H (in English notation A - E flat - C - B and A flat - C - B), used in Schumann's Carnaval. He was romantically involved with one Ernestine von Fricken, who came from the town of Aš, whose name in German is "Asch". These letters also appear in Schumann's own name. Every piece in the whole cycle is based on one or other of these motifs.
• H, A, E, A, Es (in English notation B - A - E - A - E flat) is used by Thomas Mann in his novel Doktor Faustus for "hetaera Esmeralda", the prostitute Esmeralda his protagonist Adrian Leverkühn is involved with.
• A, D, A, A, F for Jehan Alain, used by Maurice Duruflé in his Prélude et Fuge sur le nom d'Alain (op. 7).
• G, A, D, E for Niels Gade, used once in a piece written in his homage by his good friend Robert Schumann.
• B, A, D, D, G, for Joseph Haydn, used by Maurice Ravel in his Menuet sur le nom de Haydn.