Kreuzspiel
Encyclopedia
Kreuzspiel is a composition by Karlheinz Stockhausen
Karlheinz Stockhausen
Karlheinz Stockhausen was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. Another critic calls him "one of the great visionaries of 20th-century music"...

 written for oboe
Oboe
The oboe is a double reed musical instrument of the woodwind family. In English, prior to 1770, the instrument was called "hautbois" , "hoboy", or "French hoboy". The spelling "oboe" was adopted into English ca...

, bass clarinet
Bass clarinet
The bass clarinet is a musical instrument of the clarinet family. Like the more common soprano B clarinet, it is usually pitched in B , but it plays notes an octave below the soprano B clarinet...

, piano
Piano
The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...

 and four percussionists
Percussion instrument
A percussion instrument is any object which produces a sound when hit with an implement or when it is shaken, rubbed, scraped, or otherwise acted upon in a way that sets the object into vibration...

 in 1951 (it was later revised for just three percussionists, along with other changes).

Stockhausen regarded Kreuzspiel as his first original composition, as opposed to the style-imitation exercises he did as part of his music studies (Stockhausen 1989, 34 & 55). According to the composer, it was influenced by Olivier Messiaen
Olivier Messiaen
Olivier Messiaen was a French composer, organist and ornithologist, one of the major composers of the 20th century. His music is rhythmically complex ; harmonically and melodically it is based on modes of limited transposition, which he abstracted from his early compositions and improvisations...

's "Mode de valeurs et d'intensités" (1949) and Karel Goeyvaerts
Karel Goeyvaerts
Karel Goeyvaerts was a Belgian composer.-Life:After studies at the Royal Flemish Music Conservatory in Antwerp, Goeyvaerts studied composition in Paris with Darius Milhaud and analysis with Olivier Messiaen...

's Sonata for Two Pianos
Sonata for Two Pianos (Goeyvaerts)
Sonata for Two Pianos , also called simply Opus 1 or Nummer 1, is a chamber-music work by Belgian composer Karel Goeyvaerts, and a seminal work in the early history of European serialism.-History:...

 (1950), and is one of the earliest examples of "point" music
Punctualism
Punctualism is a style of musical composition prevalent in Europe between 1949 and 1955 "whose structures are predominantly effected from tone to tone, without superordinate formal conceptions coming to bear"...

. Kreuzspiel was premièred at the Darmstädter Internationale Ferienkurse in the summer of 1952, conducted by the composer. According to Stockhausen, the performance "ended in a scandal" (Stockhausen 1964, 11).

Kreuzspiel has been analysed in print more often than any other work by Stockhausen, though all but one (Borio and Garda 1991) restrict themselves to just the first of its three stages.

Though routinely described (by the composer as well as others) as a "serial
Serialism
In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...

" composition, Kreuzspiel does not employ a referential, recurring twelve tone
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...

 ordered set. Rather, it uses constant reordering of twelve-element (linked pitch, duration, dynamic, and—in the original version—attack) sets—a device sometimes called "permutation
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

al serialism
Serialism
In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...

" (e.g., Blake and Eisler 1995, 111). It also uses a permutational 7-element system to control register
Register (music)
In music, a register is the relative "height" or range of a note, set of pitches or pitch classes, melody, part, instrument or group of instruments...

 (Toop 1974, 159–61).

The composition consists of three linked movements
Movement (music)
A movement is a self-contained part of a musical composition or musical form. While individual or selected movements from a composition are sometimes performed separately, a performance of the complete work requires all the movements to be performed in succession...

, or "stages". In the first stage, six notes begin in the highest register, and six others begin in the lowest register. These gradually move into the four middle octaves until an equal distribution of pitches throughout the entire range is achieved at the centre of the movement. from that point to the end of the movement, the process is reversed, so that all notes arrive again in the two extreme registers, only the six notes originally in the top are now at the bottom, and vice versa. The second movement carries out a similar formal process, only starting in the middle register, spreading out to all seven octaves, and the contracting again to the middle. The third movement superimposes the first two (Stockhausen 1964, 11–12; Stockhausen 1989, 55–56).
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