Kreuzspiel

 () is a composition by Karlheinz Stockhausen written for oboe, bass clarinet, piano and four percussionists in 1951 (it was later revised for just three percussionists, along with other changes). It is assigned the number 1/7 in the composer's catalogue of works.
History.
Stockhausen regarded "Kreuzspiel" as his first original composition, as opposed to the style-imitation exercises he did as part of his music studies. According to the composer, it was influenced by Olivier Messiaen's "Mode de valeurs et d'intensités" (1949) and Karel Goeyvaerts's Sonata for Two Pianos (1950), and is one of the earliest examples of "point" music. "Kreuzspiel" was premièred at the Darmstädter Ferienkurse in the summer of 1952, conducted by the composer. According to Stockhausen, the performance "ended in a scandal".
Analysis.
"Kreuzspiel" has been analysed in print more often than any other work by Stockhausen, though all but one restrict themselves to just the first of its three stages.
Though routinely described (by the composer as well as others) as a "serial" composition, "Kreuzspiel" does not employ a referential, recurring twelve-tone 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 "permutational serialism" (e.g. Howel) It also uses a permutational seven-element system to control register.
The composition consists of three linked movements, 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 then contracting again to the middle. The third movement superimposes the first two.)
Compositional control of these shapes is determined in the first stage through the parameter of duration, while in the second stage the dominant element is pitch.