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Kreuzspiel

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Kreuzspiel
Kreuzspiel is a composition written by Karlheinz Stockhausen in 1951 scored for oboe, bass clarinet, piano and four percussionists. The work starts off with sparse piano and percussion and gradually get thicker. The notes the piano plays are separated by huge distances of more than a few octaves. The interplay between the percussion and the piano continue for some time until the woodwinds enter. The woodwinds continue the same thematic principle that is exemplified in the opening measures with the piano. The movement concludes with the piano and percussion.
Stockhausen divides the pitches in 2 rows of six. He then shifts the first note of the first row and the last note of the second row to the beginning and end of the opposite rows respectively, resulting in a braid like trading of the pitches. By the end of the piece the first and second rows will have switched octaves completely.
Harmony in the piece seem to exist by coincidence, due to lining up contrapuntal lines over each other. In fact I would not go as far as to call this collection of notes lines, but more points that might connect. One might argue that there is no harmony, as the notes that do line up over each other either don’t function at all or are separated by huge intervals making it almost impossible to hear cohesively.
Scored for scored for oboe, bass clarinet, piano and four percussionists this piece has a unique texture due to the placement of the notes and how the different timbres of the instruments connect as oppose the actual orchestration. The notes actually flow seemingly as one coherent linear piece made up of many notes to give it a smooth texture if we listen to the piece as a collective, as opposed to a more rigid texture if we tune into its the nuances.
The density of this piece moves from spares to dense back to sparse ending like it began with piano and drums. The process of this piece uses math as a way to compose. The notes placement, both pitch-wise and rhythmically,

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