Kreuzspiel

Stockhausen was one of the leading exponents of the Darmstadt school that, in the immediate postwar period, proposed integral serialism as a historically necessary musical organizational technique. At the same time, however, he was one of the first to distance himself from it, if not programmatically, then at least as a compositional fact. For him, the greatest problem inherent in integral serialism and pointillism is their static nature. It is clear, in fact, that the dispersion of parameters achieved with this technique implies an almost total absence of evolution: if for each note, duration, and dynamic, one must follow a series that forces the use of all values before any repetition, it is clear that the resulting piece will hardly have any internal evolution, but will merely be the representation of its organization. This fact, in itself, is not necessarily a bad thing, nor is it an unforeseen side effect. Serialism, in fact, denies internal evolution to counteract Romantic and post-Romantic aesthetics, in which pieces have a dramatic development, that is, they seek to take the listener on an emotional journey. This was considered obsolete by Webern and his followers. For the latter, music should represent only itself and its own organizational model. This is not new: this idea is also common to much pre-Romantic music, such as The Art of the Fugue.

The lack of development, however, was a problem for Stockhausen, and already in his early works he devised often ingenious methods to circumvent it, while continuing to use the serial technique. To do so, he must act on those few parameters that are not involved in the integral organizational obsession, the most obvious of which is the register in which the notes appear.

For example, in Kreuzspiel, for oboe, bass clarinet, piano, 3 percussionists (1951), the development is confined to the dimension of the octave, but it exists. At the beginning of the piece (actually from bar 14 as the process is preceded by a short introduction), 6 notes of the series appear in the upper octaves and the other 6 in the lower ones; The central octaves are empty.

During the first six expositions of the series (corresponding to the first six lines of the permutation square), many notes change register and infiltrate the central octaves, a process further accentuated by the increased use of woodwinds compared to the piano (the initial idea was to employ both female and male voices), until, at the end of the sixth line of the permutation square, all octaves are evenly filled.

Then, with the following six lines, the notes retreat again toward the extreme registers, but in such a way that the notes that initially appeared in the high register end up in the low register and vice versa. This process is evident when listening, and considering that it also gives the piece its title, one can imagine its importance to the composer.

Interested readers can click on the image on the right to examine the diagram of the entire process.

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