Analysis

In order to better illustrate the consequences of Stockhausen’s line of thought, it is worth turning to his woodwind quintet Zeitmaße with special attention to the roles that tempo, meter, and rhythm play in formal organization. Stockhausen himself uses this piece as an example of his techniques in “…how time passes….” One of the defining works of the 1950s, Zeitmaße has received considerable attention, and scholars have thoroughly examined the serial structures of each musical element and the other compositional patterns that organize the work. ¹ Pascal Decroupet points out that the clarity of the work’s contrast in tempo and meter is highly ordered, though the tempi themselves are famously embodied in the performer’s technical abilities with the indications to go as fast or as slow as possible. ² As the name of the piece implies, the contrasting passages of Zeitmaße are characterized by different qualities of meter, rhythm, and tempo. Rather than measure these passages out quantitatively, they will be reduced to a sort of unity. In the following ‘qualitative’ analysis, three operations occur, which use the idea of rhythm, timbre, and pitch as models for a qualitative description of phrasing, subdivision, and tempo. First, clear phrases will be imagined as durations of a single ‘note’; second, consistent rhythmic subdivisions are categorized into distinct timbres or ‘voices’; and third, prominent metric units and related tempo changes will translate roughly into a contour of some low, approximate pitch space. This analysis of Zeitmaße thereby bypasses the precision of mathematically defined rhythmic relations (even those based on serial organization). Durations of phrases, while measured out by metric units, are not counted but felt as relative length of notes. Similarities in rhythm and meter can be identified in the same way that timbres are more obviously identified in listening: as the heard consistency of a distinct voice as it changes register, vowel timbre, and pitch within a performance. And the contrasting tempi of different passages can be imagined as the ‘fundamental’ frequency of some very low pitch.