“Evoking Cyclic Time: Toru Takemitsu’s Requiem for Strings”
Requiem for Strings is an early piece that brought Takemitsu widespread recognition. When describing the Requiem, Takemitsu states that the work has no clearly differentiated beginning or end, thereby lacking the kind of articulations necessary for our usual definition of musical form. In spite of Takemitsu’s claims, I argue that the Requiem does have a precise beginning, one that influences and provides relationships and references to later events in the music. However, the formal and structural indistinctness create for listeners the impression of “circularity.”
In this paper, I identify the elusiveness of the perception of pulse and meter at many moments of the piece, as well as the obscurity of the origin of pitch materials, which contribute to this impression of circularity. But the most important feature that creates what I call “cyclic time form” is the cyclic repetition of the distinctive three-note musical figures. Copious recurrences of figures often overlap with one another or are embedded within other larger repetitions, and it is this specific feature that creates a complexity that challenges the listener’s perception of form. In many traditions outside that of the Western-European, time is a circle that turns on a daily, yearly, and even cosmic scale. The cyclic concept of time can be perceived as one type of linearity, however the linearity does not form a one-directional line but rather appears as a spiral movement. The unique role of repetitions in the Requiem is to evoke cyclic time, reflecting Takemitsu’s Eastern heritage.
“Compositional Techniques in Two Chamber Works by Karel Husa”
This paper explores diverse compositional techniques found in two chamber works by Karel Husa: Sonata a Tre for clarinet, violin, and piano (1981) and Variations for piano quartet (1984). Analysis and sketch study reveal interesting aspects of tone row presentation, aggregate completion, mirror symmetry, and cellular construction of cadenza-like passages.
Sonata a Tre, movement I features an additive and rotational pitch class presentation technique articulated through various contrapuntal procedures. Passages featuring this seven-PC grouping alternate with contrasting interjections making use of four additional PCs. Husa withholds the twelfth PC for over fifty measures; when it enters, he puts particular emphasis on it. Variations, by contrast, features different orderings of four trichords and of the PCs within them. The result is aggregate completion of a different sort.
A separate but equally interesting issue is Husa’s use of symmetry. Many of his sketches and scores show a keen interest in mirror symmetry in pitch space. Unlike some symmetrical writing, where the axis is present only in the abstract, Husa brings out the axis in many symmetrical passages such that he creates pitch focus or even pitch centers. This is the case in several interesting passages from Variations and Sonata a Tre, some of which evince temporal procedures related to the Fibonacci series.
Cadenza-like sections in both works feature small motivic cells presented in various combinations and orderings. Here, rapid-fire presentation and reordering take precedence over explicit serial procedures.