Nancarrow's Canons: Projections of Temporal and Formal Structures.(Conlon Nancarrow )(Critical Essay)

RARELY HAS A COMPOSER been devoted as persistently to the compositional technique of canon as Conlon Nancarrow (1912-1997). Some three-quarters of his fifty-one "Studies" for player piano feature canons, often strict canons of two to twelve voices lasting the duration of the piece. The studies, which were composed from the late 1940s through the mid-1990s, are brief but remarkably complex and compelling works. Despite their shared canonic organization they exhibit a wide range of rhythmic, textural, and formal structures. In a few instances Nancarrow's canons are traditional, in that the entrances and endings of the participating layers are staggered, and the layers proceed at the same tempo. (1) More commonly, however, the layers proceed at different, proportionally related speeds, in what are known as "tempo-proportion" canons. Nancarrow, for whom "time is the last frontier of music," (2) found the tempo-proportion canon to be a technique particularly well suited for exploring his primary compositional inte rest, rhythmic and temporal asynchronicity: the shared melodic material of the canonic voices can help to make their relatively different speeds perceptually clear. This seems to be the impetus for Nancarrow's interest in canon: "let's say you have two tempi going at the same time--and if you have them both at the same, let's say, melodic proportions, it's easier to follow the temporal changes." (3)

A number of twentieth-century composers incorporated canonic procedures into their music, of course. At one level, canon continued its historical role as a pedagogical tool elemental to the study of both counterpoint and performance. Those contemporary composers who have written a substantial number of canonic works often have done so in the context of collections having a pedagogical intent, carrying forward the tradition of such composers as Antonio Caldara and J. S. Bach. (4) Bela Bartok's Mikrokosmos (1926-39), particularly vol. 1, (5) and Forty-four Duos for two violins (1931), and Paul Hindemith's Sing- und Spielmusiken fiir Liebhaber und Musikfreunde (1928) and Schutwerk fur Instrumental-Zusammenspiel (1927) (6) are important examples. In these types of works the canons are usually quite simple and straightforward: melodic contour and rhythm are imitated strictly, with minor adjustments made for synchronized endings. But there are other contemporary composers who, like Nancarrow, have utilized canon in more "serious" works and have expanded its compositional possibilities, sometimes to make an overt historical connection to the centuries-old technique, and sometimes to infuse canon with a more modern spirit. Canons appear in works by such composers as Elliott Carter, Luigi Dallapiccola, Peter Maxwell Davies, Gyorgy Ligeti, Steve Reich, Igor Stravinsky, and Anton Webern. (7)

While Nancarrow was not alone in writing canons he seems to have done so out of his own impetus, not in response to canons he heard elsewhere. Nancarrow, though American-born, composed in near-isolation in Mexico City for most of his career. His formal compositional training was minimal. He did study counterpoint briefly with Roger Sessions (1934-35), and composition with Walter Piston and Nicolas Slonimsky (during the same time period). Nancarrow claimed that the more significant influences on his compositional development, however, were Henry Cowell's treatise New Musical Resources, (8) which he read in 1939-1940, and jazz, which he grew up playing and listening to. (9) The connections to Nancarrow's music are quite apparent. Cowell advocated the use of complex polyrhythms, polymeters, and polytempos, all of which effects are common in Nancarrow's studies. Cowell even suggested the player piano as a useful instrument on which to produce complex rhythmic structures. The polyrhythms common in jazz certainly f ind direct parallels in Nancarrow's music, and many of his works clearly evoke jazz and popular styles. Neither Cowell nor jazz seems to have provoked Nancarrow's interest in canons, however; if anything, that interest might be linked to his studies with Sessions. Three factors in particular characterize Nancarrow's unique use of canons: (1) the prominence of canon in his output, appearing as it does in the majority of his works; (2) his primary emphasis on tempo-proportion canons, utilizing proportions that range from 2:3:4 to 60:61 to e:[MUSICAL NOTES NOT REPRODUCIBLE IN ASCII] and (3) the performance medium of the player piano, which enables the accurate realization of such tempo proportions, coupled with tremendous rhythmic complexities.

Nancarrow's heavy usage of such a strict compositional procedure as canon might make these works seem somehow formulaic and self-evident: to say, for example, that the two or three or more voices of a work are in a tempo-proportion canon at 3:4 or 3:4:5 or the like is to explain the work fully. But the technique of canon is much richer for Nancarrow than that, yielding a wide variety of textures. As discussed by Kyle Gann, Nancarrow's canonic technique follows an approximate progression from the early, fairly straightforward tempo-proportion canons to the later canons he calls the "sound-mass" canons, in which the canon itself is not the focus of the work, but, rather, the means to achieve a highly complex, multidimensional texture. (10) The paradoxical fertility and attraction of the canonic technique for Nancarrow is precisely this ability to project not only perceptually clear tempo and textural structures, but also obscured and otherwise rich textures, which accounts for his longstanding use of the techni que over the evolution of his style. This paper focuses on canons in three studies, Numbers 14, 24, and 20.11 These works exhibit in miniature the wide stylistic, formal, and textural variety found in Nancarrow's canons, and serve as a good introduction to his music.

Before turning to the studies, an overview of Nancarrow's canonic techniques will help clarify the perception issues fundamental to the canons. In keeping with his stated compositional emphasis on rhythm and tempo over pitch, Nancarrow's canonic pitch imitation is always direct, never by inversion or retrograde. Given this constancy of the melodic dimension, Nancarrow addresses temporal issues by using four primary canonic procedures that accommodate layers with different speeds; I term the four canon types converging, diverging, converging-diverging, and diverging-converging. These are illustrated in hypothetical two-voice settings in Example 1, along with a conventional canon. The horizontal lines in the example represent the individual voices, while the vertical and angled lines that connect them show the placement of equivalent points in their melodic material. In a converging canon (Example 1b) the entrances are staggered--the slowest voice enters first, followed by ever faster voices--and the voices eve ntually meet up at a simultaneous final articulation. In a diverging canon (Example 1c) the voices enter simultaneously and gradually move apart, the fastest voice completing the material first and dropping out of the texture, followed by the next fastest, and so on. In the converging-diverging canon (Example 1d) the voices enter as if in a simple converging canon. They do not stop when they reach their point of synchrony, however, but continue beyond it, taking that point as the beginning of a diverging canon. As a result, both the entrances and endings of the voices are staggered. In the diverging-converging canon (Example 1e) the entrances and endings are simultaneous. The voices diverge at the start and then exchange speeds at some point so that they come back together, arriving eventually at a simultaneous final articulation. In the tempo-proportion canons Nancarrow often states the ratios of the tempos as a subtitle to the work; if not, metronome markings are usually provided so that the ratios can be c alculated. The ratios range from simple rational ratios (3:4 in Number 15) to irrational ([square root of (2 2:2)] in Number 33). There are also some canons that do not follow one of these four plans, but rather incorporate a technique of gradually changing speeds, so that the relationship between the voices constantly changes. (12)

Several perception issues arise with regard to the canons: Can the individual voices be followed? Can the tempo proportions be heard? Can a particular canon actually be heard as a canon? The answer, of course, depends on both the listener and the piece. As stated above, Nancarrow's canonic studies constitute a widely diverse group of pieces. In some works canon is deployed straightforwardly and the canonic process is quite perceptible. But in other works the canonic process may be obscured by the complexity of the canonic line, the number of voices, the fast speed at which it proceeds, or the specific canon type used.

There are two special properties of the tempo-proportion canon that seem to have drawn Nancarrow to the technique. First, Nancarrow's primary aesthetic goal is to project different tempos, and he cites canon as an aid in this: "One reason [to use canons] was my interest in temporally dissonant relationships. ... When you use canon, you are repeating the same thing melodically, so you don't have to think about it, and you can concern yourself more with temporal aspects." (13) In some of his studies canon does seem to help articulate the tempos. And even if the canonic voices or process are obscured, some of the component gestures of the voices are still distinguishable, and their respective speeds thereby evident. Canonic organization ensures that the voices share melodic gestures. The second special property of the tempo-proportion canon is its impact on a larger scale, whereby distinctive formal processes are produced, whether or not the canon itself is perceptible: each of Nancarrow's four basic canon types (converging, diverging, converging-diverging, and diverging-converging) creates a unique formal shape. The points of synchrony--whether at the beginning, ending, or middle of a piece or passage--operate as significant structural moments and thus help to articulate the design of the studies. As a result, the works achieve a directed flow toward and from these focal points. Not only can the technique of canon therefore help to clarify tempo relationships, temporal dissonance, and (sometimes) texture, but it is also responsible in large part for the well-formed, process-driven structure of many of the studies.