Varèse's Hyperprism and Penderecki's Polymorphia

Christopher Meister

This paper concerns itself with comparing two different pieces of twentieth-century music as self-contained and internally-referent information structures. To that end, the following questions will be addressed: how does one part of a piece compare with another; where are the significant compositional similarities, and in what ways do these similarities fashion themselves into larger structures and organizational patterns? The pieces to be examined are Hyperprism, by Varèse, and Penderecki's Polymorphia; Hyperprism will be discussed first, then Polymorphia, and as the latter is analyzed such comparisons will be made between the two as seem pertinent.

The Varèse contains a large percussion complement, and the present analysis concerns itself with the pitched instruments only. In order to examine briefly their harmonic content, this paper borrows from Larry Stempel's 1979 Musical Quarterly article "Varèse's 'Awkwardness' and the 'Symmetry in the Frame of Twelve Tones'". According to Stempel, much of Hyperprism's harmonic structure may be explained as one kind or other of chromatic segment. The simplest and least ordered of these segments are shown in Examples 1a and b.


Example 1a and b: Varèse, Hyperprism, chromatic segments

(c) 1924 by G. Ricordi & C.; Copyright renewed. Reprinted by permission of Hendon Music, Inc.

Within the overall category of chromatic segments, special treatment appears to have been reserved for chromatic trichords whose middle pitches have been displaced either up or down an octave (see Examples 2 a-e). Frequently, "up" and "down" displaced trichords will be played off against each other. Notice that this "updown" play creates a [1] loose sort of symmetry.


Example 2a through e: Varèse, Hyperprism, chromatic segments

(c) 1924 by G. Ricordi & C.; Copyright renewed. Reprinted by permission of Hendon Music, Inc.

Despite the considerable gains towards understanding Hyperprism that this harmonic analysis offers, it fails to address the matter of the composition's non-amplitudinal "dynamics." The remainder of this paper's first half sketches out a model of Hyperprism's behavior, which might be expanded to include Stempel's pitch work. This model divides Hyperprism's musical activity into five "eventcategories." (Example 3a. In this and similar examples, temporal alignment is represented vertically, and measure numbers appear above the topmost staff.) The five categories are 1) piccolo (flute)/clarinet, 2) filter, 3) tremolo/trill, 4) brass, and 5) solo. Each of these events cuts in and out of the sonic collage fairly independently of the others. Although Varèse is not particularly meticulous about an appearance's taking up the exact musical gesture that its previous disappearance had left off, the continuity is nevertheless obvious, and each event has its own [2] formal-dramatic pattern of behavior.


Example 3a: Varèse, Hyperprism, mm. 1-20 Event Relationships

b)                                                                     c)

 ex3cna.jpg ex3cnb.jpg


Example 3b and c: Varèse, Hyperprism, Example 3c: Varèse, Hyperprism, mm. 28-30, mm. 47 -48. Exploration of New Relationships Maximum Concrescence

(c) 1924 by G. Ricordi & C.; Copyright renewed. Reprinted by permission of Hendon Music, Inc.

The event-categories, however, do not behave in solely independent fashion: their primarily linear progressions are to some extent influenced by an interactive inclusional association among them, whereby a musical moment will appear simultaneously in more than one category (see example 3a, in which dashed lines indicate this inclusional associativity). This occurs when a section of the music contains enough traits of two (or more) categories to be included in both. The ramifications of this multiplicity of a gesture's interpretation are most profound near Hyperprism's beginning, for it is here that a single event, the filtered one, generates most of the other categories: for instance, the filter event in measure 4 begets first a constituent of the brass event, then in measure 6 the tremolo event, and later the piccolo/clarinet event in measure 14. The piccolo/clarinet event, which is itself a second-generation gesture, fathers the initial solo event, which begins in measure 18. Following this initial generation of material, the music explores new associations among the event-categories. For instance, the tremolo of measure 17 may be described as the brass gesture below and the piccolo/clarinet gesture above finding a new way of relating to each other. (So far the brass and piccolo/clarinet categories have found common ground through only the filter event at measure 14, not through the tremolo/trill).[3]

A further example of Hyperprism's concrescence may be seen in Example 3b measures 28-30, during which three separate events converge into one.This begins with the piccolo/clarinet event meta-morphosing into a filter event with the addition - on the clarinet pitch concert B-flat - of first a muted trumpet in measure 29, and later a non-muted trumpet in measure 30. This entire sonority (piccolo, piccolo clarinet, two trumpets) remains on the same pitches, but transforms itself into a tremolo event at the fermata of measure 30: all three categories, the filter, the piccolo/clarinet, and the tremolo, have at this point converged into a single gesture. The most extreme instances of interrelation among the categories are those at measures 47-48 (Example 3c) and an identical but longer passage at measures 56-59; it is here that gestures belonging to the piccolo/clarinet, filter, and brass events achieve an extraordinary level of concrescence. This happens in that together they create the impression of a single, animated texture, and each of the categories' gestures co-exists with the others in a state of near-equivalence. All of the gestures share enough similar traits to be included within the tremolo/trill category in example 3c. But, curiously, the dissipation of these categorical characteristics throughout the texture at these two moments of maximum convergence appears to have concomitantly induced an exhaustion of the will to concrescence, for after these two moments of maximum convergence the number and level of interrelationships drop abruptly. (See figure 1 which is a graph of the form of Hyperprism and figure 2 which is a graph of the number of associations per convergence.)

This model of inclusional convergences contains a place in it for the augmented triad begun by the horns in measure 15. This is an awkward harmonic gesture to explain, in that it does not fit well into the predominantly chromatic-segment harmony. However, if harmony is considered to exist within Hyperprism's inclusionallyassociative fabric, one might argue that this augmented triad's abruptness is buffered by the ensuing trumpet entrance in measure 16. This occurs in that the trumpets play only one major third, half as many as the horns, and they also repeat their interval, repetition being one of the brass event's characteristics. This presentation of the trumpets' major third (enharmonically spelled as a diminished fourth) more closely approaches Hyperprism's compositional norms than did the horns' augmented triad: even a disparate [4] harmonic undercurrent is absorbed into the mainstream of the compositional flow.


Figure 1: Varèse, Hyperprism, Form


Figure 2: Varèse, Hyperprism, Event-categories incorporated per convergence