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 "up-down" play creates a loose sort of symmetry.^[1]

                       

                                     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 "event-categories."  (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 formal-dramatic  pattern of behavior.^[2]

 

 

 

 

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

       

 

                                                       

        Example 3b: Varèse, Hyperprism,                                 Example 3c: Varèse, Hyperprism, mm. 47 -  48.

        mm. 28-30. 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).                         

 

                        A further example of Hyperprism's concrescence may be seen in Example 3b measures 28-30, during which three separate events converge into one.^[3]  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 inclusionally-associative 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 harmonic undercurrent is absorbed into the  mainstream of the compositional flow.^[4]

 

                                                       

 

                                                                             

                                                Figure 1: Varèse, Hyperprism,  Form

 

                

  

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

 

 

 

         

                 

 

          

                                                                                                                                                                       

                                                                                          

                     

                                    Example 4: Polymorphia, Mono-intervallic and Symmetrical Pitch Formations:

              a: no. 24, Quarter-Tones.  b: no. 31, Half-Steps.  c: no. 7, Three-Quarter-Tones. d: Whole-Tones.  e: no. 27, Perfect Fourths

                            (c) Penderecki POLYMORPHIA (c) 1963 by Herman Moeck Verlag, Celle. (c) Renewed. All Rights Reserved Used by permission

                                     of  European American Distributors Corp., sole U.S. and Canadian agent for Herman Moeck Verlag, Celle.

                       

                      Example 5: Polymorphia, Symmetrical Non-Mono-Intervallic Pitch Formations. a: no.59, b; no.7.

                (c) Penderecki POLYMORPHIA (c) 1963 by Herman Moeck Verlag, Celle. (c) Renewed. All Rights Reserved. Used by permission

                                         of  European American Distributors Corp., sole U.S. and Canadian agent for Herman Moeck Verlag, Celle.

 

                         

                     

                                                                                    

                            Example 6: Polymorphia. a: no. 37, b: no. 59, c: no. 60, d: no. 67.

                                    Polymorphia's Only Non-Symmetrical Pitch Formations

                (c) Penderecki POLYMORPHIA (c) 1963 by Herman Moeck Verlag, Celle (c) Renewed. All Rights Reserved Used by

                permission of  European American Distributors Corp. sole U.S. and Canadian agent for Herman Moeck Verlag, Celle.

 

                        To sum up the discussion so far:  Hyperprism operates as a collage of musical  gestures belonging within one or more behavioral categories.  Judging from the  concrescionally-depletional effect that the two areas of maximum convergence created for  the remainder of the piece, it seems reasonable to hypothesize that any gestural  confluence - a musical moment's belonging to more than one category at a time - may have  some sort of lesser and more localized impact upon the course of the music. In Hyperprism  Varèse pared the function of harmony in order to imbue the non-pitch elements of timbre and  articulation with an increased precedence in the compositional organization.  Polymorphia  exhibits the same emphasis of timbre and articulation at the expense of traditionally  pitch-oriented compositional processes. However, there exist significant differences between  the two pieces' material and organization.  For instance, Hyperprism's occasional employment  of "up-down chromatic trichords" are its sole display of near-symmetrical chord structures^[5].  By contrast, Polymorphia's chord forms are virtually all symmetrical, some mono-intervallic (Example 4), some not (Example 5).  Very few exhibit no symmetry (Example 6).  In addition,  Polymorphia's harmonic structures are drawn from a wider intervallic field than  Hyperprism's^[6] (see Examples 4 - 6).

 

                        But Polymorphia's proliferation of intervallic structures is only one facet of its  compositional network, in which the harmonies are treated as detachable entities to be  mapped onto other, likewise detachable and mappable articulations, timbres, and shapes.  For instance, a fair amount of information is exchanged just among shapes alone:  the  bottom of figure 3 presents two prime shapes, "band" and "glissando," and all the other  shapes in this section (glissando within a band, expanding band, and band upon glissando)  are built from these two prime shapes.  The top of Figure 3 is a simplified graph of where  these shapes occur in the total pitch-space and when in time.  And the middle portions of Figure 3 tell what timbres and intervallic structures are present at what time.                 

   

                                                                Figure 3: Polymorphia., graphic reduction of no.s 1-22

 

                        Besides considering these shapes to exist within a "bandness" or "glissness"  scale, one might also view some of them as generating others through a mapping process:  for instance, the static band at  number 5, if mapped onto the shaped glissandi at numbers  11 or 13, yields the banded glissandi at numbers 15, 18, and 19.  This mapping works in a  small way within the shape field (or parameter), but if one were to take the mapping procedure outside of any one particular parameter and apply it between the two parameters  of shape and intervallic content - to cite but one example - the mapping applications begin  multiplying themselves.  For instance, an interval may be cross-mapped from one shape to  another; note that the canonic glissando at number 13 and the banded glissando at number  15 both share a whole-tone harmonic structure.  Conversely, one shape may have more than  one chord-form mapped onto it.^[7]  And when timbre enters into the picture, the mapping  possibilities begin multiplying quite rapidly.^[8]

 

                        This appears to be a case of freer employment of a wider field of harmonic, timbral, articulatory, and even shape material than was found in the Varèse. In Hyperprism,  despite any transformations created by the inclusional associativity, one could rightly speak  of the "identity" of an event-category being maintained throughout, largely due to the  narrower field of material and the more linearly-invariant mapping associations; but in the  Penderecki, the personality metaphor seems inappropriate:  instead, parametric phenomena  "glom on" to each other, creating global units - bands and glissandi - recognizable in their  macro-structure, but complicated to the point of being bewildering in their compositional  interrelationships. Before proceeding to the remainder of Polymorphia, a few comments  regarding #'s 1-22 are in order.  First notice that all of the sounds are long, bowed ones:  none are short.  Second, all are pitched, either definitely or indefinitely.  Third, within the field  of intervals, all are used with the exception of the quarter-tone, major and minor thirds and  perfect fourths.  And finally, from the beginning to #22 more and more sounds are piled on. 

 

                        Significantly, from #'s 22-44 this whole situation reverses itself (Figure 4).  First,  all the sounds are short ones, save those few briefly hanging over from the previous section;  second, from #'s 22-38 the perfect fourth and quarter-tone, two intervals virtually ignored in  the first section, play a major role; and third, unpitched tones are introduced alongside the  pitched tones for the first time, thus creating a pitched-versus-unpitched argument which  extends from #'s 22-44. Even though this whole section in figure 4 is limited to only short  sounds, much of its interest is the result of the course of this pitched-unpitched argument:  from #'s 31 to 37 the pitched side of the argument gains ground, to the point of eventually  saturating both pitch-space and intervallic content between #'s 37 and 38.  (See Example 6a.)  But afterwards, from #'s 38-88, only the unpitched sounds are used, these becoming increasingly  removed from pitched territory, to the point of not being produced on the instrument at all.              

               

                                                                 Figure 4: Polymorphia., graphic reduction of no.s 46-67

 

                        Another facet of Figure 4 which bears discussion is the existence within it of two  successive accretions; the first is the pitched-unpitched argument from #'s 22 to 38, which  collapses, making way for the second, totally unpitched accretion from #'s 38-44.  Similarly,  the initial section, #'s 1-22 of figure 3, may also be considered an accretion and subsequent  collapse.  Since each of these large-scale accretions is built from its own set of musical  characteristics,^[9] it becomes clear that a very few compositional operatives define the  conditions for a considerable stretch of music.  Were one to compare Penderecki's accretions  with those in the Varèse, he would find that in Polymorphia, they occur for minutes at a time  and are the main sections of the piece, whereas in Hyperprism the accretions appear to  function as signposts of the larger sections, analogous to codetta and coda of sonata form.^[10]

 

                        This last parenthetical remark raises the question of form in Polymorphia.  Examination of the "articulatory" section of figure 5 shows that all the sounds from #46 to the  end are long ones, as they were between #'s 1-22.  Additionally, timbres, shapes, bands, and  glissandi similar to those of figure 3 are developed throughout in figure 5; from this it seems safe  to infer that Polymorphia's form is essentially an ABA in its large-scale outlines.               

 

                        But besides being a recapitulation of Figure 3, Figure 5 is also a summation of the previous discourse. Note that the intervallic content of Figure 5 incorporates each of the two  previous sections' sets of intervals in addition to adding some intervals of its own:  clearly,  the entire harmonic content of the piece is being summed up right here.  And besides functioning as a harmonic summation, this third section additionally incorporates the long-versus-short and pitched-versus-unpitched arguments of the two preceding sections.

 

                    

                                                            Figure 5: Polymorphia., graphic reduction of no.s 46-67,  bridge pitched and unpitched sounds.

 

                        This incorporation, or "synthetic" phrase, takes place near the very end of  Polymorphia in the following manner:  first, note in the lower half of the timbral-articulatory  portion of figure 5, that at #63 the instruments begin playing a behind-the-bridge "ugly  creaking" (Penderecki's term).  This sound is a continuous series of short, individual  "creakettes," and as such this unpitched sound incorporates for the first time both the long  and short articulatory antitheses.  Immediately after beginning this behind-the-bridge creaking,  the performers are directed to play on the tailpiece and on the bridge itself, thus producing  the first truly long, unpitched sound: the pitched-unpitched, long-short events are being  mapped onto each other in new combinations.  And these new mappings find their most  inclusive expression in the creaking bands begun at #62: these incorporate both long and  short sounds as did the behind-the-bridge creaking; and since their inharmonic (unpitched)  content partially obscures the tones' pitches, these quasi-pitched, creaking bands additionally  bridge pitched and unpitched sounds.

 

                        Examination of Figure 6, a three-dimensional model of information exchange in  Polymorphia,  provides an overall sense of how information functions throughout the piece.  To explain the model briefly:  time runs from left to right, and rehearsal numbers are placed below the X-axis; the Y-axis is divided into "long" and "short" halves; and the receding Z-axis  is divided into pitched and unpitched halves, the unpitched portion being denoted by a "P"  with a line above it.  The heavy  lines  show  when  and  to what degree the music is in which  of  the  available  quadrants;  and  the  remarks  interior  to  each  of  the  heavy-line "large-operative"  boxes  show  the  field  of  mappings  within  each  box  among  the parameters of pitch, timbre, and shape: a line between two parameters means that most of one parameter's elements will map onto most of another's.  Comparing the relationship between the interior mappings and the "large-operative" articulatory-pitch boxes yields significant information.  For instance, in the first "long" section (to #22) we see an increase in the  number of mapped elements within each parameter and a resulting increase in the number of mapping combinations  among the parameters.  At #22, moving into the short area and just partially into the unpitched area affects a striking reduction in the number of mappings among the parametric  elements; moving entirely into unpitched territory eradicates both pitch and shape, and the only shape left is the large-scale, accretionary one.

 

 

 

 

                                                Figure 6: Polymorphia., Long- and short range information exchange and mapping

 

                        This inter-parametric mapping has been so depleted by the move into short,  unpitched territory that even the return to the long and pitched quadrant at #44 is not  sufficient to ensure an immediately corresponding return to the former level of mapping  activity:  the  number of combinations available at #44 is minimal, and it takes until #56  before the number of combinations reaches its former level of #22.  And comparison of #'s  46 and 59 in Figures 5 and 6 shows that the increase of interparametric mapping is associated with a rapid turnover in both timbral and harmonic parameters; this turnover  seems to create an instability within and among the pitch, timbre, and shape parameters  which could well be construed as catapulting the thrust towards concrescence into the "larger  operative" areas of pitch and articulation occurring between #'s 62 and 63.              

         

                        Finally, comparing Figures 6 and 2 provides a sense of how concrescence  fluctuates in each piece.  In Polymorphia the area of maximum concrescence appears very  near the end; in Hyperprism, towards the middle.  This is most likely the result of each  composer's approach to information, whether conscious or not:  Varèse's convergences are  byproducts of the interactions among the event categories, each of which is primarily  concerned with maintaining its own identity in the face of the others; but in Penderecki the  large-operative information itself determines the course of the inter-parametric events,  which have no personal identity save that of existing within the general thrust toward  concrescence.   

 

 

 

 

Bibliography    

 

Breeden, Daniel Franklin.  "An Investigation of the Influence of the Metaphysics of Alfred  North Whitehead Upon the Formal-Dramatic Compositional Procedures of Elliot Carter." DAI,  37 (1976), 678A (University of Washington).   

 

Penderecki, Kryzstof.  Polymorphia.  Celle, West Germany:  Hermann Moeck Verlag, 1963. 

__________.  Polymorphia.  Cond. Henryk Czyc, Chorus and Orchestra of the Cracow  Philharmonia.  Philips, 839 701 LY, n.d.   

 

Schuller, Gunther. "Conversation with Varèse."  Perspectives of New Music, 3  (Spring-Summer 1965), 32-37.   

 

Stempel, Larry, "Not Even Varèse Can Be an Orphan."The Musical Quarterly, 60  (1974),46-60.

 

__________. "Varèse's 'Awkwardness' and the 'Symmetry in the Frame of Twelve Tones':  An Analytic Approach."  The Musical Quarterly, 65 (1979), 48-66.   

Varèse, Edgard.  Hyperprism.  New York:  G. Ricordi & Co. 1924.   

 

Webern, Anton.  Concerto, Op. 24.  Vienna:  Universal Edition, 1948.

 

Whitehead, Alfred  North.  Process and Reality:  An Essay in Cosmology.  ed. David Ray Griffin and Donald W.  Sherburne.  New York:  The Free Press, 1978.