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Varese bound.

Jonathan Bernard's analytical study, The Music of Edgard Varese,[1] promises that "the set of theoretical constructs developed here and used as a basis for extensive analysis of the oeuvre does represent a breakthrough, for it arises directly from those features of Varese's aesthetic and method which most dearly distinguish him from his contemporaries" (xxiv). What might this breakthrough be, especially given the "for" that suggests not only that the method is Varese-inspired but also that no one else's work has arisen out of Varese's distinctiveness? Many of the aspects of Varese's music usually considered most characteristic have been addressed (if not systematically) by, among others, Chou, Erickson, Babbitt, and Cogan.[2] Among them they have discussed timbre, the constitution of sound masses, the use of percussion, symmetrical and cellular pitch processes, the electronic quality of even the pre-electronic works.

The opening sentence of Bernard's analysis of Hyperprism identifies what he distinguishes: "Pitched material begins in m. 2 ... " (193). The observation is true enough, but we hear the piece begin with a crash more than a measure before. The analysis will get to this fact - "no parallel stasis here: percussion begins the piece" - in order to talk about "rhythmic connections between the pitched and unpitched realms" (196), but only after describing both the pitch configuration that is eventually symmetrical around [C#4 sub.4] and duration in the pitched instruments.

The subject of Bernard's system, then, is pitch, the breakthrough is in pitch methodology. It is the denial of octave equivalence, which produces a completely linear rather than cyclic pitch space. The first part of this paper will sketch the fine of thought that he takes in the effort to identify Varese's inventiveness with pitch.

The introduction takes up "problems of interpreting" Varese's statements about his work (xx), among other things citing his "preference to speak analogically, not analytically" (xix). In this way, it arranges to disregard Varese's ideas about music. Robert Erickson, on the other hand, has said that "one has to ... understand that, when [Varese] says |different shapes or groups of sound,' he is speaking seriously and precisely, and that he is grappling with musical dimensions for which no theory existed. By applying spatial concepts in a very radical way he at least provided himself with a framework for thinking about what he was doing, and he may have provided us with notions and ideas more pertinent to the discussion of timbral organization than we have thought" (Sound Structure, 51).

Bernard rejects "a preoccupation with object rather than process" because "no attempt simply to classify [Varese's pitch, rhythmic, timbral, and dynamic structures] as a repertoire of possibilities available for deployment ... will get very far, for such a repertoire grows before long to unmanageable proportions" (xviii). There is no reason to assume that "classification ... as a repertoire of possibilities" is the only, or even the best, way to analyze "Varese's pitch, rhythmic ...," and interest in either object or process need not imply exclusion of the other. They could be complementary.

However, "object" is most strikingly the Varesian notion of sound mass, and Bernard himself identifies some of the characteristic features that both constitute and differentiate them: "enormous dynamic contrasts, frequent interjection of silence, and a vast palette of timbral differentiation. These act together with long durations to divide a work into temporal successions of readily discernible entities" (110). Sound masses are kept clearly separate through mutual contrast and "non-blending." to use Varese's word, in every imaginable aspect of the single mass. If they seem nearly palpable, it is because every imaginable aspect of the music cooperates in their reification. They are peripheral to Bernard's method.

Though he acknowledges "a vast palette of timbral differentiation" in Varese's music, Bernard asserts that "on the balance, Varese does seem to have leaned more toward than away from the attitude that color, though of more than decorative or ornamental significance, was less important than other factors (notably pitch and register) in shaping sound masses and setting them in motion" (22). He cites the fact that "Varese's aspirations for timbre in his work included its removal from any |incidental, anecdotal, sensual, or,,picturesque' function and its use instead as |an agent of delineation, like the different colors on a map separating different areas, and an integral part of form'" (46; italics added). But, whereas Varese is clearly saying that he can envisage timbre as integral rather than incidental, Bernard goes on to say that "timbre, in other words, was for Varese a partitioning device," its role to solve analytical problems: "registral overlap often poses analytical problems that only timbral differentiation can resolve .... One result of the importance of timbre for Varese is that the lowest and highest pitches of timbral groupings can serve, in the spatial sense, as demarcators" (46). And where timbres do not parse the music into the kinds of pitch/ interval regularities sought, one can ignore them: "space between timbrally defined groups may be used, or not, to define segmental sizes" (footnote 15 on page 253, referenced on page 95).

In the course of this argument for the subordination of timbre, Bernard focuses, uncharacteristically, on a linquistic point: " [Varese] did remark on [timbre's] potential as a contributor to other structures comprising the overtones of written pitches, but invariably such remarks were couched in the conditional tense [sic]. Any more powerful role for timbre would require the invention of new kinds of instruments" (130).

It may very well be true that such remarks were invariably conditional. But, if Varese had dreams about how timbre might function in an electronic future, it does not mean that he never tried to approximate his dreams with the means at hand. As Chou Wen-Chung asserted: "Clearly, . . . Varese opened up new horizons not in the fifties with his electronic works but in the twenties with his works for conventional instruments .... These instrumental works of his are not merely |electronic' in sound, as has been pointed out, but more significantly, |electronic' in concept" ("Sketch," 163).

When Bernard turns to percussion timbres, he begins by recognizing Varese's "special love for these instruments - for their seemingly endlessly varied possibilities of timbral combination, and for the discoveries waiting to be made with every exotic newcomer." But "exactness of sound definition assumes priority in an analytical situation" (159) and, in short, the percussion are treated as dependent on the pitched instruments: "even in the presence of unpitched events, then, pitched material has the requisite coherence to maintain a continuity of its own. For this reason, to the extent that they bear any relationship at all to pitched material, unpitched events take place in a kind of shadow world, where ... they reinforce, reflect, prefigure, or otherwise complement events in the pitched sphere " (160). Hyperprism's opening crash is, in Bernard's ears, insubstantial as a shadow; "complementation," for Bernard, is hierarchical rather than reciprocal.

Near the end of the book he reassures readers that "the vast variety of possible combinations among the percussion instruments need not be an obstacle to analysis. The intricate details of Varese's percussion scoring do present a potential pitfull, in that one runs the risk of becoming preoccupied with intricacy for its own sake and feeling compelled to classify all of its aspects" (182; italics added). But "vast variety" is no "obstacle," nor "intricacy" a "pitfall." if our analyses are meant "to maximize the numbers of different ways in which things can be distinct entities." as Benjamin Boretz put it.[3]

Even Bernard's systematic observations about rhythm, which he ranks second to pitch, are framed in terms of "pitch stasis" (134ff.; italics added). He proposes a set of categories to distinguish degrees of (im)mobility ranging from "frozen music" to "rapid motion" (e.g., measures 40-42 of Hyperprism), in the latter of which there is "a very high event-density ... Because so much is happening all at once, the processes become fiendishly difficult to unravel, and the analyst is left grasping at straws .... The best recourse in such cases is the expedient compromise" (110; italics added). And the pitch orientation is further enhanced by images of pitch's confinement, struggle, and escape from stasis.

Although he asserts that "absolute (that is, exactly measured) duration is irrelevant in most analytical situations," he says that, when duration is in control, it needs to be measured: "beat-counting is not always inappropriate. It is useful in situations where duration has independent stature, where pitch events have temporarily ceased to progress .... In these situations, duration assumes the function of directing progression, and it becomes necessary to measure it in some way" (134).

By the end of the methodological exposition, the new, Varese-inspired analytical ideas promised by "the set of theoretical constructs developed here and used as a basis for extensive analysis ... arise directly from those features of Varese's aesthetic and method which most clearly distinguish him from his contemporaries" (xxiv) have come to

However much Varese might have wished to work outside the continuum [a misnomer, Bernard is referring to a "pitched spectrum" he describes as "calibrated"] - and there is plenty of evidence that he did ... - he had nothing of comparable power to serve as a permanent substitute, and he knew it. In writing for pitches, while awaiting technical breakthroughs that would free music from the tempered scale, Varese was forced into compromises he would not otherwise have made, but this is really beside the point. What matters is that the piece we ham now are written principally for pitches and must be interpreted through the nature of the pitch continuum as it existed then and as it exists now. (159-60; italics added)

This leaves only the domain of pitch in which to construct a distinctly Varese-derived system, and that only in terms of the "pitch continuum"' traditionally conceived. Where Varese managed to escape the "tempered scale," as with Hyperprism's D-half-flat (measures 68-74), Bernard's analysis first lists the mistakes of other analysts-some have considered it a joke that avoids "closure"; some would like it to be Db; someone "has even interpreted it as both D and Db" - and then points out how "from one point of view the ambiguity is actually useful," in order, finally, to decide the case "on spatial grounds" in favor of "calling [it] |D-like"' (211). So much for Varese's attempts to transcend traditional pitch space.

The dismissal of sound dimensions other than pitch arises from the precedence accorded methodological expediency and tidiness (or manageability) over individualizing the works that the book was, after all, written to tell us about. Both the reasons to do this and the rationale for doing it can be found in the opening pages of Chapter 4, "Rhythm and Duration" (128-133).

There, having laid out the pitch methodology, Bernard turns to the question of "the diversity of analytical strategies that have been applied to Varese's music," characterizing" it as "lack of consensus." "Perhaps it is time," he says, "to try to curb the seemingly endless round of |Well, I hear it this way' and |Well, I hear it that way,' which resolves nothing" (128). Although earlier in the book he states that an analyst can provide only "selective illumination" and that the analyst's "choices . . . depend upon prior tbeoretical choices, which one either inherits or makes oneself" (xxiv), now he expresses distrust of the individual's viewpoint, "not, of course, that it is possible to do away with subjectivity entirely; but its scope can be limited" (128). Or at least he is uncomfortable with the position in which arguing from personal insight would place him, since subjective results "can be peremptorily dismissed by anyone who doesn't agree with the initial assumptions" (128). Presumably he conceives of his method as grounded in an authority greater than individual perception.

This exposition of beliefs is the foundation for a lengthy argument in favor of the need for one "primary, controlling," "most powerful ... domain" (131; 129). Because "for centuries before 1900, Western music had been consistently and overwhelmingly pitch oriented," Bernard asserts that "one of the compromises that Varese had to make was to acknowledge the sovereignty of pitch" with rhythm/duration . . . clearly a secondary, contributing domain," because it "shares exactitude of notation with pitch and register." Furthermore, "not all secondary domains are of equal stature." "Timbre," he tells us, "is not nearly so susceptible to regulated gradation or precise definition as pitch." And to complete the sound-dissection, "The lack of precise indications for dynamic levels effectively prevents a composer from exerting the same control over overtone complexes as over written (or |fundamental') pitches" (130-132); my exposition reverses the order of Bernard's).

This argument reveals three central tenets of the book's analytical ontology. The first is construction of the argument on a framework of supremacy and control. This fundamental assumption performs many functions over the course of the book with respect to musical works, analyses, and theoretical discourse. For example, if the source of Bernard's anxieties about the "pitfalls" of "intricate details" seemed obscure, Naomi Schor's account of the danger perceived in detail is suggestive; "what is perhaps most threatening about the detail," she says, is "its tendency to subvert an internal hierarchic ordering of the work of art which clearly subordinates the periphery to the center, the accessory to the principal, the foreground to the background."(4)

The second is a commitment to conservative, backward-looking music theory. Pitch has always been first, therefore it must continue to be. It is, given the traditions of the music-scholarly community, incontestably deserving of attention, having already been given so much. Energy and imagination will not be devoted to significantly new ways to think about it, about any other dimension, or about the relations between them.

Third is the priority granted those sound attributes that have the most discrete and exact manifestations in the durable form of notation actually they are the only dimensions ranked). This reflects a commitment to methods that depend on measurement (of distances between or temporal extension of differentiable entities). The yardsticks are "absolute interval size" (44) and, whenever pitch is "static" and anything else moves, duration (134). If pitch's "calibration in semitones" (89) is strictly adhered to, it lends itself to replicable measurements that any individual, properly trained, can make on score-specified pitches (ignoring, for now, the fact that the individual analyst must choose which pitches to make measurements between). In this system, questions of hearing it one way or another arise only as quibbles about one passage or another; what matters are the measurements, plain to see "out there" in the world.

Measurement facifilitates traditional analytical activities of comparison (of pitch-registral distances) and (trichordal) identification, grouping, and enumeration. (The methodology is summarized below.) It allows one "to measure intervallic consistency in whole works or sections of works," presumably to determine the value of the music, and to evaluate analyses by counting the number of entities invoked: "the fewer constellations invoked to describe the spatial lattice, the more consistent-and coherent-the analysis will be" (77).

The discrepancy between Hyperprism's opening and that of the analysis illuminates the highly personal nature of Bernard's presentation. His decisions may seem matters of fact because they are so commonplace, but it is he for whom pitch is primary, he who relegates description of the percussion to a paragraph near the end of the discussion, and he who decides to mention only the percussion's relations to pitched events. Staying within the bounds of pitch thinking, avoiding sound aspects for which we do not have calibrated notations, did not save him from making an interpretation of the music; the analysis is unquestionably subjective. There is nothing wrong with this, of course, but what could Bernard have made of Varese if he hadn't been trying so hard to avoid being subjective?

In fact we have an inkling because, throughout the book, he yields to invention by devising qualitative characterizations for percussion timbres (dry, resonant) and degrees of focus (clear, fuzzy, aura-surrounded).(5) And there are insightful observations along these fines throughout his analyses, for example of the "timbral resemblance" between sleigh bells and chains and a high woodwind chord in Integrales (178). Bernard's evocative analysis of measures 23-29 of Deserts concludes intriguingly: "The sparse texture of these measures, intervening as it does between the denser scoring of measures 21-22 and m. 30, provides an element of contrast and time for the elements of the chord in measures 21-22 to be absorbed before furthe development is undertaken" (163; italics added). His exemplary and detailed analysis of relative pitch in Deserts, measures 264-69 (179-80) - a vision of percussion sounds congenial to him - proceeds to a lively and intriguing analysis of measures 200-03 that addresses timbrat and pitch relations together.

A similar appeal is evident in Bernard's occasional descriptions of the qualities of static passages: "if measures 1-25 or 32-52 of Integrales are frozen music, then [measures 62-69] are in a liquefied or perhaps even gaseous state" (110). This is pleasingly allusive to a quality of sound the passage has for him, one which others might care to try hearing. Describing a progression of three rests in Octandre II, he points out that "besides this quantitative progression [from one to three beats of rest] there is a qualitative one: m. 21 is the first rest (that is, in this case, an attack rest) of any kind in the stasis; in the attack rest in m. 27 we hear the sustention of E4 in its new timbral guise (horn taking over from trombone), which is a new kind of event in the passage; m. 32 is an actual rest, completely empty of sound. This shock of silence . . ." (150; underlining added): how sensitive Bernard is here to the resonance of the silence, and how effectively the expression "this shock" points the reader to it.

This last example is from the chapter "Rhythm and Duration." In it, Bernard seems uneasy because he cannot always frame his observations as measurements. He relies on beat-counting" when he can, but he often turns to qualitative descriptions. At these times, he is more inclined to portray several dimensions cooperating in creating musical entities rather than competing for first place in our attention.(6) These observations are always brief, often tentative or hedged, which is unfortunate, I think, since they tend to be very suggestive.

Bernard and others may not even consider his remarks about the qualities of events and passages to be analysis. They are not assembled into a system; rather, they are his own individual interpretations, pointing intriguingly down perceptual-analytical roads one might wish to take. Moreover, they allow us to explore the dimensions declared off-limits by his tradition-constrained system, notably percussive sound, timbre, and sonority in general, as well as non-durational aspects of rhythm. The "seemingly endless round of "Well, I hear it this way' and |Well, I hear it that way,'" if the ways are conceived as augmenting and not supplanting each other, is the method by which the analytical community enriches the meanings we can ascribe to musical events, thereby improving our hearings of pieces.

For the remainder of this essay, I will indulge a "preoccupation with intricacy" (though I don't "feel compelled to classify" much of anything) in order to respond music-analytically to Jonathan Bernard's work. To begin with, I will explore obscured or outcast dimensions of sound by examining Hyperprism up to about menure 29 (and beyond, where I need to) and making some general proposals as I go.

Hyperprism may not be the ideal piece for examining timbre's integral formal role. The potential distinctness of woodwinds and brass is diminished because the woodwinds, layered above the brass (except in the last chord), never sound in their more characteristic, lowest register. The instruments thus make a single, relatively monochromatic pass through the frequency spectrum. A range of relatively subtle distinctions in the pitched instruments is created principally through the various resources, such as mutes, available to the brass. The most striking sources of timbral differentiation are within the percussion groups and between them and the winds.(7) (There are, of course, relative levels of distinction; drums and multi-attack instruments sound less like the winds than do the ringing metals.)

Chou Wen-chung's ideas about grouping and his descriptive terms for timbre, attack, and envelope suggested ways to hear and describe the profusion of percussion sounds in Hyperprism. The percussion groupings used were adapted from David Reed Bloch.(8) Not to be pursued here, I must confess, are such things as Chou's "motivic" analysis of Ionisation, or Bernard's hint about such relations in Hyperprism, described as "connections which . . . produce a network of mutual, approximate influence [between percussion and pitched instruments] involving such characteristics as alternation, rolls, flutter-tonguing, and crescendo" (196 and Example 5.4).(9) Bernard's description of Integrales, measures 79-93, evoked the percussion fireworks that begin and end the passage: "the percussion parts consist of a kaleidoscopic series of variations in instrumental combination. . . . Interestingly enough, the percussion tums out to be grouped quite clearly by bar lines" (169).

Hyperprism opens with crashing and booming, whose impetus dissipates in the fading ring and low roll. Renewed action proceeds along two lines: percussive bursts and sustained beams. The first, short, burst in the bass drum is almost obliterated by the beam of increasing sound released from the lion's roar. Thereafter bursts succeed each other at regular intervals, but without ever creating a directed process. In the first two, rattlings and jingling intrude on a drum line. In the third, two oscillations are mutually obstructive. Then the durational pattern changes: two short bursts - a drum line with halo, a succession of jingles and rattles - are followed by one long one - a higher drum line with both jingling and oscillating rattles. This succession repeats once with an added line in its long burst. Then a second repetition transforms the short bursts: the first becomes a dry tune and the second a drum solo, while the long burst only adds timbres to each of its lines.

After the lion's roar subsides, a piercing, nasal beam sustains a pitch it seems to have picked out of the fading ring. Coincident with the third percussion burst, another beam sounds quietly lower down. Thereafter, both beams sound almost constantly through the discontinuities of the percussive fireworks.

The higher beam moves repeatedly,between its and other brass sounds. Every time except the first, its nasal whine slides in, like a siren, from off center and diminishes in intensity once its pitch has stabilized. When the beam intensifies again, its timbre changes, the first time into a sonorous, increasingly bright sound. The second time, that sound is submerged behind an increasingly insistent rasping. The rasping is moderated in the next emergence, which punches out a rhythm. Finally the first, sonorous timbre returns, brightens, and breaks into heavy pulsing. Then it makes a rattling side in for one last blast.

Coincident with the first slide, the low beam of the siren arcs upward, once slowly, then more quickly. Near the end of the second arc, a low growl grows louder and fades. Then the siren sounds, but does not arc. A second growl intensifies tremendously, falls silent, then fades. (In retrospect, did this beam begin with the lion's roar?)

Bernard describes the percussion at the opening as "in constant flux" (196) and, therefore, not static. Nevertheless, his eye is so focused on the fixity of pitch that he undervalues non-pitch motion, even while addressing it as "claboration and variation in other domains" (135). His discussion of brass timbres in the opening measures shows how "the pattern of durations established by the alternation of [C#.sub.4] between trombone and horn also works in favor of an end to pitch stasis" (193-94). As I have described the opening eleven measures of Hyperprism, even if pitch is fixed, both [C#.sub.4] and D2 move in timbre, dynamics, and articulation to reveal different sonic surfaces.(10) More generally, any sound dimension can contribute to movement, even if that movement seems aimless" machine-like, or otherwise undirected.

Varese upsets the usual order of things by creating movement within single, sustained pitches through change in dynamics, timbre, and other dimensions. He also turns things on their car by making pitch, as frequency, an aspect of timbre. Robert Cogan has demonstrated this point in a spectral analysis of Hyperprism, framed in terms of relative density (New Images, 96-101). Milton Babbitt has given a characteristically technical account of the phenomenon, associating timbre with formant and observing that "the distribution of pitches in a chord, . . . taken together with associated dynamics, is determined by the degree of resultant density . . . desired, or . . . a distribution is chosen that makes . . . a [desired] dynamic level attainable. . . . Crescendi, such as those in the tres vif section of Octandre, produce not what can be most accurately described as a change in loudness of a fixed sonority, but a continuous alteration of the number, relations, and densities of the partials of the total spectrum; the percussion instruments themselves constitute timbral resonance regions sliced out of the frequency continuum" "(Observations," 46). He goes on to say (recalling Chou) that "such concern with and structural utilization of the timbral consequences of dynamic, registral, and durational values approach the condition of nonelectronic |synthesis.'"

Robert Erickson terms these timbral-registral singularities "fused" (Sound Structure, 20-21).(11) Looking at pitch as an aspect of timbre (and, in relation to Babbitt and Cogan, oversimplifying), one could conceive of a synthesis of timbres, the notated pitches of which would mark the strongest frequencies. As a result, interval can be thought of not only in the usual (distance-measuring) way, but also as a quality of a sonority.(11) Where fusion occurs, interval quality is highlighted, but the two aspects need not be exclusive: when [4] and [8] (a number enclosed within brackets indicates, in Bernard's notation, an "absolute interval") arise in the upcoming double fusion (measures 15-16), we surely remember having heard them as significant distances in the opening measures' trombone/horn slides toward [C#.sub.4].

At measure 12 the pattern-defying fireworks display ends. In its place a higher expanse of shimmering metals is quietly etched by pitched bands and a low curve. The tenor trombone, no longer muted, sounds near the bottom now, with the flute suspended high above. The two are separated by the distance of a double octave. Transported from brassy [C#.sub.4], the medial [C#.sub.5] is prevented from fusing with either C by its movement from the whiny, muted trumpet to a rounder open trumpet to the more pointed clarinet. The movement makes of the double octave two asymmetrical |cracked' octaves:(13) [C.sub.4-C#sub.5], [13], and [C#.sub.5-C.sub.6], [11]. The sound of these two intervals is, of course, ubiquitous in Varese's music,(14) making the octave, even if rarely heard, everywhere evident. (The notion of |cracked' interval is almost certainly extensible to the perfect fifth, as replaced by the tritone.)

When [C#.sub.5] settles into the clarinet, the timbrat progression from brass to higher, more narrowly focused woodwinds is completed. As the ringing dissipates, the clarinet fuses with the flute harmonic, transforming intervalas-distance into interval-as-quality. Their thin, sharp [11] will persist through the dense sound of rigid, hammering brass and the return of the percussion.

With the woodwinds, three brass groups gather to create a complex sonority: depth-sounding trombones; well above, mute-pinched trumpets; and higher, bright horns. Though the widely separated outer masses both fuse [11]s, the higher one seems to float, while the interference of the lower one's partials makes it seem more growl than resonance. The inner two overlap (penetrate, in Varese's language), and create a double fusion differentiated by rhythmic activity and timbre. Their double fusion densely colors an [11] band, articulated by a concentration of [4]s: the horns fuse two [4]s into a span of [8]; the trumpets, entering a moment later, fuse a disparate span of [4].

Acceleration aggravates the clamor of the hammering brass, culminating in a bray, at the height of which comes the opening percussion explosion again. Agitation passes to the percussion while the woodwinds go on sustaining. In these last measures, increasingly unbridled wind-and-percussion noise spreads across the whole spectrum.

Out of it flows the flute's piping, as cymbal-haloed drums initiate a new phase. Energy channels into the flute's flexible tune and complementing percussion klangfarben line.

When the trumpet joins it a short time later, the flute sustains again, higher than before. Almost immediately, the percussion initiate a new fireworks display. They begin with the short-short-long pattern and, as the winds withdraw, go on to short metallic bursts that encircle snare-led eruptions. Suddenly, the flare-ups recede as the siren's beam begins to sound very low. Ushered in by its rise, the woodwinds pierce the top of the space, joined by metals and the snare's high white noise.

Throughout the passage, sonority cannot be disentangled from the quality of movement. Shortly, it will positively be movement.

In the wake of a concentrated, brass-percussion oscillation in measure 39, pitches scatter in diffusion ("rapid motion" for Bernard, who notes their "(apparently) near-complete formal dissolution" (112)).(15) The relative timbral monochromaticism of the pitched instruments diminishes awareness of the movements of individual lines. Incoincident attacks disperse entries over simultaneous duple and triple subdivisions of beat (or two-beat) spans. And [11]s and [13]s tend to be divided between, rather than coupled within, timbres (as in measures 14-16 and elsewhere). Like the percussion fireworks, the divergent activity of these measures resists comprehension.

Bernard believes "that complex cross-rhythmic passages do not always signal an intention to differentiate internally. . . . No matter how accurately the passage in question is performed, the result is a sound entity that in the aggregate is unique but of which the component parts are indistinguishable" (134). On the contrary, I think that the components are meant positively to draw attention in simultaneously diverging directions.

By sketching an analysis "beyond the fringe," so to speak, I intend only to suggest what can be made of Varese's music if descriptive interpretation is accorded analytical value. But, having, I hope, demonstrated that the regal isolation of pitch and interval is unjustified, let me return to meet Bernard on his own ground. To do that, I will summarize his methodology, discuss several examples that chart interval constructs and operations in an analysis of the first twenty-nine measures of Hyperprism, and since the discussion is critical, propose an alternative analysis that answers some of my objections. (Readers may wish to read Bernard's account of these measures on pages 193-200.)

The basic assumption of Bernard's measurement system is that "if the vertical dimension has primary status in Varese's musical frame of reference, then the partitioning of vertically defined space takes on crucial significance" (41). Within that space, "criteria of absolute size and distance . . . must form the basis of structure." The "inescapable effects" are that "inversional equivalence [by which he means octave complementation (102)] cannot exist, . . . [and] octave equivalence must be ruled out" (43). However, the rejection of octave equivalence does not prevent elaborating several categories of "doubling" (102-10).

By eliminating octave equivalence, Bernard eliminates pitch class, the "primary domain" in analysis of post-tonal music. Of course, he does not also eliminate the notion of "primary domain": he immediately confers priority upon pitch. He calls it "pitch/register." defining it as "a condition in which pitch content and registral disposition are taken to define, as one, the nature of an entity" (44). But reference to "pitch" or "pitch content" as distinct from "pitch class" or "pitch-class content" already entails register; "pitch/register" is redundant. It must be a heritage of assimilating pitch to pitch class that makes discntangling them seem such a "breakthrough."

But to return to basics, "immediate succession often reveals the strongest relationships between musical formations. Each new formation must result . . . from what has preceded it." Discontinuity between sound masses disappears into "a continuum of change" (44).

Symmetry is a central organizing principle: Bernard distinguishes two types, "mirror" (inversional) and "parallel" symmetry (which is not symmetry at all, being the result of transpositional duplication of a pitch configuration). In addition, he identifies four "processes" which are "controlled" by "principles of symmetry" (48).(16) They are: projection, transposition by another name; rotation, pitch inversion by another name;(17) expansion, derivation of a larger from a smaller interval by displacement of the endpoints by an equal distances in opposite directions (50); and contraction, which "is simply the reverse of expansion" (51).

Bernard does not explain the need for a new term for transposition. Based on his choice of Varese's term "projection," it seems probable that, in this instance, he wanted to adopt a notion something like Varese's. He prefers "rotation" because it "avoids potential confusion with inversion in thc tonal sense" (49), which would seem implausible if the text did not also evince confusion about the distinction between octave complementation, which he necessarily rejects, and inversional equivalence, which he uses. But, to tell the truth, despite the movements or connected processes that these names would suggest if they were used as verbs, making them nouns has stopped the action. In fact, "operations" seems a more accurate characterization than processes, since, as he uses the terms, they do not comprehend gradual successions of states as, typically, processes do. Chou's examination of Integrales and "in the light of [Varese's] terminology" portrays the music much more convincingly as continuously changing ("Sketch," 158-61).

These assumptions ground two methods of measurement. Single intervals (usually larger than [14]) are depicted as transformed by projection, expansion, and contraction. Typically, they extend over mid-range temporal spans. Their successions are traced in figures drawn on graph paper. (See Example 1.) Small-interval relations that persist only briefly are modeled by a system of trichords. Trichords do not usually span intervals greater than [14] and "groups of smaller external ... compass than [6] are relegated to the realm of microstructure" (99). Since trichords "seem to be the results of musical transformations rather than descriptions of the transformations themselves,' Bernard warns that "the analyst must remember that the trichords are not static objects, congealed lumps of sound, but rather manifestations of process" (77). However, both his exposition of the system and the analytical texts encourage readers to think of trichords as objects.

A constellation of trichords is a set of trichords that includes "a basic form together with its three [first-order] derivatives." A basic form is a configuration "consisting of two unequal adjacent intervals." say [3][8]. Bernard's practice is not to list the framing, "boundary interval" of any trichord ([3] + [8] = [11]) and, of the remaining pair, to list the smaller interval first, because a "configuration and its rotation [inversion] are defined as equivalent." He generally will denote a constellation by shorthand reference to its basic form; "[3][8]" and "the constellation about [3][8]" are not clearly distinguished. Three first-order derivatives are "generated" by unfolding and infolding. Given a set, by displacing one of the internal intervals, [11], one can derive [3][11] or [8][11] by unfolding; or, by displacing the smaller internal interval, here [3] inside the larger, [8], one can derive [3][5] by infolding (74-75).(18)

Two constellations intersect "when two basic forms hold a first-order derivative in common"; the constellations about trichords [5][8] and [3][8] intersect in [3][5]. Two trichords are second-order derivatives of one another when one has a first-order derivative that is also a first-order derivative of the second; e.g., [2][3] is a second-order derivative of [5][8] because [2][3] is a first-order derivative of [3][5] and [3][5] is a first-order derivative of [5][8]." Intersecting constelltions can be joined into families (97).

Bernard classifies trichordal "segmentations" as real, using [1][5] as his example, if "either (a) one segmentational criterion delineates this trichord unambiguously or (b) a constellation to which [1][5] belongs exerts palpable control over structure in [a given] passage" (87); failing that, it is a "potential segmentation." Lattice." a term never defined, seems to refer to the complex of trichords identified in some span of a piece.

The foregoing describes processes of derivation for trichords abstracted from any musical context. In the analyses, however, Bernard tends not to characterize processes that transform or proliferate trichords. For example, his account of measures 40-42 of Hyperprism, one of the more complex passages he analyzes trichordally, first points out "the pervasive influence of [3][8], [3][10], and [1][9], the last now a basic form embracing [1][10] and [1][8]." He continues: "at approximately midway through the rapid motion the constellation [4][7] reenters the lattice. It seems to be eclipsed at the final position of m. 42 but is actually carried to the lower region of the pitch stasis that begins in m. 45. At the moment of m. 42, [3][8] dominates, supplemented by [1][9] (as [1][10]) and [3][10]. Somewhat more weakly represented - really only in potential - is [2][11]: [(C-D).sub.5]-[C#.sub.6] and [D.sub.5]-[(C#-E ).sub.6]" (203 and Example 5.12). Trichords are usually identified as present or powerful; the processes by which they arise are rarely described. If Bernard wants musical events to be understood as "manifestations of process," the language he uses must be chosen to portray processes; since it does not, trichords seem to be "static objects."

Example 1 (Bernard, Example 5.6) is a graph of the "spatial environment" of measures 1-29 of Hyperprism. The grid "calibrates" vertical pitch distances, a single square representing a semitone. Distances that Bernard considers significant are measured and the measurement is shown in brackets, sometimes beside a long vertical bracket, sometimes not. (I surmise that, when no bracket is shown, he is measuring the space between rather than within entities; it is a distinction worth making consistently.) A solid or dotted line with an arrow tends to depict an operation.

The duration of each pitch, and duration in general, is not represented, because "absolute (that is, exactly measured) duration is irrelevant in most analytical situations." The resulting lack of an at least approximate representation of duration sometimes makes the figures difficult to read. However, when Bernard points out "the pragmatic value of allowing as many pitch/registral events as possible to be represented on a single graph," I have to agree (134).

At first, figures like this one seemed foreign and even inaesthetic - unwarrantedly "scientific" - to me. However, with familiarity, they proved revealing. In addition to examining Bernard's graphs, I made a similar depiction of all of Hyperprism (not included here, although conclusions drawn from it have been) to check intervallic, registral, and pitch (or pitch-class) relations that I might have overlooked in our usual variable-distance graphs (i.e., traditional notation). Incorporating information beyond the pitch-interval skeleton of Bernard's figures is quite easy to do without overloading the graph. My figure differs from his in representing the whole piece, to facilitate making long-range connections; differentiating timbres, to clarify sound-mass relations; indicating relative temporal extension by solid lines trailing from pitches, to show simultaneity (useful particularly in diffused passages like measures 39-43); and indicating recurrence of pitches after intervening events by dotted lines. The representation could be improved further, and I must admit that, despite all the time spent with graph paper, I still translate back into musical notation in order to try hearing putative relations.

Bernard's example can be compared to Example 2, in musical notation, which incorporates much of his information, though often under a different interpretation. I have drawn it in at least two degrees of detail and used notehead shape to differentiate instrumental timbres: standard noteheads are used for both trombones and woodwinds (they never remotely overlap); rectangles for horns; and diamonds for trumpets. Since octaves are sometimes equivalent for me, additional octave distances are indicated by subscript for intervals larger than [13]; e.g., [25] in Bernard's terms is [[13].sub.1] for me.(19) ([13] is not [[1].sub.1] because it is a cracked octave.)

Bernards points out that the distance between the opening [C#.sub.4] and the [D.sub.2] that sounds with it is the same as the distance between that same [C#.sub.4] and the [C.sub.6] that sounds after it ceases. But for me, the two spaces differ. This is in accord with Varese's thinking about contrast; equivalence would have been the occasion for compositional differentiation. [C#.sub.4] and [D.sub.2] are out in the open among the percussion bursts. [C.sub.6] is in a different temporal span from [C#.sub.4], since it sounds only as the trombone replaces [C#.sub.4] with [C.sub.4]: [C.sub.6], with [C.sub.4] and [C#.sub.5], is inside the encircling metal luminescence.

Though [C.sub.4] ebbs away, the upper [11], C#5-C6, persists, and two more [11]s arise at equal distances [9] or [2]) in opposite directions from the first span's [C#.sub.4] and [D.sub.2]. The lower one, [F.sub.1]-[E.sub.2], sustains an [11] frame, like [C#.sub.5] - [C.sub.6]. Between them, [B.sub.3]-[B .sub.4] is distinguished by its dense intervallic interlock and its articulative activity. It stretches the middle boundary another semitone down from [C.sub.4] (though the tentative lines of the trombone's glissando and the horn's run have already left impressions). Then, the flute goes on alone, circling in the span of the uppermost [11], and the trumpet joins it in [13], ending the circling. Isolated again with the clarinet, they sound [B 5.sub.5]-[A.sub.6], another [11].

In the opening measures [C#.sub.4] is, narrowly speaking, the spine of a figure that extends inward from [A.sub.3] and [F.sub.4]. By measure 29, the pitch-class extremities of this soft-edged augmented triad are exchanged and symmetrically displaced, to coalesce as the outer registral limits of the first section. Though Bernard notes the symmetry of [F.sub.1]-[E.sub.2] and [B .sub.5]-[A.sub.6] around [C#.sub.4], he does not mention the pitch-class relation of their outer pitches to the first augmented triad. Within those limits, [F.sub.1]-[A.sub.3] pitch events tend to be disconnected individuals or skeletal [11]s, but [A.sub.3] is the beginning and [A.sub.6] the endpoint of successive upward relocations of activity leading from brass to woodwinds. Because he recognizes only pitch (and not pitch class), Bernard's analysis cannot include an account of the basic shape of the passage; because he does not allow himself to acknowledge pitch aspects other than those he has defined, the analysis cannot incorporate observations about such features as differences of pitch density in different registers (though they are evident in his graphs).

In the foregoing analytical text, I have generally avoided language that suggests movement or process between pitches when they are in different sound masses. In those cases, I do not think that, between an initial pitch and its successor, any medial point is represented in a process of transformation. Medial time is between and not within the span of the initial and the final; at the time designated (by Varese in cooperation with a piece's performers), the new value will be returned. In short, I am more inclined to agree with Bernard's concepts understood as operations (as he uses them) than as processes (as he calls them). This, I know, is contrary also to Varese's thinking, but movement is more vivid to me in or around masses, and it is only intermittently pitch movement (e.g., in the flute solo).

Turning now to what Bernard calls "internal structure," I take up the component of his system with which I most disagree, the concentration on trichords. Bernard's rationale for settling on trichords to model local relations illustrates the distrust of personal observation. He explains that "the relationships outlined here for trichords could conceivably be defined for larger collections of pitches. However, even for tetrachords the number of derivatives would increase to the point of being unwieldy" (75-76). And shortly thereafter, "Note, however, that the decision to define spatial operations in terms of trichordal groups has nothing to do with the literal size of pitch groups in Varese's music. After all, trichords are no more common than groups of several other cardinalities. ... The choice of the trichord as unit is based upon the unique characteristics of groups of three in a spatial context, not upon any empirically observed preference on Varese's part for sound masses, or even subdivisions of masses, made up of three notes" (76-77). He does claim, later, that "the system of trichords [etc.] ... arises from common assumptions about the nature of musical space as Varese regarded it: a neutral spectrum calibrated in semitones, in which volume of space and its partitionings, almost entirely unfettered by the obsolete notions of octave and inversional equivalence [octave complementation], are the primary structural determinants" (89), but this statement is not addressing the question of cardinality.

Thus the trichord construct seems to be a particularly arbitrary choice of filter. Nor does Bernard apply it to grant meaning to groups of pitch events. Rather, by submitting events to trichordal segmentation, even where the fit is poor, he can determine which trichord or trichords control a particular span of music.

Examples 3, 4, and 5 reproduce three examples from Bernard that lay out trichord relations in the opening twenty-nine measures of Hyperprism; brackets or surrounds isolate the trichords and bracketed numbers identify intervals constructed (usually) from registrally adjacent pitches. Example 3 (Bernard, Example 5.7) identifies several occurrences of the trichords in the constellation about [3][8], and the related [5][8], in the first nineteen measures. Their connecting first-order derivative, [3][5], does not occur in the figure (though it is shown in Example 3.25). Example 4 (Bernard, Example 5.8) overlaps the span of Example 3, backtracking to span measures 17-23, and shows occurrences of [2][11] and the micro-structure [2][3]. Example 5 (Bernard, Example 5.9) spans measures 21-27 and shows [1][7] and [1][9] (derivatives of a non-existent [1][8]) and two "derivative-related" trichords, [3)[7) and [3][10], evident only "in potential." Bernard points out that "the last two pitched events of the passage are single intervals: [13] and [11]. Their explicit isolation in this context suggests that they are to some extent independent entities" (200).

Example 3, especially, troubles me. Its parsings override perceptible features of the piece, like rhythmic grouping, for the sake of the consistency of the trichord complexes, as in the case of the two [5][8]s identified in the flute line. I am concerned that a decision like that to retain [F.sub.4], creating [5][8] with [C.sub.4]-[C#.sub.5], is made solely to "account for [C.sub.4], ... a pitch up to now omitted from the analysis" (199) - to cover the ground completely. And, though I agree with Bernard that [B.sub.3] and [B .sub.4] Can be thought of as the boundaries of a mid-level brass complex (whose [4]s clash at their [D.sub.4]-[E .sub.4] semitone overlap), I would like to know what, besides concern for consistency, picks out [D.sub.4], among all the internal pitches, for inclusion with them in a [3][8] trichord.

In other words, this seems to me a highly contrived interpretation of the music.(20) Its effect, I think, is to diminish, if not eliminate, events' distinctive features, thereby denaturing them. For example, the [3][8] [D.sub.4]-[B .sub.4] - [C#.sub.5] in measures 14ff. is pieced together from the horns' reiterated [D.sub.4]-[B .sub.4], mixed with the clarinet's distinctly different, sustained [C#.sub.5], and the [3][11] [B .sub.4]-[C#.sub.5]-[C.sub.6] above is a similar hybrid. Reasons are given to identify these trichords ([D.sub.4] is "as far below [C#.sub.5] as [C.sub.6] is above [C#.sub.5]" (196), and [D.sub.4]-[B. sub.4] are the boundaries of the [4][4] [(D-F#-B ).sub.4]), but among their features is their heterogeneity, and the difference between heterogeneously and homogeneously formed entities is not addressed in this case or in general.

Looking at the same problem from a different angle, Bernard does not distinguish intervals that arise within a single sound mass and participate in its formation from intervals that occur between different masses and result from interaction among them. To return to measures 14ff., [B .sub.4] and [C#.sub.5] are picked out as members together of the [3][8] and [3][11] just mentioned, and of one more [3][11], but timbral-rhythmic differentiation makes them part of two different masses. The [3] between them is the distance between two masses, whereas the other interval in all three cases can be understood as within a single mass: [D.sub.4]-[B .sub.4] is within the horn mass; [B.sub.3]-[B .sub.4] is the boundary of the brass double fusion; and [C#.sub.5]-[C.sub.6] is the woodwind fusion. To summarize both perspectives on the problem, Bernard seems not to appreciate that, even though the distances between three pitches may match the distances between others nearby, he may need to explain why he chooses to construct the resulting entities; there may even be reasons to prefer not to reify the relation.

The three figures together raise questions about coordination among depictions of the same or succeeding spans. Bernard addresses only something like the question of coordination between trichords and larger symmetries; I infer from the examples he presents that symmetries tend to "control" trichord relations (89-96; Example 3.20 depicts measures 45-58 of Hyperprism"). Even his extended analyses do not usually give more than very oblique hints about how he might conceive of the interaction and (dis)continuity of representations. This is indicative of a general problem: the theory extrudes a large amount of data, which is left almost entirely unprocessed. Entities are identified, operations labeled, but how they are all related is a story left to the reader's imagination.

As a contrast, the analysis that follows here is consciously interpretive both in its identificational choices and in its provision of a relational account. It tells part of the story of two configurations that strike me as characteristic of Hyperprism. Both appear in Bernard's data; one is a trichord, [2][11], that he notices at the beginning and end of the flute solo (199; see Example 5).

Though I will return to the flute solo, I will begin near the end of the piece, where the clearest instances of "[2][11]" are. Example 6 sketches the clarinet-piccolo configuration in measures 68-75. (Bernard's Example 5.18 includes these measures.) Melodic presentation here parses the trichord in two ways: the piccolo plays [11] followed by [2]; the clarinet plays [13] followed by [11]. Then, as Bernard points out (212), the piccolo plays [F#.sub.6] into the piccolo-clarinet G7-[A. sub.6], a leap of [13] into a simultaneous [11]. I am inclined to think of this cracked-octave presentation - [11] and [13] constructed above or below a single, nodal pitch, [2] being derived from the juxtaposition - as the basic module of a "crystal" (to borrow again from Varese). Perhaps perversely, my analytical sketches will refer to this module; to prevent confusion, I will notate it in the text, using braces, as {11}{13} or {13}{11}.

Frequently, occurrences of {11}{13} are paired as simultaneities or melodic successions, and the pairs typically are inversionally related. The inversional index is rarely duplicated between any two occurrences I have identified in the piece: as Varese noted of crystals, the module may be the same but the shapes it creates are all different. Because of the inversional relation, the composite configuration is often symmetrical, as Bernard notes in the case of the clarinet-and-piccolo duet and in the flute solo.

Example 7 sketches pitched sonority in measures 59-68, which encompass two phases: the first recasts the opening of the piece up to the flute solo; the second is the trombone transformation of the flute solo. The bass trombone and second horn outline the deep [11], [F.sub.1]-[E.sub.2], again, joined by the first horn's [F#.sub.3] [[13].sub.1], above the trombone. (The lion's roar, entering just after the second horn, sounds like a rough relative; the siren that sounds throughout recalls the siren/low trombone beam from early in the piece.)

The tenor trombone takes over [F#.sub.3] from the horn (reversing the timbral order of [C#.sub.4), repeatedly conveying [F#.sub.3], via glissando, to [F.sub.3]. (The temporally cracked double octave, [F.sub.1]-[F.sub.2], succeeded by [F.sub.3], seems reminiscent of the early registrally cracked Cs at measure 12.) It breaks the cycle with a leap up [11] to [E.sub.4], from which a frequently stepwise line migrates back down [13] to [E .sub.3]. The line, having first skipped [4] from [E.sub.4] to [C.sub.4], drops down-up {13}{11} through [C.sub.4]-[B.sub.2][B .sub.3] and then pops up-down {11}{13} through [A.sub.3]-[G .sub.4]-[G.sub.3]. Having returned to [F#.sub.3], it slides once again to [F.sub.3], and passes (laughing) through [E.sub.3] to [E .sub.3], which is joined by the mysterious D-half-[flat.sub.2]. (Bernard's analysis is quite different and can be found on pages 208-11.)

Now to return to the flute solo (Example 2a-c). After holding out [C.sub.6], its movement takes it to [F#.sub.6] by way of two inversionally interlocking {11}{13} modules: [C.sub.6]-[B.sub.4]-[B .sub.5] and [G.sub.5]-[F.sub.5],-[F#.sub.6]. (The pitch-class and configurational similarities to measures 68-71, shown in Example 6, should be evident.) [F#.sub.6] is succeeded by a tune that seems to start in the middle and, sidestepping first one way then the other, stops again to reiterate B heard earlier at the top of the sixteenths. Then faster, wider sidestepping leads back to [F#.sub.5], where the line slows into a last {11}{13} (as Bernard notes) so that [G.sub.5]-[F.sub.5]-[F#.sub.6] from the beginning of the tune hooks up to [F.sub.5]-[E .sub.5]-[E.sub.6]. The clarinet/piccolo [B .sub.5]-[A.sub.6], which nearly tops the final measures of the section, connects back through the long, mid-tune [B .sub.5] to [B.sub.4]-[B .sub.5], to frame the solo both registrally and temporally.

There is much more to say about {11}{13} in inversional pairs, about C-B-[B .sub.5] as the referential pitch-class level of that configuration, and about [11]s and [13]s, interlocking at different distances, as a chord-constructing principle. Nevertheless, I will move on to the other configuration I have alluded to, which is [4][4].(21)

Example 2b shows a dense (semitone packed) trombone-horn [4][4] span as surrounding [C#.sub.4]. Initially, the Span below [C#.sub.4] extends only from [B.sub.3], making the figure asymmetrical in relation to [C#.sub.4]. When the horn extends from [A.sub.3], a symmetry is created around [C#.sub.4] and, almost immediately, the opening phase ends. The horns are next heard in [4][4] fusion quickly joined by the low-trumpet [4]. This single [4] can, by this point and in such close proximity to the horns, seem to be part of an incomplete [4][4]. So it is of interest that, when the flute starts moving, it is with [B.sub.4]-[G.sub.5], and that a line can be heard extending from [G.sub.5] through [F.sub.5] (which pitch is reiterated after a time during which the line extends above [G.sub.5]) to [E .sub.5]. (Across the same span a different set of relations based on ephemeral symmetrical centers and on [3]s and [6]s, shown in Example 2c, seems to play out. To a degree, this duplicates Bernard's analysis. I must admit, however, that the line is remarkably ambiguous and other readings also seem appealing.) When the flute reaches [A.sub.6], it completes the symmetrical transformation of [A.sub.3]-[C#.sub.4]-[F.sub.4] into [F.sub.1]-[C#.sub.4]-[A.sub.6] and, with that, the first large section of the piece ends.

In the opening fourteen measures of the piece cracked octaves and augmented triads co-exist without much interaction. But then the horn and trumpet composite mass (measures 15-16) packs three [4]s, by overlapping, into [11] creating as close a connection as can be. In later passages, the two configurations arise sometimes independently, sometimes interactively; the following outline of events after measure 30 will sketch their history. In the process it will indicate pitch and pitch-class relations (including longer-span connections) about which Bernard is silent:

Abruptly in measure 30, a brass/percussion complex blasts an [[11].sub.1]-framed sonority. Reiterations lead to a purposeful, upper-voice descent to a second sonority, a "contraction," as Bernard points out, of [4] in the two outer voices (160-61). The succession of sonorities in the uppermost horn alternates [F#./[G .sub.4]-[D.sub.4], the simultaneity of the two lowest horns in measure 14-16, while the bass trombone alternates [G.sub.2]-[B.sub.2], a [4] implied by the trumpets (in another octave) in measures 15-16 but not played. (There is another melodic [4] buried in an inner horn. The "chords" are otherwise constructed primarily from timbrally similar [13]s or [11]s that extend inward from the boundary pitches.)

There follows the pitched diffusion in measures 39-43, whose lower edge, by outlining [A.sub.3]-[C#.sub.4]-[A.sub.3], recalls and transforms events heard at the piece's opening. Though coincident attacks are rare in this passage, each of these pitches is attacked simultaneously with a note [11] or [13] above: [A.sub.3] sounds with [G#.sub.4] in the upper trombone, [C#.sub.4] sounds with the trumpet's [C.sub.5], and [A.sub.3] returns with the trumpet's [B .sub.4]. Otherwise, though [11]s and [13]s are ubiquitous, they are timbrally or articulatively diffused, as described above.

In the trombone/horn fusion that follows (at measure 45), C# recurs as the lowest pitch class, but an octave lower than in the diffusion. All the fusions in that complex (omitting the horn [A.sub.4]) frame {11}{13} modules. (See Example 8.) The lower two fusions are separated by the [4] between the trombone's [D.sub.4] and the trumpet's [F#.sub.4]; the distance between the upper two is literally [3], but the timbral reinforcement given [B.sub.5] (it is the piccolo's reiterating bottom pitch and the only pitch shared with the clarinet) also projects [4] between G and B, F#-D's counterpoint in the outer voices at measure 30. The span of the lower two is [13], that of the upper, from the reinforced [B.sub.5] to [C.sub.7], another [13] (note that the piccolo will return to this region, inverting the B -B-C configuration, in measure 68). Each replicates {11}{13} in its own way and the three together create a symmetry that spans [[11].sub.3] - which [A.sub.4] pierces well off center.

The third large section of the piece begins in measure 59 with its recurrence of [F.sub.1]-[E.sub.2]; the focal [F#.sub.3], [[13].sub.1] above F, stretches out {11}{13}. Lines extend inward chromatically to F# to fill in [D.sub.3]-[F#.sub.3] - [B .sub.3], thereby melding the piece's initial pitched gesture with the pitch-class level of the horn fusion at measure 14 (indeed with the pitch-class content of measures 14-16). Timbre and time of occurrence differentiate the upper from the lower span.

The trombone touches on the rarely represented C-E-G # (Example 8) as it fashions a tune from short and long-range {11}{13}s.

After the piccolo-clarinet interlock, the piccolo rises to its final [G.sub.7] from [B.sub.6] through a figure that extends from [E .sub.7] downward before jumping off to [G.sub.7]: finally B-E -G occurs as a complete, connected [4][4]. D-half-flat, sounding below, is the pitch-class axis of symmetry of G-A.

D-half-flat is succeeded in the next span by the horn fragment's outer [C#.sub.3]-[D.sub.4] (measures 84-85), a succession that creates close cracked octaves-{11 1/2}[{12 1/2}.sub.1]. The fragment's [D.sub.4]-[C#.sub.3]-[C.sub.4] is, of course, {13}{11}.

The final sonority accumulates. Its outer [[8].sub.5] places [B.sub.1] below the piccolo's [G.sub.7] to frame the piece between A-C#-F at the beginning and G-B at the end. The once asymmetrical [A.sub.4] returns in the third horn, at the center of [G.sub.7] and [B.sub.1].

But, then, it is not the end. The low region's [B.sub.1]-[B .sub.3]-[C.sub.4] (a last {11}[{13}.sub.1] at the referential pitch-class level) falls silent, exposing the first horn's [E.sub.4], just as the piccolo trill to A , perhaps creating a final [[4].sub.3]. Being a [4] little heard before, does it, with the trill (another way of being between pitches and of exceeding the final symmetry), point beyond the piece? The metals join the dynamic intensification with a roll that increasingly fills the upper region with sound that will ring on after the final cut.

This outline, in addition to pointing out {11}{13} and [4][4] connections, is meant to show that pitch and pitch-class relations are worth drawing. Bernard's analysis demonstrates that certain intervals saturate each moment (notably [11]s and [13]s that occur in a large number of the trichords he identifies), and his large-interval figures sketch a framework. However, one of the most disappointing features of his work is the absence of any inclusive account of what all the trichords and register manipulations add up to.

Another disappointing feature is the fact that Bernard's commitment to pitch sovereignty often puts his analyses at odds with Varese's desire to create unbounded, free sounds and with the vibrant pieces that resulted. I don't deny that understanding pitch can be very satisfying or that it 's a convenient thread from which to hang an analysis. When one can tell a good story about pitch, one feels one has something, whereas accounts of other things may seem less satisfyingly clearcut. But pitch is not, by far, the whole story.

The thesis of this paper has been that the profound distrust of subjectivity, evident in this book, keeps its author from recognizing to what degree his methodology is determined by his own "theoretical choices." This in turn prevents his examination of those choices. Among them, one of the most pervasive is an uncritical belief in the natural truth of primacy. It has led him to sentence everything except pitch, and occasionally duration, to obscurity and to contrive regularities that can be translated into control. Stasis is the story of the book. Confined within a frozen pitch model, escape is attempted only through inchoate thoughts about movement and an incipient language for describing percussion sonority. Escape would be possible along these routes (among others), but only with more concerted, attentive effort. Such an effort would require a close engagement with all aspects of the music, and the method's theoretical commitments preclude this.

Belief in primacy also affects the book's relation to wider theoretical discourse. Bernard rarely acknowledges that his forerunners in this work, including even Varese, have contributed to his thinking. This suggests that he follows a widely practiced, though misconceived, model of discourse, according to which the success, even survival, of one's ideas depends on supplanting one's predecessors'. But such a model does not accurately reflect how discourse is conducted: as exemplified by this case, the efforts of all the individuals I have mentioned (and more) contribute to the effort to understand Varese's music. A better model would be one of cooperation, in this case, among Varese's advocates: Bernard's work both draws on and adds to the effort to clarify and enhance hearings of Varese's music.

The Music of Edgard Varese, properly speaking, has not yet been written. There is all that Bernard relegated to the shadows to reinstate. Chou, Erickson, Babbitt, Cogan, and, now, Jonathan Bernard - as well as others - can act as guides, and there is substantive, interesting work to be done. Bernard's observations of rhythmic qualities and percussion sound seem to me a particularly promising starting point for further investigation. Meanwhile the most rewarding way that I can recommend reading Jonathan Bernard's The Music of Edgard Varese is as one person's highly individual interpretation of the music.(22)


(1.) New Haven: Yale University Press, 1987. Robert Gauldin's review (Music Theory Spectrum 10 (1988): 140-43) presents an outline of Bernard's book. Simon Trevise's (Music Analysis 8, no. 3 (1989): 337-41) is brief but incisive; it expresses some of the same reservations I will articulate, but from the point of view of Forte's version of pitch-class set theory. Elizabeth West Marvin's (Journal of Music Theory 34, no. 2 (1990): 359-68) offers an extended summary of the method preceded by a consideration of Bernard's exposition of Varese's aesthetic background. (2.) The papers I have in mind (and will refer to below by short title) are Chou Wen-chung, "Varese: A Sketch of the Man and His Music," Musical Quarterly 52 (1966): 151-70 and "Ionisation: The Function of Timbre in its Formal and Temporal Organization" in The New Worlds of Edgard Varese: A Symposium, I.S.A.M. Monographs No. 11, edited by Sherman Van Solkema (Brooklyn: Institute for Studies in American Music, 1979), 27-74; Robert Erickson, Sound Structure in Music (Berkeley: University of California Press, 1975); Milton Babbitt, "Edgard Varese: A Few Observations of His Music" in Perspectives on American Composers, edited by Benjamin Boretz and Edward T. Cone (New York: W. W. Norton & Co., 1971), 40-48 (reprinted from Perpectives of New Music 4, no. 2 (Spring-Summer 1966)); and Robert Cogan, New Images of Musical Sound (Cambridge: Harvard University Press, 1984), 96-101. All are cited in Bernard's extensive, partially annotated, though not comprehensive, bibliography. (3.) "Meta-Variations, Part IV: Analytic Fallout (I)," Perspectives of New Music 11, no. 1 (Fall-winter 1972): 149-50. (4.) This is drawn from a defense of detail in Reading in Detail: Aesthetics and the Feminine (Methuen: New York, 1987), 20. (5.) By endorsing descriptive characterizations of percussion timbres, I risk promoting a classification scheme that could "grow before long to unmanageable proportions." I worry about such typologies, too, but my worry is about routinely assigning descriptions without attending to the aural information they only indicate, rather than about "unmanageability," which I prefer to see as the open-endedness that might encourage a search for the most precise way to put an impression into words. (6.) Chou Wen-chung observes that "of course, this growth of sound in space is by no means the result of pitch organization alone, ... but the consequence of interaction among all properties of sound, as Varese stated" ("Sketch," 161). (7 ) That Bernard chose to present analyses of Hyperprism and Density 21.5, which is obviously even more timbrally limited than Hyperprism, to demonstrate his method is further evidence of his disregard of timbre. (8.) Chou, "Ionisation"; David Reed Bloch, "The Music of Edgard Varese" (Ph.D. dissertation, University of Washington, 1973), 211-12. (9.) Elizabeth West Marvin's "The Perception of Rhythm in Non-Tonal Music: Rhythmic Contours in the Music of Edgard Varese" (Music Theory Spectrum 13, no. 1 (1991): 61-78) and Jean-Charles Francois's "Organization of Scattered Timbral Qualities: A Look at Edgard Varese's Ionisation" (Perspective of New Music 29, no. 1 (Winter 1991): 48-79) arrived too late to influence this paper. Marvin's promising observations of similarities in melodic and rhythmic contour in Octandre and (especially) Density 21.5 suggest that her methods may illuminate all of Varese's music. Francois, a percussionist, offers original insights into Varese's music including a refined typology of percussion sounds and observations of the relation between duration of decay, "density of articulations," and pitch; his paper offers analytical concepts - at last - to address the complexities of percussion sound (and, I think, timbre generally). (10). The idea that movement within a sound mass exposes different surfaces over the course of its span was suggested by Roland Jordan during a colloquium at Washington University in Winter, 1990. My list of moving aspects is drawn from Robert Morgan, who uses the opening of Hyperprism to Point out that "since ... the pitches remain fixed, part of the burden of ... |thematic' development is shifted to ... timbre, dynamics, and articulation." See "Notes on Varese's Rhythm" in The New Worlds of Edgard Varese: A Symposium," 11. (11.) Richard Swift objects to Erickson's loose definition of "fused ensemble timbre" in his review of Sound Structure (Perspectives of New Music 14, no. 1 (Fall-winter 1975): 148-58). Though his point about "privileged personal pronouncements" is well taken, I think that the notion is useful, if difficult to define (my own attempt is not the last word). (Swift's principal point is that Erickson deals with timbre independent of other musical dimensions, and that is indeed a shortcoming whether the dimension is timbre or pitch.) (12.) A question asked me by Bruce Samet and the discussion that ensued with him and Joseph Dubiel eventually led to the invention of this distinction. Readers interestcd in further "defamiliarizing" or even dissolving the concept of interval may wish to read David Lewin's "musings" on the subject (all on the interval-as-measurement side of my distinction) in "Forte's Interval Vector, My Interval Function, and Regener's Common-Note Function." Journal of Music Theory 21, no. 2 (Fall 1977): 227-35. (13.) "Cracked octave" was coined by Andrew Mead in conversation. (14.) Obvious as this observation is, the only mention of it that I remember seeing is in Keith Tedman, "Edgard Varese: Concepts of Organized Sound" (Ph.D. dissertation, Sussex University, 1982), 106. (15.) Jackie Dempsey calls a similar phase of Octandre a "haze" in "Experiencing Octandre" (Masters thesis, Washington University, in progress). (16.) Chou traces a symmetrical process, which some of Bernard's resembles, through Desert, measures 41-45, in "Sketch," 161 with Example 7. (17.) The explanation given of inversion/rotation illustrates the depth of confusion about pitch and pitch class: "rotation is sometimes called inversion, used literally - in the sense meant, for example, when it describes the operation that produces the I-form of a twelve-note row from the P-form beginning on the same pitch" (49). "Twelve-note rows" and all their transformations (including inversion) are, of course, pitch-class, not pitch, successions. (18.) This model may remind readers of Benjamin Boretz's discussion of pitch-class trichord relations in the opening of Erwartung (review of George Perle, Serial Composition and Atonality in Perspectives of New Music 1, no. 2 (Spring-Summer 1963): 132-33), where the sense of a transformational process (whatever the success of the analysis) is strongly evoked, and in Schonberg's op. 15, no. 1, measures 1-7 ("Meta-Variations, Part IV: Analytic Fallout (II)," Perspectives of New Music 11, no. 2 (Spring-Summer 1973): 181-86). Robert Morris's "A Similarity Index for Pitch-Class Sets" (Perspectives of New Music 18 (1979-1980): 454-55) includes a graph showing degree of relatedness among pitch-class trichords. David Lewin defines and renames Bernard's transformations (FLIPEND and FLIPSTART) in Generalized Musical Intervals and Transformations (New Haven: Yale University Press, 1987), 189. (19.) My analysis of Density 21.5 ("A Flow of Energy: Density 21.5," Perspectives New Music 23, no. 1 (Fall-Winter 1984): 334-47) takes a stance closer to Bernard's on the question of octave equivalence. (20.) This is the subject most extensively addressed by Trevise. (21.) For Bernard, this three-pitch configuration is not a trichord: "a basic form made up of two equal adjacent intervals (such as [4][4]) has a more limited range of possibilities, for infolding reduces it to a dyad, and it has only one distinct unfolded form. A configuration consisting of two or more intervals of equal size in adjacent disposition is more accurately interpreted as the result of single-interval projection. Since repeated extension does not efface its original spatial identity, a single interval may build upon itself to form a chainlike pattern" (75). Consistent with the view that they result from "single-interval projection," [4][4]s are shown only in graphs like Example 1. To me, the distinction seems false. (22.) Conversations with Jackie Dempsey as she worked on her Masters thesis at Washington University (1989-1990) were invaluable in developing my thinking about Varese music and Jonathan Bernard's work.
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Title Annotation:Jonathan Bernard's book 'The Music of Edgard Varese'
Author:Guck, Marion A.
Publication:Perspectives of New Music
Date:Jun 22, 1992
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