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The Listening Composer

University of California Press

Shortly after I was invited to assume the Ernest Bloch professorship I came upon an article by John Updike that made me even more uneasy than I would otherwise have been about the entailed responsibility in presenting a series of public lectures. I have never heard him but am informed, by people who have, that Mr. Updike is an excellent lecturer. Nevertheless, this is what he has to say, in the June 16, 1988, issue of the New York Review of Books , on the subject of creative writers as lecturers: "Asking a writer to lecture is like asking a knife to turn a screw. Screws are necessary to hold the world together, the tighter the better, and a screwdriver is an admirable tool, more rugged and versatile and less dangerous than a knife; but a knife with a broken tip and dulled or twisted edge serves all purposes poorly. Of course, if a knife is repeatedly used as a screwdriver, it will get worn into the shape of one; but then don't expect it to slice any more apples." I've been a college teacher for about forty years, so the role of lecturer is not unfamiliar to me, but whenever I've been called upon to address an audience on the subject of my own work as a composer I've had an uncomfortable sense of engaging in some inappropriate and awkward activity, like trying to turn a screw with a knife or to slice an apple with a screwdriver.

The subject of these lectures is of my own choosing. In what sense is that subject my own work, my own life as a composer?

A few years ago1985, the Berg centenary, to be preciseI received a phone call from the producer of a television show, inviting me to give a talk on Alban Berg. I explained that I would not be able to accept, because of conflicts due to a pending concert of my own music. "But you're not the same George Perle who composes, are you?" said the voice at the other end of the line. But I am indeed the same George Perle, and especially so in connection with these talks, an alternative title for which might have been "Tradition in 20th Century Music." But given the plethora of totally opposed compositional styles, compositional techniques, and even compositional languages today, can one speak of "Tradition in 20th Century Music," and if so, what can one mean by it? I have interpreted the above quotation from John Updike as an admonition to lay my cards on the table right away and admit that I do not present a consensual view of my subject. My words come from my own perspective as a composer, a personal perspective formed by my own need to find a way to write music that would do what music has always done, that would be coherent in the way music has always been coherent, that would be new in its language and materials only to the extent that the realization of this aim in our time demands newness in its language and materials.

My second book, published in 1977, bears the same title as an article I published thirty-four years earlier, Twelve-Tone Tonality . The title alone is enough to suggest that, in spite of our common interest in tonality, my view of tradition is not the same as that of the sponsors of a recent competition for compositions "in any style which relies partially or wholly on any major/minor key systems or modes." Neither is my perspective the same as that of an article on current trends in contemporary composition which appeared in the magazine section of the New York Times a few years ago under the title "The New

Romance with Tonality." But if the qualification of "tonality" in my title deprives me of the advantages of a shared perspective, doesn't it also suggest a similar deprivation in my relation to the tradition of twelve-tone composition?

My own romance with tonality is an old one. It predates my 1943 article by more than two decades. In fact, when I fell in love with tonality for the first time Schoenberg had not even quite arrived at his concept of an ordered statement of the twelve pitch classes as a consistent basis for atonal composition, though he was on the verge of this discovery. The first piece I can recall hearing as a coherent, integrated musical experience was the Etude in F minor from the Trois Nouvelles Etudes of Chopin. My Russian immigrant father had bought a piano in anticipation of the arrival of his niece, a pianist, from the Old Country. I was six or seven at the time. The experience of hearing her play this piece was so intense, so startling, as to induce a traumatic change of consciousness. What could I have known about "tonality"? Yet I must have "understood" this music, I must have been able to "follow" it. And what is it that we "follow" in a piece of music, what is it that gives it coherence and direction and sense, if not, in the largest sense of that term, its "tonality"?

This same cousin was my first piano teacher. It was not a happy relationship. My own identification was with the source of that music, transcendent though it seemed. I knew right away that what I had to do as a musician was compose, but my teacher seemed to be surprised by this notion. She gave me the impression that this was no longer done, that everything had already been composed by people who were now dead. She was living with us at the time, and so, to our mutual distress, she was often within earshot when I was supposed to be practicing. She could not understand why my practice sessions would be interrupted by long periods of silence, and she complained to my mother about this. I remember one of these silent

periods very well, because it was during this particular pause in my practicing that I had my second great musical experience, one that was very different from my first hearing of the Chopin etudenot at all transcendent and magical, as that had been, but equally decisive and compelling for its very difference. I noticed something remarkable about the simple, accompanied folksong I was practicing. Its two halves, each eight bars long, were exactly alike, except that the order of the two chords that concluded the first half was reversed at the conclusion of the second. I had discovered, all by myself, the difference between the half cadence and the full cadence. More than that, I had discovered the meaning of cadence in general. Most of all, I had discovered a connection between music and our normal life outside of music, for I saw an analogy between music and speech: the first half of the piece was something like a question, and the second half something like an answer. This was my first act of musical analysis and the beginning of my career as a theorist, but it was also the beginning of my career as a composer, for it was not until this moment that I saw music as something tangible, as something that could be "understood" in a different sense from the way I had "understood" the Chopin etude at that first hearing, as something that I, too, could learn to compose.

Both these ways of understanding were, of course, bound up with the traditional harmonic language of Western music. This meant that as my understanding of that language evolved, as my familiarity with its literature developed and as I labored to discover and to invent my own voice in it, I, too, found myself bound up with the ambiguities and contradictions that had led to a revolutionary transformation in that language in the music of Schoenberg and his circle a generation earlier. The crisis in my own development came in 1937, when I was twenty-two years old. It seemed to me that the musical language it-

self had become problematical. It no longer seemed possible to write music that was really significant, because the traditional means of harmonic progression and structure no longer worked, and while there were other ways to write music, they couldn't provide a basis for a really coherent, complex, and integrated musical language such as had been the basis of Western music for some three hundred years. The music of Debussy, Ravel, Stravinsky, Richard Strauss, Sibelius only seemed to confirm, in their different ways, the demise of the great tradition. There was a kind of indigenous American "atonal" tendency whose most successful representative was Carl Ruggles and to which my teacher, Wesley LaViolette, also belonged. Though this was hardly significant enough to call a "school" an attempt was being made to formulate certain principles for it under the rubric of "dissonant counterpoint."1 I could find nothing in this to meet my own needs and was not at all inclined to forsake my own neo-classical idiom for it. Of Schoenberg's music I had heard only Stokowski's recording of Gurrelieder and, on a distant radio station and through a great deal of static, a live performance of the Second Quartet, and I had been powerfully impressed by both. Of Schoenberg's later works I knew nothing. The American premiere of Wozzeck in 1931 had created enough of a stir that, though I was only fifteen at the time and living on a farm in Indiana, news of it reached me and I eventually managed to borrow a score from the Chicago Public Library; but it was a bit too soon, and I could make nothing of it. By the time of Berg's death on Christmas Eve, 1935, the Second Vienna School was largely written off as having had its day. An obituary by one who was sympathetic to that circle began:

Charles Seeger, "On Dissonant Counterpoint," Modern Music VII/4 (JuneJuly 1930); Henry Cowell, New Musical Resources (1930; reprint ed., New York: Something Else Press, 1969), pp. 3542.

With the untimely death of Alban Berg it would appear that the period of atonal composition is for the time being already concluded. The prospects for European music become, by this, still darker than they were already. The Schoenberg group had at its disposition no single individual who could take the place of Berg. . . . There is here in Europe no longer much prospect of progress, of recovery. German music is almost completely demobilised; France and Italy bring forward innocent little pieces and tame pasticcios; the music of the Russians fulfils, perhaps, cultural duties of significance, but it is, speaking from the point of view of musical history, continually pre-1914, to my thinking. The innovations of Arnold Schoenberg and his group threaten, together with the death of the greatest talent in this group, to become petrified; and that already now, within twenty-five years.2

If I was equally pessimistic about the state of contemporary music a year and a half later, it was only because I was not yet aware of "the innovations of Schoenberg and his group."

My first acquaintance with these innovations came through an accidental encounter, in the summer of 1937, with the score of Berg's Lyric Suite . The first page was enough to give me an insight into the nature of my difficulties. I saw at once that it was possible to comprehend the twelve notes of the semitonal scale as an integral and autonomous collection, that it was possible "to dissociate, so to speak, the chromatic scale from 'chromaticism,'"3 and I suddenly understood that I had unconsciously been searching for such a possibility.

I was not instantly transformed by this experience into a composer of twelve-tone serial music. Of the post-diatonic "system" that

Willem Pijper, Musical Times 77 (May 1936): 414.

George Perle, Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg and Webern (Berkeley and Los Angeles: University of California Press, 1962; 5th ed., 1981), p. 1.

Schoenberg was rumored to have devised I could not have known more at the time than what Henry Cowell had reported in his chapter on "dissonant counterpoint" in his speculative book New Musical Resources :

Schnberg, though, has another quite different new system of counterpoint of his own which he has worked with consistency, which he employs with straightforward logic in his later works, and which is formulated so that he teaches the method to his students.

 . . . Schnberg in his system does not formulate new polyphonic materials, but takes from ancient counterpoint devices which had become almost obsolete, such as retrograde, inverse melodic line, etc., as well as better-known contrapuntal usages, and applies them to a twelve-tone scale in which each tone is independent. By an ingenious method of geometric diagram he is able to discover every possible variation of the themes and is therefore able to select the form of development which seems to him the most perfect.4

The obsessive analytical studies of the Lyric Suite that I undertook from the moment I played the opening bars at the piano were motivated in the first place by the extraordinary and immediate effect of this new and complex music. But I also hoped that they would give me some insight into Schoenberg's "new system of counterpoint" and into whatever it was that Cowell meant by his "ingenious method of geometric diagram." In this I was disappointed. Neither from the Lyric Suite nor from any other work of Berg's is it possible to deduce the basic premises of Schoenberg's twelve-tone system. The twelve-tone collection unfolded by the first three chords of the Lyric Suite is inconsistent with the twelve-tone series that commences in the sec-

Cowell, New Musical Resources , p. 41.

ond bar, according to whatever principles of derivation we can discover in Schoenberg's serial compositions. Between these two independentaccording to Schoenberg's systemtwelve-tone sets a six-note chord is interposed, but where is the complementary six-note collection that would give us the "missing" six notes of the twelve-tone "aggregate"?5 The implications, for the concept of twelve-tone harmony, of the accompaniment to the first thematic statement of the series, and the procedures by which that accompaniment is derived from the series, are diametrically opposed to Schoenberg's practice. At the bottom of the first page of the score there is a second thematic version of the series, derived through the cyclical permutation of the first version. Such a procedure is not necessarily inconsistent with the premises of Schoenberg's system, but it is something we do not find in his work. And accompanying a three-part canon on this cyclically permuted statement of the series we again find something that is inconsistent with these premises, a retrograde statement of the first three chords in the form of a straightforward linear statement of the cycle of fifths which can only be construed as a second series. So much for the first nine bars of the Lyric Suite as a means toward understanding Schoenberg's "new system of counterpoint"! But perhaps none of these discrepancies is so much at odds with Schoenberg's serialism as the twelve-tone aggregate which we come to at the conclusion of the exposition of the first movement, which is not derivable in that system from either of the two series (ex. 1. 1).

Since the tonal coherence and musical sense of the movement were unmistakable to me, I assumed that the introductory chords, the thematic series and the harmonic elements derived from it, the cyclically permuted statements of the thematic series, the linear statement of

This is Milton Babbitt's term for a collection of the twelve pitch classes.

Image not available.

Example 1.1

the cycle of fifths, and the hexachordal scales of the concluding subject must all be higher-level manifestations of a deeper background structure which still remained for me to discover. In making such an assumption I had taken the first step in what Joseph Kerman, in his friendly comments on Twelve-Tone Tonality , calls a "private reading of serialism."6 But that private reading, as Professor Kerman points out, is "emblematic of [my] traditional orientation." And a tradition, of course, is not private. Neither can one really lay claim to a purely personal perspective on a "tradition." If a tradition is not shared, it is not a tradition. I might even say that the real subject of these lectures is an explanation of the ways in which my "reading of serialism" is not exclusively "private," of the ways in which my perspective is not merely personal.

The alternative title that I have proposed for these lectures, "Tradition in 20th Century Music," implies that this tradition is a departure from an earlier tradition. But if we are really to understand the respects in which this tradition is new, we have also to understand in what respects it is not different from the tradition that precedes it.

In every edition of Schoenberg's Opus 11 that precedes the Gesamtausgabe we find the same notational discrepancy in the tenth bar from the end of the first movement (ex. 1.2). On the second beat of this bar the note on the third space of the upper staff is preceded by a sharp sign on the third line. Either the note or the sharp sign is misplaced,

Joseph Kerman, Contemplating Music (Cambridge, Mass.: Harvard University Press, 1985), p. 93.

Example 1.2
Schoenberg, Op. 11, No. 1
Copyright 1910 by Universal Edition. Renewed Copyright 1938 by
Arnold Schoenberg. Used by permission of Belmont Music Publishers.

but which is it? In my analysis of this piece in Serial Composition and Atonality I attribute a special role to the augmented triad, which not only "emerges . . . as the primary structural detail of a large part of the development section," but which also determines, through Schoenberg's ingenious large-scale exploitation of its special propertyinvariance of pitch-class content at three pitch levelsthe overall tonal structure of the movement.7 If we resolve the notational discrepancy in Example 1.2 by shifting the problematical note to the third line of the staff, "all four 'augmented triads' appear in sequence in this and the following bar, to confirm and clarify, at a strategic moment in the formal design, the harmonic basis of the composition."8 Edward T. Cone proposes a different reason for resolving the notational discrepancy in the same way. Taking issue with the "correction" given in the Gesamtausgabe , which resolves the discrepancy by shifting the sharp sign to the third space, he writes:

Misguidedly, I had looked forward in the present publication to a confirmation of which creates an augmented triad that sounds to me much more idiomatic here than the minor triad formed by the apparently correct even the major-minor clash produced by

Perle, Serial Composition and Atonality , pp. 14f.

Ibid., p. ix.

the latter seems insufficiently dissonant, within the vocabulary of this piece, to support the crescendo that it must. Hence I am inclined to mistrust the accepted solution, even if it turns out to have the authority of the manuscript behind it. The misprint might have arisen as a result of a correction or a revision made by the composer at some stage of proofreading, but incompletely adopted by the engraver or the printer.9

My reason for preferring to derives from revolutionary structural principles that mark Opus 11, No. 1 as a signal work of a new musical language. Professor Cone's argument is based on a principle of musical rhetoric that is as relevant to Beethoven and Wagner as it is to the new music of Schoenbergthat an increase in dynamic intensity will seem incongruous if it is joined to a concomitant decrease in harmonic tension.10

A striking example of the way in which dynamic changes can point up and clarify the meaning of structurally significant harmonic details is found in the opening bars of Varse's Density 21.5 (see frontispiece and endpapers). In the first five bars the tritone unmistakably emerges as the boundary intervsal, and the midpoint of that interval, e , as unmistakably functions as a pivotal note, dividing the tritone into two minor thirds, functionally differentiated by the filling in of e-g , but not , by a passing note. A continuation of that passing-

Ibid., pp. ix f., quoted from Edward T. Cone, "Editorial Responsibility and Schoenberg's Troublesome 'Misprints,'" Perspectives of New Music XI/1 (FallWinter 1972).

A composer may, of course, purposefully suppress an expected crescendo for the sake of the special effect of the suppression itself, as Beethoven does in the transition to the Finale of the Fifth Symphony, in the sixteen bars of increasing harmonic and melodic tension which culminate in the two sustained chords that complete the progression from C minor to C major. The frustrated crescendo is all the more powerful in its effect when it is finally released only upon the attainment of the climactic closing bars of the passage and when the dynamic energy that should have been given twenty-three bars to realize its potential is constrained to do so in a mere eight.

Example 1.3

note motion in the three bars that follow gradually extends the upper limit of the boundary interval until closure is achieved in the arrival of the octave, on the downbeat of bar 9 (ex. 1.3).11 If I describe the octave, as something "achieved," it is because the composer himself describes it in this way, through the simultaneous attainment of a new dynamic level, fortissimo , and through the Luftpause which separates it from the preceding passing notereally a leading tone within the new context established by the octave as a boundary interval.

But if the attainment of closure, through the octave, is an "achievement," it is one that creates a crisis for the composer, as we can hear in his subito substitution of mf for the fff to which the crescendo sign seems to point in bar 9, and in his seeming inability, through two whole bars, to move beyond and c , the point of closure and its leading tone. His partitioning of the octave in the first ten bars places Varse with Scriabin and the Schoenberg circle among the revolutionary composers whose work initiates the beginning of a new mainstream tradition in the music of our century. Varse's octave is symmetrically partitioned by the tritone, and , instead of asymmetrically by the fifth degree of the diatonic scale into a perfect fifth and perfect fourth. The minor third, in turn, symmetrically partitions each statement of the tritone. The result is a closed cyclic system, the diminished-7th chord, which provides no internal basis for transposition or conversion. Having closed the minor-3rd cycle upon achieving the octave, the composer finds himself with no means of

Marc Wilkinson, a pupil of Varse, describes the pitch organization of the whole piece in terms of the unfolding of the three diminished-7th chords ("An Introduction to the Music of Edgard Varse," The Score and I.M.A. Magazine 19 [1957], as I do in the following pages.

modulation or transition to another minor-3rd cycle or to some other type of harmonic structure. He can continue his composition only by wilfully breaking the symmetry that determines pitch relations in the first ten bars. That wilful break occurs in the sudden crescendo to fff which brings us to a new note, d , on the downbeat of bar 11. The dynamic markings tell us that both the arrival of the octave in bar 9 and the change to a new harmonic area in bar 11 come as something of a surprise to the composer himself, or so he would have us believe. A very different message would have been conveyed if these crucial moments in the unfolding of the movement had been presented as they are in my revised version in Example 1.4.

Example 1.4

The harmonic language of this music would have seemed strange to Beethoven, but I think he might well have discovered a key to that language, though perhaps only after several hearings, in Varse's structural use of dynamics, which is so much like his own. The second movement of the Fifth Symphony offers a striking illustration of this affinity in the sudden fortissimo on the German 6th chord in the seventh bar of the second theme, which takes us from the tonic key, major, to C major. Here is Tovey on the beginning of this movement:

In form the movement is unique, if dimly suggested by Haydn's special form of variations on two alternating themes. But here the themes are of quite peculiar types. Violas and cellos . . . state the first theme in a single broad phrase, the end of which the higher instruments echo and carry on into a series of echoing after-

thoughts. Then the second theme begins, very simply, pauses on a wistful note, and suddenly bursts into a blaze of triumph in a remote key, C major, the tonic of the whole symphony.12

Why the sudden "blaze of triumph"? Through the change of key Beethoven makes his way out of a compositional impasse, just as Varse had done by his introduction of a new pitch class outside the closed field of pitch relations on which the harmonic sense of everything up to that point had depended. But where Varse simply cuts the Gordian knot, Beethoven's "triumph" is a brilliant intellectual achievement, drawing wonderfully subtle yet wonderfully logical inferences from the first theme of the movement. The "echoing afterthoughts" extend the first theme by reiterating the V-I cadence of the first eight bars through fourteen additional bars. The second theme (ex. 1.5) commences with two more statements of V-I in , and it is then (bar 27) that it "pauses," on a pianissimo diminished-7th chord that introduces what I hear as a questioning rather than a "wistful" note. After so many "echoing afterthoughts" of the major cadence, should not the second theme be in another key? An affirmative answer, fortissimo , comes with an enharmonic addition of to the major triad, converting it into a German 6th chord that resolves to a V-I cadence in the new key. With the first entrance, in C major, of horns and trumpets, the second theme "bursts into a blaze of triumph," but both the triumphant new motive in the new key and the progression from to C had been quietly presaged in the antecedent phrase of the first theme (ex. 1.6).13

Donald Francis Tovey, Essays in Musical Analysis (London: Oxford University Press, 1935), vol. 1, p. 41.

There is a striking interrelation of dynamics with harmony and formal design throughout the presentation of the two themes. In Example 1.6, for instance, everything is marked piano except for the forte on the penultimate bar. It is this which calls forth the "series of echoing afterthoughts."

Example 1.5
Beethoven, Symphony No. 5, 2nd mvt.

Example 1.6

Example 1.7

I referred a moment ago to the revolutionary implications of Varse's symmetrical partitioning of the octave in Density 21.5 , as opposed to the asymmetrical partitioning that characterizes the octave in diatonic music. Let us suppose that we are hearing this work for the first time. At what point would we recognize it as an "atonal" rather than a tonal composition? Suppose the composer had completed the first phrase by descending from g to (ex. 1.7)? I think this would have led us to hear the G as a dissonant upper neighbor resolving to the dominant. Having taken us as far as I show in Example 1.3, does the composer still have the option of subsequently employing a progression such as I show in Example 1.7, or does Example 1.3 establish a context that would be inconsistent with such a progression? Is the that I have appended to the first phrase of Density 21.5 analogous in its implications to the chord that I have appended to the first phrase of the Tristan Prelude in Example 1.8? Not at all, because, in fact, this phrase does eventually resolve to the tonic triad, though in a long-range and extraordinary way, and with the major form of the triad substituted for the minor. The difference be-

Example 1.8

Example 1.9

Image not available.

Example 1.10

tween what Wagner does here and what some other composer might have done is a stylistic one. In the context of Wagner's musical language the V-I cadence still retains its relevance. But the concept of the perfect fourth or fifth as a referential interval relative to which the tritone requires resolution, as implied in Example 1.7, has no relevance at all to Density 21.5 .

Here is the beginning of another famous opening phrase, closer in character to the Varse in that it too is for solo flute and prominently features the interval of a tritone (ex. 1.9). Suppose we continue as shown in Example 1.10, interpreting the tritone, , as a dissonant interval and resolving it into the minor third, . In fact, what Example 1.10 shows is Debussy's own continuation of the first two bars, except that he paraphrases this conventional resolution of the disso-

Example 1.11

Example 1.12

nant tritone by displacing to the upper octave (ex. 1.11), thus enlarging the ambitus to a new and more strongly dissonant interval, the octave plus a semitone, and at the same time providing space for the unfolding of the complete E major triad.

But, before we get to this displaced resolution, the repetition of the tritone and the whole-tone ascent from g suggest a step in the direction of the Varse composition, i .e., in the direction of a symmetrical rather than the conventional tonal interpretation of the tritone.14 Would we have been surprised if Debussy had continued to the octave of the lower g , as in Example 1.12? You may prefer Debussy's own version of the opening bars of L'Aprs-midi d'un faune to the one I have just proposed, but this should not lead you to draw any conclusions about the respective merits of the different harmonic worlds represented in the two examples. I'm sure you found my tonal version of the opening of Density 21.5 equally uninteresting in comparison to the original.

Example 1.12 immediately puts us in the harmonic world of Den -

Perhaps it is because of this whole-tone ascent that Debussy spells the lowest note as g instead of as the that the key would imply.

Image not available.

Example 1.13

sity 21.5 and of Le Sacre as well. The tritone boundary of the principal theme of the Introduction to Le Sacre (ex. 1.13) plays the same structural role for Stravinsky as it does for Varse in Density 21.5 . It symmetrically partitions the octave and is itself symmetrically partitioned into two minor thirds. (I will explain later why I regard this, rather than that fragment of a Lithuanian folksong we have all come to know so well, as the principal theme of the Introduction.)

As Leverkhn's Devil in Thomas Mann's Dr. Faustus tells us, "Composing itself has got too hard, devilishly hard." The very act of composing today raises questions, or should raise questions, that at one time did not need to be asked. Professor Cone finds a passage in Schoenberg's Opus 11 as given in the Gesamtausgabe "insufficiently dissonant . . . to support the crescendo." What determines "sufficiency" of dissonance in the harmonic language of Opus 11, and how, indeed, do we define "dissonance" in that language? We have seen how dynamic relations play the same structural role in an atonal composition by Varse that they play in a tonal composition by Beethoven. What other elements in the practice of those composers whom Tovey regarded as The Main Stream of Music remain similarly relevant to those whom I would regard as the main stream of twentieth-century music? When we substituted, in Example 1.12, the octave of the lower g natural for Debussy's octave-displaced , we eliminated the function of the latter as a note of resolution, and thereby the special effect of the octave displacement as well. What meaning can octave displacement have in general for atonal or

twelve-tone music? I propose to put this question in another way: when are the twelve elements of the tone row "pitches" and when are they "pitch classes"?15

Registral displacement and the determination of dynamic values are concerns that are directly relevant to the act of composition. We have so far overlooked other, implicit, questions that are of a more restrictedly theoretical character. When Professor Cone refers to degrees of "dissonance" in Schoenberg's Opus 11 he is reverting to the layman's use of that term, which has to do with the relative "harshness" of a collection of pitches, a quality that I tried to define more explicitly in my first book:

Each of the different intervals has its own sonic quality or what has been called, for lack of a better term, "degree of tension." In isolation from any compositional context one can evaluate the "degree of tension" of the intervals from the "minor second" to the tritone as varying inversely with the size of the interval, and of those from the tritone to the "major seventh" . . . as varying directly with the size of the interval.16

In reference to music in the major/minor system, however, "dissonance" has only to do with the harmonic function of a collection of pitches. In tonal theory, any collection of pitches that is not a major or minor triad or a component of a major or minor triad is a "dissonance," and requires resolution to a "consonance." Since we have no accepted terminology for describing the relative "degree of tension" of a collection of pitches in post-tonal musica highly ambiguous concept in any caseProfessor Cone is quite right to borrow a

We are, of course, indebted to Milton Babbitt for this useful and necessary term, which is devined as follows in the New Grove : "The set of all pitches that are transpositions of some given pitch by zero or an integral number of octaves. All d s, for example, are members of the pitch class d ."

Perle, Serial Composition and Atonality , pp. 30f.

non-professional usage that he would never employ under other circumstances and that we can all understand. I have described Varse's Density 21.5 as a post-tonal work in which the octave is symmetrically partitioned into a diminished-7th chord, and Schoenberg's Opus 11, No. 1 as a work in which another symmetrical structure, "the augmented triad, . . . determines . . . the overall tonal structure of the movement." In the traditional tonal theory from which we borrow this nomenclature for the two chord-types their names have very explicit implications that have no relevance whatever to post-tonal music. Both of them, like the twelve-tone scale itself, are cyclic structures, which is to say that each of them unfolds a single recurrent interval in a series that closes with a return to the initial pitch class. These interval cycles play a fundamental role in the harmonic organization of post-diatonic music and can easily be identified simply by naming the cycle.17 Professor Cone's reference to a "major-minor clash" is more problematical, since it could lead one to conjecture that the pitch collection to which he thus refers is a particular chord-type with special characteristics that derive from the fact that it can be dissected into these familiar harmonic structures of traditional tonality.

At the beginning of this lecture I distinguished between two kinds of musical "understanding," one of which I inferred from my earliest recollected musical experience, my intuitive and spontaneous re-

I have proposed a nomenclature in which the letter "C" followed by an interval-class number (0 through 6) designates the cycle. For example, the "diminished-7th chord" in Density 21.5 is "C3"; the "augmented triad" in Opus 11, No. 1 is "C4." Since transpositions of any given interval cycle are mutually exclusive as to pitch-class content, we can identify the specific pitch-class collection by any one of its component pitch classes. I identify these by the integers 0 through 11, with 0 for pitch class c , 1 for , 2 for d , etc., and the specific transposition by employing as a subscript the lowest pitch-class number represented in the cycle. The first ten bars of Density 21.5 , for example, are based on C31 . (See George Perle, The Operas of Alban Berg . Vol. 2: Lulu [Berkeley and Los Angeles: University of California Press, 1985], pp. 199f.)

sponse to my first hearing of a Chopin etude, and the second of which I inferred from my first act of musical analysis, my discovery of periodic structure in music through my recognition of the difference between a half cadence and a full cadence. But in another sense of the word I must already have "recognized" the difference between a half cadence and a full cadence at that first hearing of the Chopin etude. Otherwise this music would have been utterly incomprehensible to me. And without this prior recognition there would have been nothing for me to analyze. Both kinds of understanding are bound up with the compositional process. I cannot imagine Varse working his way to the octave in the first nine bars of Density 21.5 through an unfolding only of pitch and rhythmic relations, and then soberly scrutinizing these nine bars in order to determine what kind of dynamic values might be appropriate to go with the notes. I think the listening experience is extraordinarily complex, spontaneous, intuitive, nave, and sophisticated, all at the same time, and that the composer already participates in the listening experience in the process of composing. And I believe that the component of navet is at least as essential a part of it as any of the others. Here is what the Nobel laureate Sir Peter Medawar has to say about creativity in science:

Observation is the generative act in scientific discovery. For all its aberrations, the evidence of the senses is essentially to be relied uponprovided we observe nature as a child does, without prejudices and preconceptions, but with that clear and candid vision which adults lose and scientists must strive to regain.18

"Clear and candid" listening is the "generative act" in composition. In my analysis of the first nine bars of Density 21.5 I explained why Varse marked his arrival at the octave with a Luftpause and a fortis -

Peter Medawar, Pluto's Republic (Oxford: Oxford University Press, 1982), p. 99.

simo , but I think it's quite possible that when he was composing these nine bars Varse didn't "know" why, and didn't stop to find out. He simply "heard" it this way, and now the performer must "hear" it this wayit isn't enough for him to perform it this way merely because he sees the composer's "expression" markings on the printed page; if he's to get them right he must "hear" that what they mark is the arrival of the octaveand, eventually, so will the listener, or, at least, those listeners who really listen. And yet none of them may "know" why, in the way that I, and now you, too, know why.

Does this mean that a composer doesn't need the other kind of understanding of the difference between a half cadence and a full cadence? On the contrary, I find the notion of a composer who is not also a theorist incomprehensible, by which I do not mean that he has to write articles for, or even read, Perspectives of New Music or The Journal of Music Theory . The two kinds of musical understanding are directly, not inversely, related. They are related, one might say, in the way the area of a circle is related to its circumference. If we take what is inside the circle as a measure of the composer's conscious knowledge we can take its circumference as a measure of his intuitive knowledge, a measure of what impinges on whatever is outside the circle.

In addressing all these questions from my own viewpoint as a composer, I am speaking, I believe, for other composers, tooat least some other composers. Obviously, I am not speaking for a young composer, recently interviewed in the New York Times , "who began his composing career as a Serialist," then went on to "electronic and chance works," and eventually came to a "style [which] brought him to prominence a decade ago [that] involves Minimalist compositional techniques and rock instrumentation." Though I have no expectation that my work will ever achieve the kind of acceptance that this "musical pilgrim," as the New York Times calls him, found in his "prog-

ress" from "Serialism" to rock, the critics have often commented on the relative "accessibility" of my music compared to that of some other contemporary composers, and they have attributed this to a certain "humanity" in my attitude to the listener, a certain benevolence which leads me, as one critic has put it, to "meet the listener half-way." The fact is that when I compose I never think of and never have thought of meeting the listener. Or to put it another way that is more consistent with what I have just been saying about the process of composition, I'm the only listener with whom I'm concerned when I compose. Much as I appreciate the good opinion of music critics, I have to disclaim the suggestion that I am more "humane" than other composers.

Though no one has ever suggested that Anton Webern tried to "meet the listener half-way," and though the music I write is very different from his, my sense of what I am doing when I compose is very close to what his seems to have been:

In one of his last letters to Hildegarde Jone, Webern describes the row of [a] projected cantata "The last 3 notes are the 'retrograde' of the preceding ones, a condition that also obtains in the first half of the series. 'Motivically,' too, these 6 notes are the product of an arrangement that is very strictly controlled from several points of view: so they stand there on a foundation of laws !" For Webern composition was research into the "foundation of laws" that governs tone relations, and since both tone and man are part of nature it was research intoand here Webern quotes from Goethe"the laws according to which nature in general, in the particular form of human nature, tends to produce and does produce when she can. . . ." Composing is not an "aesthetic" activity, but something analogous to the investigations of the "researcher into nature [who] strives to discover the rules of order that are the basis of nature."

A keynote of Webern's lectures on the new music was the aphorism "music is natural law as related to the sense of hearing," which he adapted from Goethe's "Color is natural law as related to the sense of sight." In one of the last letters to Reich, he writes: "Imagine the effect on me when I found this passage in [Hlderlin's] notes on the translation of Oedipus: 'Again, other works lack infallibility , compared with those of the Greeks; at least until now they've been judged by the impressions they make, rather than by their ordered calculus and all the other procedures by which beauty is produced .' Need I even say why I was so struck by the passage?" Elsewhere he quotes Goethe on the art of antiquity: "These high works of art were at the same time brought forth as humanity's highest works of nature, according to true and natural laws. Everything arbitrary or illusory falls away; here is necessity, here is God." "If only I could at last be understood a little!" he writes to Reich, referring to plans for an ISCM concert in Basel at which a number of his early pieces, then already thirty years old, were to be played. But in the end what have performances and an understanding audience to do with research into the "rules of order that are the basis of nature"?10

George Perle, "Webern's Twelve-Tone Sketches," Musical Quarterly LVII/1 (January 1971): 24f. The following footnote to the above paragraph is quoted from this article: "Except for the excerpt from the letter to Jone [Webern, Letters to Hildegarde Jone and Josef Humplik (Bryn Mawr: Theodore Presser Company, 1967), pp 17f.], all of the above quotations are taken from [Webern, The Path to the New Music (Bryn Mawr: Theodore Presser Company, 1963)]. Where Webern, in the informal lectures contained in this volume, tries to explain the 'natural laws' that govern sound and the relation of these 'laws' to the art of music, he shows himself to be as uninformed, naive, and inconsistent as most other composers, but this is beside the point. What is relevant is Webern's conception of the creative process as an expression of 'natural laws.'"

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