new temporalities

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New Temporalities in Music Author(s): Jonathan D. Kramer Source: Critical Inquiry, Vol. 7, No. 3 (Spring, 1981), pp. 539-556Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1343117Accessed: 19-08-2014 21:33 UTC

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New Temporalities in Music

Jonathan D. Kramer

Western thought has for several centuries been distinctly linear. Ideas of cause and effect, progress, and goal orientation have pervaded every aspect of human life in the West at least from the Age of Humanism to the First World War. Technologies, theologies, and philosophies have sought to improve human life; capitalism has sought to provide a frame- work for material betterment, at least for the few; science has been dominated by the temporally linear theories of Newton and Darwin; even our languages are pervaded by words that refer to goals and pur- poses.

In music, the quintessential expression of linearity is the tonal system. Tonality's golden age coincides with the height of linear thinking in Western culture: having roots in the fifteenth and sixteenth centuries, tonality became fully developed shortly after 1600; the system started to crumble in the late nineteenth century, and only remnants still function today. Tonality is one of the truly great achievements of Western civilization, and its development was no accident. But let us not be lulled by the pervasiveness of tonal music into believing that it is in any way universal.

Tonality is a system that embodies a set of complex hierarchic relationships between tones. Since the tonic is endowed with ultimate stability, tonal music is always in motion toward tonic resolution. Tonal motion is, strictly speaking, a metaphor-nothing really moves in music except vibrating parts of instruments and the molecules of air that strike our eardrums. But the metaphor is apt. People who have learned how

? 1981 by The University of Chicago. 0093-1896/81/0703-0001$01.00

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540 Jonathan D. Kramer New Temporalities in Music

to listen to tonal music sense constant motion: motion of tones in a melody, motion of harmonies toward cadences, rhythmic and metric motion, and dynamic and timbral progression. Tonal music is never static because it deals with constant changes of tension. Knowing how to listen to tonal music is a very special skill, which Westerners begin to acquire at a very young age. Most of this learning takes place subconsciously, but I maintain that even the most committed amateur, who may claim to listen only to the pretty tunes in tonal music from Schubert to Richard Rodgers, does in fact understand with considerable sophistication the subtleties of tonal listening. Listening to tonal music has become comfortable to Westerners not only because we have learned a complex skill but also because the linearity of tonality neatly corresponds to many goal-oriented processes in life. But we should not be fooled by the com- fort of tonal listening; it is learned behavior.

Anthropologists who have studied several nonlinear cultures have shown that some of the basic tenets of our civilization and its music are really quite arbitrary. For the Balinese, for example, temporal processes are not linear, and their music is not linear: it contains rhythmic cycles, which to Western ears seem to repeat endlessly. But the Balinese are not bored by this music because they do not think in terms of specific du- rations to be filled by "meaningful" events. Balinese music, like Balinese life, is not oriented toward climax. Activities in Bali are understood and appreciated not as means toward goals but rather as inherently satisfying. Thus it is not surprising that Balinese musical performances simply start and stop, having neither beginning gestures nor ultimate final cadences.'

There are numerous other examples of peoples whose time conception is not linear: Trobriand Islanders, southern Indians, many tribes

1. Balinese calendars are not used to measure duration; they mark off ten concurrent cycles (of differing social meanings and degrees of importance) of from one to ten days in length. According to Clifford Geertz, "the cycles and supercycles are endless, unan- chored, uncountable, and, as their internal order has no significance, without climax. They do not accumulate, they do not build, and they are not consumed. They don't tell you what time it is; they tell you what kind of time it is" ("Person, Time, and Conduct in Bali," The Interpretation of Cultures [New York, 1973], p. 393). See also Christopher Small, Music, Society, Education (New York, 1977), pp. 45-47; Gregory Bateson, "Bali: The Value System of a Steady State," Steps to an Ecology of Mind (New York, 1972), p. 86; and Colin McPhee, "Dance in Bali," in Traditional Balinese Culture, ed. Jane Belo (New York, 1970), p. 311.

Jonathan D. Kramer is an associate professor of music theory and composition and director of electronic music at the College-Conservatory of Music of the University of Cincinnati. A practicing composer, he is also currently at work on a book, Time and the Meanings ofMusic, of which the present essay is a part.


Critical Inquiry Spring 1981 541

of Africa, the Hopi in the American Southwest, and the Javanese.2 The existence of such cultures proves that temporal linearity is not a necessary component of human existence but is rather a cultural creation-a magnificent and fruitful creation, to be sure, but nonetheless arbitrary. Of course nonlinearity is equally arbitrary: time is not an absolute reality but rather means different things to different peoples.

What can be constructed, no matter how magnificent, can also be destroyed. Temporal linearity in Western art has lost its universality. The twentieth century has seen disaffection with life goals and real challenges to the idea of progress (progress, particularly in technology, still runs on at an ever-faster pace, but people are increasingly disillusioned with the results). In music the distintegration of linearity began with its in- tensification. As the tonal vocabulary became richer in chromaticism toward the end of the nineteenth century, kineticism increased. Late- Romantic music-such as Brahms' Intermezzo in E Minor opus 116 no. 5 (1892) or Hugo Wolf's Das Verlassene Miigdlein (1888) from his settings of Eduard M6rike's poems-is always searching for goals that only oc- casionally materialize. Progression in this music is defined more by voice leading than by outright root movement, which is reserved for especially large articulations. Late-Romantic music pushed root-defined continuity farther and farther into the background, leaving voice leading as the sole means of foreground progression.3 Voice-leading prolongations of slowly moving structural harmonies became the norm. Only rarely do we hear harmonic root progressions in the foreground-so typical of music a century earlier-functioning as the primary support of large- scale harmonic movement. The early atonal music of Arnold Sch6nberg and his followers resulted from the disappearance of those background harmonies. Stepwise motion in the foreground was retained as the only means to achieve localized continuity of melodic lines, but the definition of large-scale goals for this motion became problematic. In the absence

2. See Dorothy Lee, "Lineal and Nonlineal Codifications of Reality," in Explorations in Communication: An Anthology, ed. Edmund Carpenter and Marshall McLuhan (Boston, 1966), pp. 141-46; Richard Saylor, "The South Asian Conception of Time and Its Influence on Contemporary Western Composition" (paper delivered at the National Conference of the American Society of University Composers, Boston, 29 February 1976); Small, Music, Society, Education, p. 55; Benjamin Lee Whorf, Collected Papers on Metalinguistics (Washington, 1952), p. 39; and Judith Becker, "Gong Music: Change and Permanence in Javanese Culture" (paper delivered at the Fourth Triennial Conference of the International Society for the Study of Time, Alpbach, 4 July 1979).

3. "Background," "foreground," and "middleground" are terms loosely derived from Heinrich Schenker. They refer respectively to the deep structure, surface detail, and the many hierarchic levels between these extremes.



of the a priori goal definition of the tonal system, cadences had to be created contextually.4 Thus some early twentieth-century music created a new kind of linearity. This music, like tonal music, is in constant motion created by a sense of continuity and progression, but the goals of the motion are not unequivocally predictable. I call this new species of musical time "nondirected linearity"-a temporal mode unthinkable, even self-contradictory, in earlier Western music but quite appropriate given the breakdown of goal orientation in much of the music of this century.5 Nondirected linear music moves by a variety of means and with varying degrees of localized stability at cadences, yet it avoids the implication that certain pitches can become totally stable. Such music brings us along its continuum, but we do not really know where we are going in each phrase or section until we get there.6

Whether it is clearly goal oriented, strictly nondirected, or some- where between these extremes, linear music exists in a time world that admits, and even depends on, continuity of motion. But there is another, equally significant, body of recent music that is distinctly nonlinear, music that responds more directly to the disintegration of linear thought in Western culture, music whose temporality comes curiously close to those of several non-Western societies.

As this century has found new temporalities to replace linearity, discontinuities have become commonplace. Discontinuity, if carried to a pervasive extreme, destroys linearity. (The opposite reaction to lin-

4. For a useful discussion of atonal cadence procedures, see Alden Ashforth, "Linear and Textural Aspects of Schdnberg's Cadences," Perspectives of New Music 16, no. 2 (Spring- Summer 1978): 195-224. According to Ashforth, the primary factors that create cadences in Sch6nberg's music are motivic dissolution, pitch and motive reiteration, change of type of melodic motion (stepwise versus disjunct, up versus down, extreme versus middle register), voice leading, change of textural density, and change of timbre. Ashforth prom- ises to deal with harmonic and rhythmic factors in a further study.

5. While much twentieth-century music-early and recent-exhibits this nondirected linearity, a large amount of music continues to direct its motion toward predictable goals. Goals are suggested either (1) by essentially tonal means (see, for example, the linear analysis of Hindemith's Second Piano Sonata [1936] by Felix Salzer, Structural Hearing, 2 vols. [New York, 1962], 1:248-50 and 2:298-305), in what is aptly called a neotonal style, or (2) contextually. In the first movement of Webern's First Cantata opus 29 (1939), for example, a four-note chord becomes a quasi-stable sonority by virtue of frequent emphasis in a variety of settings; it comes to assume the character of a goal largely by reiteration and perseverance. See my "The Row as Structural Background and Audible Foreground: The First Movement of Webern's First Cantata," Journal of Music Theory 15 (1971): 174-77.

6. Some stylistically varied examples of nondirected linear music are Sch6nberg's Sechs Kleine Klavierstiicke opus 19 (1911), Erik Satie's Socrate (1919), the first of Charles Ives' Three Places in New England (1911), Edgard Varese's Hyperprism (1923), Alban Berg's Cham- ber Concerto (1925), lannis Xenakis' Syrmos (1959), Aaron Copland's Nonet (1960), Luciano Berio's Sequenza III (1963), and George Crumb's Echoes of Time and the River (1968).



earity-undifferentiated continuity-is discussed below.) There were two enormous factors, beyond the general cultural climate, that promoted composers' active pursuit of discontinuities. These influences did not cause so much as feed the dissatisfaction with linearity that many artists felt. But the impact has been profound.

One factor contributing to the increase of discontinuity was the gradual absorption of music from totally different cultures, which had evolved over centuries with virtually no contact with Western ideas. The impact on Debussy of the Javanese gamelan orchestra, which he first heard at the 1889 Paris Exhibition, has often been noted.' Debussy was the first of a large number of Western composers to fall under the spell of Eastern music. On this side of the Atlantic, Charles Ives and many of his followers felt no native allegiance to European linearity. Ives was more comfortable with a style of American music-written more for the Sunday afternoon band concert in the park than for the concert halls of Boston and New York-that was only optionally linear.8 Composers' involvement with non-European musics-whether Asian, African, or American-has probably yet to peak. Cross-cultural exchange in music will, of course, never destroy aesthetic boundaries, but music of non- Western cultures continues to show Western composers new ways to use and experience time.

The second tremendous influence on twentieth-century musical discontinuity was technological rather than sociological: the invention of recording techniques. Recording has not only brought distant and ancient musics into the here and now, it has also made the home and the car environments just as viable for music listening as the concert hall. The removal of music from the ritualized behavior that surrounds concertgoing struck a blow to the internal ordering of the listening experience. Furthermore, radio, records, and, more recently, tapes allow the listener to enter and exit a composition at will. An overriding progression from beginning to end may or may not be in the music, but the listener is not captive to that completeness. We all spin the dial, and we are more immune to having missed part of the music than composers might like to think.

The invention of the tape recorder in particular has had a profound impact on musical time. Tape can be spliced; thus, events recorded at different times can be made adjacent. A splice may produce a continuity

7. The gamelan is a type of orchestra common in the East Indies, consisting of an assortment of instruments of the marimba, xylophone, and gong type. It is significant that Debussy was a composer in search of a new aesthetic, an escape from an overpowering Wagnerian influence. He was deeply attracted by the gamelan because he was ready for its new world of sounds and time. See Small, Music, Society, Education, pp. 103-8, and Leonard B. Meyer, Music, the Arts, and Ideas (Chicago, 1967), p. 73.

8. See Robert P. Morgan, "Spatial Form in Ives," and Neely Bruce, "Ives and Nine- teenth Century America," in An Ives Celebration, ed. H. Wiley Hitchcock and Vivian Perlis (Urbana, Ill., 1977), pp. 148-53 and 29-41.



that never existed prior to recording, but the opposite effect has inter- ested composers more: the musical result of splicing can be overpowering discontinuity. The listener is instantaneously transported from one sound world to another. Just when a splice might occur can be as un- predictable as the nature of the new sound world into which the listener might be thrust.

Not all tape music, of course, avails itself of the potency of extreme discontinuity, but the possibility is there to be used or not used. It is surely significant that Karlheinz Stockhausen wrote his first self-consciously discontinuous "moment forms" shortly after his years of working intensively in two early tape-music studios, in Paris and Cologne.9 Today, scarcely thirty years after tape technology first became available to composers, extreme discontinuities are commonplace. The aesthetic of discontinuity has spread far beyond tape music. Composers of tape music carry this aesthetic back into their instrumental writing, and even composers with no interest in electronics have been struck by the power of spliced discontinuity.

Thus music has become progressively more discontinuous in recent generations. The temporality of twentieth-century music (and really of all contemporary arts), like the temporality of inner thought processes, is often not linear. Our minds can follow but one branch of the tree of associations; we must return later if we wish to explore another branch. We constantly project fantasies, hopes, and fears into the future; we recall and juxtapose more- and less-remote pasts; we turn our attention from one thought chain to another, often without apparent reason. The temporality of the mind is seemingly irrational. But time in our daily lives is basically ordered-by schedules, clocks, and causal relationships. It is only against this backdrop of order that the increasing discontinuities of daily life are understood as nonlinear. The conflict between the comfortable order of daily habits and the discontinuities that impinge on that order has become especially acute in recent decades (though we become numb to it as it too becomes habit); but the conflict between the fundamental linearity of external life and the essential discontinuity of internal life is not peculiar to the twentieth century. Thought was surely as nonlinear in 1800 as it is today, but now art (followed at a respectable interval by popular entertainment) has moved from a logic that reflects the goal-oriented linearity of external life to an irrationality that reflects our shadowy, jumbled, totally personal interior lives.

We live in a time-obsessed culture. One symptom is that time rep- resentations in art have become closer than ever before to our internal temporal processes. Our art objectively represents time in a manner close to our internal rhythms, and it thereby brings time closer to ourselves

9. For Stockhausen's formulation of moment form, see his "Momentform," Texte zur elektronischen und instrumentalen Musik, 3 vols. (Cologne, 1963-71), 1:189-210.



and to our obsession. A culture obsessed with time produces art obsessed with time (and, of course, time-obsessed articles about that art).10

Extreme discontinuities threaten the linearity of musical time. One result is a small but significant body of contemporary music that exhibits what I call "multiply-directed time" or "multiple time."" Recent up- heavals in our aesthetic understanding of time allow us to hear multiple time not only in contemporary but also in some earlier music as well. Multiple time depends on an underlying linearity which is sufficiently straightforward and perceptible that we can understand a reordering of it. Thus, for example, when some processes in a piece are moving it toward a goal yet the goal is placed elsewhere in the music, the time sense is multiple. In order for us to experience the reordered linearity that is the essence of multiple time, we must be able to comprehend the function of a musical gesture even when it occurs in the "wrong" part of a composition. Thus in multiple time we encounter such intriguing anomalies as an ending in the middle of a piece, several different con- tinuations of a particular passage, transitions that are broken off, and so on. Tonal music is particularly susceptible to such reorderings. They appear as witty games, such as that in the trio of Mozart's Jupiter Symphony (1788), where the cadence formula repeatedly comes at the beginning of the phrase, or as profoundly altered progressions, such as occur in the first movement of Beethoven's last String Quartet (1826).12 Such multiple meanings in the temporal sense of tonal music can be deeply significant to listeners today. Multiple time does not really inhere in this tonal music: in earlier, less chaotic eras what I am calling temporal reorderings were probably heard as intriguing foils of expectation. But the significant fact is that we today, conditioned by new definitions of tem-

10. I am indebted on these points, and on the subsequent ideas on multiple time, to Judy Lochhead. She read an earlier version of this article and offered many valuable insights through correspondence and discussion. I am also indebted to her "The Temporal in Beethoven's Opus 135: When Are Ends Beginnings?," In Theory Only 4, no. 7 (January 1979): 3-30. This article is in part a response to my "Multiple and Non-Linear Time in Beethoven's Opus 135," Perspectives of New Music 11, no. 2 (Spring-Summer 1973): 122-45.

11. I first discussed multiple time in "Multiple and Non-Linear Time in Beethoven's Opus 135." While my use of the term "multiple" is essentially the same there and in the present essay, my use of "nonlinear" is more restricted now than earlier.

12. I have dealt with both these pieces in some detail. I elaborate on Mozart's wit in "Beginnings and Endings in Western Art Music" (paper delivered at the Fourth Triennial Conference of the International Society for the Study of Time, Alpbach, 4 July 1979). In "Multiple and Non-Linear Time," I discuss the first movement of Beethoven's last String Quartet, citing the occurrence of the final cadence in the tenth measure of the piece, the intertwining of two different strands of continuity, and the preparation of the climactic recapitulation by three separate upbeats, one far in advance of the climax and one actually considerably after it.



porality in our time-obsessed culture, can find appropriately multiple meanings in this music.13

We might expect, then, a rich body of multiple-time music composed in the twentieth century. But in fact I find few examples. The reason is that without clearly perceptible tonal linearity it is difficult to perceive a reordering as such. We might look to neotonal music, but I find no examples in this literature, perhaps because the conservative aesthetic inherent in the continued use of tonal procedures precludes such radical temporal experiments.'4

But there is a handful of nontonal multiple-time music. Consider the Sch6nberg Trio (1946). Gestures are continually interrupted and transitions frequently do not go where they seem to be heading, yet by the end we feel that all loose ends have magically been sewn together. This difficult and profound piece is temporally complex, yet even here the multiplicity of time is not as clearly defined as in a reordered tonal work such as Beethoven's opus 135. (The reason is that the linearity that is reordered is nondirected on the larger hierarchic levels.) But there is no other way to understand the Trio's discontinuous temporal world. Surely it is not a moment form, because the fragments that continually interrupt each other are neither static (the piece is full of directed energy, progressing rhythms, evolving textures, and linear pitch connections) nor self-contained (the fragments rarely cadence internally).'15

Multiple time is discontinuous time; the discontinuities segment and reorder linear time. In pieces in which there is no fundamental linearity and the music is still markedly discontinuous, there is no reordering: the time sense is essentially different. I call this next species of musical time "moment time," after Stockhausen's formulation of moment form.

13. Other examples of tonal music in which multiple time can be readily heard include the opening movements of Mahler's Third (1896) and Seventh (1905) Symphonies, the finale of Berlioz's Symphonie fantastique (1830), Beethoven's Creatures of Prometheus Overture (1801) and the first movements of his Sonata in E-flat opus 31 no. 3 (1803) and Quartet in B-flat opus 130 (1825).

14. It is hard to imagine an aesthetic that would produce, for example, Walter Piston's Fourth Symphony (1950) and also suggest temporal reorderings.

15. Other examples of nontonal multiple-time music include the first movement of Debussy's String Quartet (1893) and, more significantly, his ballet Jeux (1913). Jeux's often fragmentary material, its frequent changes of tempo, its nondevelopmental form, and its discontinuities made it a highly influential piece among the Darmstadt composers (Stock- hausen, Pierre Boulez, Herbert Eimert, et al.) who were working self-consciously with discontinuous time in the 1950s and '60s. Among more recent multiple music are Edwin Dugger's Intermezzi (1969), a conscious attempt to create multiple time in a nontonal idiom, and "We're Late" from Lukas Foss' Time Cycle (1960). I am indebted to my student John Colligan for pointing out the multiple time in "We're Late."



Whereas a composition in multiple time has a clear beginning (or several unmistakable beginnings), which may or may not occur at the start of the piece, a work in moment time does not really begin; rather, it simply starts, as if it has been going on all along and we happened to tune in on it. A multiple form has one or several final cadences, not necessarily at the close of the piece; a moment form ceases rather than ends. At its close we have the impression of having heard a series of minimally connected sections-called moments-that are a segment of an eternal continuum. The moments may be related-motivically, for example-but not connected by transition. The crucial attribute of moments is their self- containment. If a moment is defined by a process, that process must reach its goal, must be completed, within the confines of the moment. If, on the other hand, a section leads to another section (whether adjacent to it or not), then it is neither self-contained nor in moment time. Mo- ments are often defined by stasis rather than process: a moment, for example, may consist of a single extended harmony. Since there is no linear logic that connects moments, their order of succession seems arbitrary. Actually, the order may or may not be arbitrary, but it must seem so on the surface if the piece is to be heard in moment time. The extreme of moment time is "mobile form," in which sections of the piece may be put together in any of a number of possible orderings from one performance to the next, perhaps within certain restraints.16

One might expect to find mobile forms existing in multiple time as well as moment time, since the linearity underlying multiple music could be reordered in a number of ways. But I know of no instance of such music. As I mentioned, nontonal linearity is usually not susceptible to reordering (the Sch6nberg Trio is a rare instance of nontonal multiple time, but it does not at all suggest mobile form). Hence multiple time is more a phenomenon of the contemporary mind perceiving earlier tonal music than a temporal mode utilized by recent composers. Since the instances of unequivocal multiple time in contemporary music are few, it is no surprise that mobile multiple music seems not to exist.

Stockhausen did hint that such music is theoretically possible. In his composition seminars at the University of California at Davis in 1966-67, he described the ideal mobile form, requiring that the work's mobility be apparent on only one hearing. This would be accomplished, he explained, by initiating several directional processes in one section, each of which would be completed in a different section. Only one of these different sections could immediately follow the initial section in a given

16. A typical example of mobile form is Barney Childs' Music for Cello (1963?), which contains a number of fragments to be read in any order by the performer. Also important are Earle Brown's Available Forms 1 (1961) and Stockhausen's Momente (1961-72) and Mixtur (1964). The latter is a particularly straightforward example of a mobile form in moment time.



performance. This ideal would indeed produce mobile multiple music.'7 However, the student compositions based specifically on this model nonetheless turned out sounding like moment forms, probably because of the fragility of nontonal linearity: lacking the a priori of motion provided by the tonal system, nontonal linearity readily succumbs to the focus of discontinuity. Inject a few large discontinuities into a nontonal linear piece: the linearity becomes transformed into either (1) moment time, because the sections seem self-contained-their goals cannot be unequivocally implied in an atonal idiom-or (2) multiple time, if the pro- files of beginnings, endings, climaxes, transitions, and so on are so strongly conventionalized (as in the Schonberg Trio) that their functional implications remain with them even when they are subjected to apparent reordering.

The degree of discontinuity between sections in moment time is considerable. The contrast between moments must all but annihilate by comparison any incidental contrasts within moments. Yet the moments must still seem to belong to the same piece. Although moment time arises readily from extreme discontinuities, the contextually correct degrees of discontinuity necessary for a successful moment form are difficult to compose-numerous student failures have convinced me that excessive discontinuity can destroy context. On the other hand, several pieces that contain remnants of linear thinking still can be heard mean- ingfully in moment time because they exhibit the requisite high degree of discontinuity between sections. Stravinsky's Symphonies of Wind Instru- ments (1920) is such a work. This piece demands to be heard in moment time despite its stepwise pitch connections, climax, opening fanfare, and final cadence. It is a moment form, albeit an early and impure example.'8 Its temporality belongs primarily to moment time because its sections

17. Perception of mobility on one hearing has perhaps been achieved in at least one of Stockhausen's works, but for different reasons. The time sense in Zyklus (1959) is a nondirected linearity (because there is a large number of directional processes that move throughout the whole piece) rather than moment or multiple time, but the mobility is unmistakable since any starting point on the circle of the composition will coincide with the beginning of one and the middle of several processes.

18. Edward T. Cone has analyzed Symphonies in a manner that suggests multiple time. Putting together the interrupted strata in Cone's graph, however, does not result in the progressive continuity one might expect from his description. Cone's analysis ultimately supports a moment-time hearing of the work on a middleground level and a linear hearing on the foreground and background levels. I am comfortable with this possibility, except that I do not feel complete closure at the end (as Cone apparently does), owing in large part to the short, unprolonged final "tonic." This partial open-endedness is quite appropriate in moment time. See Cone, "Stravinsky: The Progress of a Method," in Perspectives on Sch6nberg and Stravinsky, ed. Benjamin Boretz and Cone (New York, 1972), pp. 153-60, and my "Moment Form in Twentieth Century Music," Musical Quarterly 64, no. 2 (April 1978): 181-87.



are self-contained and because there is considerable discontinuity between them.19

If the order of moments is (seemingly) arbitrary, if the piece has no beginning and no ending, then does it have form? I maintain that even music purely in moment time does have discernible form and that form comes from the proportions and/or order of succession (despite its apparent surface randomness) of the moments. The self-containment of moments allows the listener to process them as individual entities. This requires a statistical mode of listening, a mode which is quite possible in the absence of temporal linearity. As we go through the piece, we accumulate more and more data concerning the form; the more data we apprehend, the more we understand the balance (or lack of it) that is generating the form.20

Some music, temporally quite different from pieces utilizing moment or multiple time, seems to adopt the requirements of moments (self-containment via stasis or process) as the essence of entire pieces. When the moment becomes the piece, discontinuity disappears in favor of total, possibly unchanging, consistency. Compositions have been written that are temporally undifferentiated in their entirety. They lack phrases (just as they lack progression, goal direction, movement, and contrasting rates of motion) because phrase endings break the temporal continuum. Phrases have, until recently, pervaded all Western music, even multiple and moment forms: phrases are the final remnant of linearity. But some new works show that phrase structure is not a necessary component of music. The result is a single present stretched out into an enormous duration, a potentially infinite "now" that nonetheless feels like an instant. I call the time sense in such music "vertical time."

A vertical piece does not exhibit cumulative closure: it does not begin but merely starts, does not build to a climax, does not purposefully set up internal expectations, does not seek to fulfill any expectations that might arise accidentally, does not build or release tension, and does not end but simply ceases. It defines its bounded sound world early in its performance, and it stays within the limits it chooses. Respecting the

19. Other examples of moment time include Messiaen's Chronocromie (1960) and Oiseaux exotiques (1955), the second movement of Webern's Symphony (1928), Roger Rey- nolds' Quick Are the Mouths of Earth (1965), Witold Lutoslawski's String Quartet (1964), Frank Zappa's Lumpy Gravy, Istvin Anhalt's Symphony of Modules (1967), Morgan Powell's Windows, and Yehuda Yannay's Continuum (1965). The variety in this list demonstrates that the moment concept is not style-dependent.

20. I have tried to show, for example, that the formal balance in Stravinsky's Symphonies comes largely from a pervasive 3:2 proportion in the lengths of moments. See my "Moment Form," pp. 185-87.



self-imposed boundaries is essential because any move outside these limits would be perceived as a temporal articulation of considerable structural import and would therefore destroy the verticality of time.21

How does a composition define its limits? Most of us tend to listen teleologically, given the prevalence of tonal music in our culture. We listen for, and even project onto the music, implication and progression. Thus even advance knowledge that a piece will be internally undifferentiated does not preclude our initial, habitual response of teleological hearing. The piece starts (not begins), and at first we try to hear linearly, storing possible implications out of which to make significant causal linear relations later in the piece. But as the piece goes on, implications accumulate with a minimum of logical consequences because the music contains no changes of structural import. We become overloaded with unfulfilled expectations, and we face a choice: either give up expectation and enter the vertical time of the composition-where expectation, implication, cause, effect, antecedents, and consequents do not exist-or become bored. People who attend concerts of "nonteleological" music (to borrow Leonard B. Meyer's term) are well aware of how many people still opt for the latter.22 Once our habit of listening linearly is deposed from its falsely universal position, however, people will probably cease to be bored by attractive vertical music. Indeed, there are already a number of young listeners not conditioned at an early age exclusively to tonal listening who consequently do not experience difficulty with vertical time. They have learned that the absence of implication, motion, hierarchy, and contrast is not nihilistic. They have learned to enter a piece and revel in its sounds. This is a music of utter concreteness, unhampered by referential meaning. It is a music of pure beauty or pure ugliness, never tempered by the passing of time.23

Once we have entered the vertical time of the composition, we have apprehended its limits. The piece has defined for us its context; it will not step outside its boundaries. Some vertical compositions have narrow limits and some have very broad limits. Some performances of John Cage's Variations V (1965), for example, approach the infinite ideal where anything could happen without upsetting the verticality of the time struc-

21. Of course it is possible to structure a nonvertical piece by first establishing and then periodically expanding its potentially vertical sound world in a dramatic fashion. An example is Reynolds' Ping (1968)-at least as performed at Mills College in the late '60s. Such music is dynamic and kinetic at the points where it redefines its world, and thus its time sense is not vertical.

22. One polemicist for the experimental in art argues that boredom is a necessary and positive component of the new art. See Dick Higgins, "Boredom and Danger," foew&ombwhnw (New York, 1969).

23. I am indebted to Don Walker for pointing out to me, somewhat inadvertently, the necessity of a positive response to what vertical music contains (as opposed to a negative response concerning such music's "deficiencies"). I am also indebted to him for several other perceptive comments on an earlier version of this article.



ture. The success of a realization of such totally open works might be determined in part by how much can be included without suggesting functional or articulative relationships between isolated, disparate, and striking events. Still, there are practical limits. I doubt that anyone at- tending even the wildest performance of Variations V would continue to have a vertical-time experience if an earthquake were to enter the time- space of the performance.

Vertical compositions are not unstructured; rather, their temporal flow is unstructured. Some vertical pieces involve considerable structur- ing of the compositional process.24 Other vertical pieces involve a great density of layered sound, with a myriad of possible relationships between simultaneous layers. The structure, however, is vertical, not linear. What- ever structure is there (or is placed there by performers or listeners) exists, at least potentially, for the duration of the performance. The form consists of relationships between ever-present layers of the dense sound world, whereas form in linear music consists of relationships between successive events. Form in non-teleological music, therefore, really is vertical.

Listening to vertical musical time, then, can be like looking at a piece of sculpture. When we view sculpture, we determine for ourselves the pacing of our experience: we are free to walk around the piece, view it from many angles, concentrate on some details, see other details in relationship to each other, step back and view the whole, see the relationship between the piece and the space in which we see it, leave the room when we wish, close our eyes and remember, and return for further viewings. No one could claim that we have seen less than all of the sculpture (though we may have missed some of its subtleties), despite individual selectivity in the viewing process. For each of us, the temporal sequence of viewing postures has been unique. The time spent with the sculpture is structured time, but the structure is placed there mainly by us, as influenced by the piece, its environment, other spectators, and our own moods and tastes. A vertical musical composition, similarly, simply is: we can listen to it or ignore it; if we hear only part of the performance we have still heard the whole piece; and we can concentrate on details or on the whole. As with sculpture, there is no internal temporal dif- ferentiation in vertical music to obstruct our perceiving the composition as we wish.

Like moments in moment time, vertical music may be defined by process as well as stasis: there is a special type of vertical music which is sometimes called "process music," sometimes "trance music." Com- positions such as Steve Reich's Come Out (1966) or Frederic Rzewski's Les Moutons de Panurge (1969) are constantly in motion, perhaps toward a

24. In Joel Chadabe's From the Fourteenth On (1972?) for solo cello, for example, each event is carefully composed (by a statistically weighted computer program), but its relationship to any other event is left totally to chance.



goal (as in the case of the Rzewski) or perhaps infinitely (as in the Reich). One might think of such works as pure linear time, but listening to them is not a linear process, despite their internal motion. Because in such pieces the motion is unceasing and its rate gradual and constant, and because there is no hierarchy of phrase structure, the temporality is more vertical than linear. The motion is so consistent that we lose any point of reference, any contact with faster or slower motion that might keep us aware of the directionality of the music. The experience is static despite the constant motion in the music.

I have mentioned several varieties of musical temporality: linear, multiple, moment, and vertical. The predominant species (if there is one) of time in a composition may not be immediately obvious. Such ambiguity raises an interesting question. Consider Elliott Carter's Duo (1974), a convincing linear form whose opening seems at first almost directionless. When I first heard this complex music, I was perplexed: I felt the work had no direction at all. When we do not perceive a work's directionality, its time world seems vertical. Conversely, a composition that has no inherent progression, a vertical form, can be learned so well that the listener has memorized the (random) sequence of events. A few years ago, for example, I listened so often to the recorded (Mainstream 5005) realization of Cage's Aria (1958) performed simultaneously with Fontana Mix (1958) that I had quite literally memorized it. My knowledge of what event was to follow lent a predictability to my listening experience: it seemed that event y not only succeeded event x but also that x implied y in some fashion. If there is implication, there is linearity.

If pieces as different as the Carter and the Cage can seem vertical or linear depending on the amount of experience that the listener has with the work, then does it not follow that the species of time experience is determined by the listener more than by the composition? Yes and no. I would not deny the power of the listener and of influences on the individual's listening experience. The creativity of listeners has too long been underrated. Now that we have learned how to experience other modes of time, we can, with an effort, apply the vertical listening mode, for example, to a decidedly nonvertical piece. Schumann's Stiickchen, from the Album for the Young (1848), to take one of many possible examples, could be heard as quite static. After all, it never leaves C major, never leaves 4/4 time, never changes tempo, its accompaniment rarely abandons steady eighth-note motion, its melody is mostly in quarter notes, there are only two incidental chromatic alterations, and there is an inner voice pedal on G throughout most of the piece.

Of course, Stiickchen is not inherently static; but now that we know how to have meaningful static musical experiences, it can be heard as



static. The effort to hear it so, though possibly rich and meaningful, is considerable-even a bit perverse. Such an effort necessarily involves a contradiction with the system of the piece. We all know how tonality works, and we all hear tonality kinetically-to avoid hearing tonal motion requires special effort. So Stiickchen is not static, and its kineticism does belong to the piece. Learning this Schumann work involves hearing its tonal implications because they are there; listening to it in vertical time, on the other hand, requires a denial of the inherent tonal structure. This situation is different from memorizing a particular recording of Aria with Fontana Mix because we are not substituting memorized succession for internal implication.

I would argue that just as there is linearity inherent in Schumann's Stiickchen, so there is linearity inherent in Carter's Duo. (I am on shakier ground here because it is more difficult to define nontonal linearity.) An older work, such as Roger Sessions' Second String Quartet (1951), might possess a more comfortable linearity, still not dependent on tonality. Here the linearity is unmistakable. Openings, cadences, climaxes, and transitions are all shaped by the composer to be recognized and thus to function in the composition. The linearity in the Sessions or the Carter or even the Schumann, as I have said, does not obligate a listener to hear directionally. It is there to be used or not, in accordance with the listener's predispositions and wishes, but the stronger the linearity, the greater the effort the listener must invest to deny it.

Of course, someone unfamiliar with a style has fewer options. Lis- tening to a style is an acquired skill-we would hardly expect a Martian to be aware of the linearity in Schumann, much less to be able to exercise free choice over whether or not to relate to that linearity. As we are becoming more and more aware of how naive our responses have been to the highly sophisticated musics of other cultures, we should hardly be surprised at a Martian's possible failure to find linearity in the Album for the Young.

Since most compositions, in this century at least, do not consistently exhibit one species of musical time on every hierarchic level, it might be useful to understand the temporal structure of a piece by considering on which hierarchic level(s) we find linearity and nonlinearity. Stravin- sky's Symphonies of Wind Instruments, an impure moment form, utilizes moment time in the middleground as one section follows another with considerable discontinuity. In the foreground, however, motivic, harmonic, and voice-leading consistency produce continuity within the moments; in the background, a linear, stepwise progression, descending in the bass and circular in the treble, defines a progression that operates over the entire piece. Conversely, Xenakis' Syrmos, which I label a non-



directed linearity, is in a sense the opposite of the Stravinsky. It is nonlinear in the foreground (each note seems to have been generated sto- chastically),25 linear in the middleground (as sections do lead by gestural and/or textural implication to immediately succeeding sections), and nonlinear in the background (since the middleground events fail to gen- erate larger structural implications).

Nonlinearity is more than the absence of linearity; it is a viable temporal mode in itself. Hence linearity and nonlinearity are the fundamental ingredients of musical time. The hierarchic levels on which they occur are crucial to the temporal nature of the music; but so is the consistency with which they operate. Are these two categories, then, sufficient to explain, in conjunction with observations on hierarchization and consistency, the various varieties of musical time I have delineated? To answer this question we must first define linearity and nonlinearity in music more specifically.

Linearity occurs when the choice of one compositional event is dependent on the nature of (or probabilities implied by) at least one previous event; nonlinearity results from the generation of each event in- dependent of all others.26 (For example, nonlinearity would probably result if each parameter of each sound were chosen by consulting the I Ching.) When each event on every level is the result of all other events on that level, total linearity occurs at that level. (Total linearity is not the same as total predictability, since a linearly determined consequent is but one of many possible results of a given set of antecedents.) In nondirected linear music, however, implication in the middleground is localized: each section results from implications heard only in the immediately preced- ing section. In multiple time, the adjacent middleground implications are ignored in favor of larger time spans: a section's nature depends on previous but not immediately adjacent music. Moment time is linear on

25. Actually, the compositional process is rather complex, although the aural result is still nonlinear in the foreground. See Xenakis, Formalized Music, trans. Christopher A. Butchers (Bloomington, Ill., 1971), pp. 79-109.

26. I am adapting these ideas, with slight modification, from Chadabe. I have found most useful his informal discussions and his "From Simplicity to Complexity" (paper delivered at the symposium "Time in Music, Rhythm, and Percussion: East and West," Milwaukee, 9 March 1979). I am using "choice" here as a metaphor. My interest is not in the compositional act but in the perceptual act. If a composer consciously decides to opt for a discontinuity so extreme that it could not have been forecast, the result might sound nonlinear despite the compositional intentionality; if a randomized compositional proce- dure produces stepwise adjacency of notes, we might well hear continuity despite the compositional randomness.

The dependence of events on earlier events suggests Markov's processes. See Meyer, Music, the Arts, and Ideas, pp. 15-21; Xenakis, Formalized Music, pp. 69-78; and Lejaren A. Hiller and Leonard Isaacson, Experimental Music (New York, 1959), pp. 22-35. For a brief discussion of the limitations of applying Markov processes to musical analysis, see A. Wayne Slawson's review of Computer Applications in Music, Journal of Music Theory 12, no. 1 (Spring 1967): 149-51.



hierarchic levels up through the moment but not beyond. Vertical music can be, paradoxically, totally nonlinear or else so totally linear that (as in process music) predictability reigns: the most likely progressions would always occur.

The attractiveness of reducing five categories (directional linear time, nondirectional linear time, multiple time, moment time, and vertical time) to two (linearity and nonlinearity) disappears when we realize that there is a continuum between linearity and nonlinearity. Even though linearity is defined as the choice of one event on the basis of previous events, we must realize that the nature of that choice might be a matter of contrast rather than the fulfillment of expectation. The contrast might be extreme, producing discontinuity. Frequent and considerable discontinuities produce nonlinearity. The linearity continuum, conceived hierarchically, may rationalize the five categories, but it hardly suffices to reduce their number.

Time was much simpler in the tonal era: all music was linear. Rates of motion varied, but not the fact of motion. But linearity has become an option in our century. It can be created or denied in many ways within individual compositions. It can be developed, contrasted with nonlinearity, contradicted, and pitted against other linearities progressing at different rates or toward different goals. Thus, like the other varieties of musical time I have discussed, it can be treated as the material rather than the context of a composition.

The categorization of musical time implicit in this article is problematic for several reasons. First, the categories apply both to compositions and to listening modes, and these can be quite different; hence the categories are not necessarily comparable. Second, distinctions between the varieties of temporality are not always readily made. For example, multiple and moment times both present discontinuous sections; vertical time might arise from the vast elongation of a single moment; linear time is often hard to define in the absence of tonality; vertical time defined by process, like linear time, is in constant motion, possibly toward a goal; goal-directed linearity and nondirected linearity are extremes of a continuum, not separate categories; and so on. Finally, most twentieth- century pieces exhibit characteristics of several different temporalities, either simultaneously (as in Symphonies or Syrmos) or successively.27

27. An example of successive temporalities is Messiaen's Cantlyodjayd (1948), a well- proportioned series of discrete blocks. Some of these blocks are clearly moments, but others are in motion toward goals found in other, not necessarily adjacent, sections. The piece is not a pure moment form but rather has elements of multiple time as well. In fact, there is a recapitulation of the opening which sounds like a partially prepared structural downbeat, a gesture that would happen in pure linear time.



We suffer the disadvantages of categorization when we choose to speak of linearity and nonlinearity, when we consider directionality, non- directionality, multiplicity, moments, and verticality, or even when we invoke progression and succession, those two vague categories often encountered in elementary harmony courses. The temporality of contemporary music is far too complex to be explained in any depth solely by categorization. Still, the categories do represent useful means of mak- ing preliminary assessments of musical time structure.28

Twentieth-century music has presented real challenges to our traditional ways of hearing. Critics often remark on experimentation that has produced such formerly impossible compositional aesthetics as mobile form, music in which the first (or at least primary) act of composition is the establishment of durational proportions,29 pieces in which it really does not matter how long they are played or by how many performers, and compositions that try to be completely predictable.30 To justify such radical new musics simply as creations in the spirit of experimentation is to say very little; they are deeply felt responses to new meanings of time in twentieth-century Western culture. I have tried to suggest both how these new meanings have come to be translated into such musical experiments and how these experiments have come to be profoundly expressive of contemporary ideas.

28. I am obviously not proposing a rigorous theory of temporality. Rather, I am trying to suggest attitudes and modes of understanding. The distinction is crucial. My emphasis is on individual works and individual temporal experiences. Some theoretical basis is necessary before analytic understanding is possible, but the focus here is more on the application of categories to compositions than on the categories themselves.

29. For a discussion of one type of precompositional proportioning, see my "The Fibonacci Series in Twentieth-Century Music,"' Journal of Music Theory 17, no. 1 (Spring 1973): 118-32.

30. Process music is perhaps a desperate attempt to recapture linearity, or perhaps it is conceived as "neolinearity" (comparable to the neomodality that often provides the pitch language of trance pieces). But the listening experience is decidedly vertical.


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Issue Table of ContentsCritical Inquiry, Vol. 7, No. 3 (Spring, 1981), pp. 449-643Front MatterThe Last Barthes [pp. 449-454]Coppola's Conrad: The Repetitions of Complicity [pp. 455-474]Solzhenitsyn, Epicurus, and the Ethics of Stalinism [pp. 475-497]Realism, Perspective, and the Novel [pp. 499-520]The New Criticism and Eighteenth-Century Poetry [pp. 521-537]New Temporalities in Music [pp. 539-556]Only Time Can Tell: On the Topology of Mental Space and Time [pp. 557-576]Photography and Representation [pp. 577-603]Critical ResponseMusical Space: A Composer's View [pp. 605-611]Rational Form in Literature [pp. 612-621]Diagrammatology [pp. 622-633]History and Innovation [pp. 634-638]A Reply to Carl Pletsch and Richard Shiff [pp. 639-643]

Back Matter

new temporalities

Documents

music jonathan

tonal motion

pervasiveness of tonal

music authors

jstor terms

motion of tones

metric motion

motion of harmonies