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New Temporalities in Music

Jonathan D. Kramer

Critical Inquiry, Vol. 7, No. 3. (Spring, 1981), pp. 539-556.

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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 sys-

tem. 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 func-

tion 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 re-

lationships between tones. Since the tonic is endowed with ultimate sta-

bility, 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

98

by The

Universi ty of Chicago

0093-189618110703-00Ol 01.00



54 Jonathan D. Kramer New Temporalities i n 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 com-

fortable 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 con-

ception is not linear: Trobriand Islanders, southern Indians, many tribes

1.

Balinese calendars are not used to measure du rat ion ; they mark off ten co ncurrent

cycles (of differing social meanings an d degre es of imp ortan ce) of fr om one to te n days

in length. According to Clifford Geertz, the cycles an d supercycles are endless, un an -

chored , u nc ou nt ab l~ , nd , as their in ternal ord er has n o s ignificance, without c limax. Th ey

d o not accumulate , they do not bui ld , and they a re not c onsume d. The y don ' t tel l you

what time it is; they tell you what kind of time it is ( Person, T im e, and C ond uct in Bali,

The Interpretation of Cultures [New York, 19731, p. 393 ). See also C hris top her S ma ll, Music

Society Educatzon (New York, 1977), pp . 45-47; Gregory Ba teson, Bali: Th e Value System

of a Steady State,

Steps to an Ecology of Mind

(New York, 1972), p. 86; and Colin McPhee,

Danc e in Bali, in

Trad itiona l Balinese Cul ture

ed . Jan e Belo (New York, 1970), p. 31 1.

onathan D Krarner 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,

Tim e and the Meanings of Mus ic

of which

the present essay is a part.





542

Jonathan D . Kram er New Temporalities in usic

of the a priori goal definition of the tonal system, cadences had to be

created c~ntextually.~hus 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 mus-

ical time nondirected linearityw-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

~ e n t u r y . ~

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 Schonberg's Cadences, Perspectives of New Music 16, no. 2 (Spring-

Summer 1978): 195-224. According to Ashforth, the primary factors that create cadences

in Schonberg'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.

Coals 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, 19621, 1:248-50 and 2:298-305), in what is aptly called a neotonal style,

or (2) contextually. I n 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 emehasis

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 ~ a c k ~ r o u n dnd 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 Schonberg's

S ec h Kleine Klavierstiicke

opus 19 (19 1 ), Erik Satie's

Socrate

(19 19), he first of Charles Ives'

Three Places in New England (191 I) , Edgard VarPse's Hyperprism (1923),Alban Berg's Cham-

ber Concerto (1925), Iannis Xenakis'

Syrmos

(1959),Aaron Copland's

Nonet

(1960),Luciano

Berio's Sequenza (1963), and George Crumb's Echoes of Time and the River (1968).



Critical Inquiry Spring 98 543

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.s 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 ex-

perience. Furthermore, radio, records, and, more recently, tapes allow

the listener to enter and exit a composition at will. An overriding pro-

gression 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 ins trum ents of the m arim ba, xylophone, an d g ong type. It is s ignificant that

Debussy was a composer in search of a new aesthetic, an escape from an overpowering

Wagnerian influence. H e was deeply attracted by th e gam elan because h e was ready fo r

its new world of sounds and time. See Small , Music Society Education pp. 103-8, and

Leonard B Meyer, Music the Arts, and Idem (Chicago, 1967 , p. 73.

8 See Robert F Morgan, "Spatial Form in Ives," and Neely Bruce, "Ives and Nine-

teenth Cen tury America," in

An Ives Celebration

ed. H. Wiley Hitchcock and Vivian Perlis

(Urbana, Ill. , 1977 , p p . 148-53 a n d 29-41,



544 Jonathan D. Kramer New Temporalities in Music

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-con-

sciously discontinuous moment forms shortly after his years of working

intensively in two early tape-music studios, in Paris and Co10gne.~ oday,

scarcely thirty years after tape technology first became available to com-

posers, extreme discontinuities are commonplace. The aesthetic of dis-

continuity has spread far beyond tape music. Composers of tape music

carry this aesthetic back into their instrumental writing, and even com-

posers 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 com-

fortable 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

ou r 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, 1963-7 l) , 1 189-2 10.



ritical Inquiry Spring

98 5 5

and to ou r obsession. A culture obsessed with time produces art obsessed

with time (and, of course, time-obsessed articles about that art).1°

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).12Such

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 reor-

der ing~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 poin ts , and on th e subsequent ideas on mult ip le t ime, to

Judy Lochhead. She read an earlier version of this article and offered many valuable

insights thr ou gh corres pond ence an d discussion. I am also indebted to her Th e Tem poral

in Beethoven's Op us 135: W hen A re End s Beginnings?,

I n

Theoq

Only

4 n o . 7 ( J a n u a r y

1979): 3-30. Th is article is in pa rt a response to my Multiple and Non-Linear T im e in

Beethoven's Opus 135, Perspectives of New Music 11, no . 2 (Sp ring -Summer 1973): 1 2 2 4 5 .

11. f irst discussed multiple time in Multiple an d Non-L inear Ti m e in Beethoven's

O pu s 135. While my use of the term multiple is essentially the sam e th er e an d in the

presen t essay, my use of nonline ar is m ore restricted now than earlier.

12. I have dealt with both these pieces in some detail. I elaborate on Mozart's wit in

Beginnings an d End ings in Western Art M usic (pa pe r delivered at the Fourth Trienn ial

Conference of the In ternat ional Society for the Study of Tim e, Alpbach ,

4

Ju ly 1979) . In

Multiple and Non-Linear Time,

I

discuss the first movement of Beethoven's last String

Qu ar tet , c it ing the occurrence of the f inal cadence in the ten th mea sure of the p iece, the

intertwining of two different strands of continuity, and the preparation of the climactic

recapitulation by thr ee se parate upbe ats, one far in advance of the climax a nd o ne actually

considerably after it.



5 6 Jonatha n D Kramer Ne w Temporalities in Music

porality in our time-obsessed culture, can find appropriately multiple

meanings in this music.I3

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.I4

But there

is

a handful of nontonal multiple-time music. Consider

the Schijnberg 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).I5

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. Ot he r examp les of tonal music in which m ultiple time can be readily heard include

the ope ning m ovements of Mahler 's Th ird (1896) and Seventh (1905) Symphonies , the

finale of Berlioz's

Symphonic

fantastique ( 18 30 ), Bee thoven's Creatures of Promethew Overture

(1801) an d t he f irst movem ents of his Sonata in E-flat opus 31 no . 3 (1803) and Q ua rte t

in B-flat opus 130 (1825 ).

14. I t is hard to imagine a n aesthetic that would produ ce, for ex am ple, Walter Piston 's

Fourth Sym phony (1950) an d also suggest tem poral reorderings.

15. Other examples of nontonal multiple-time music include the f irst movement of

Debussy's Strin g Qu ar te t (1893) an d , mor e significantly, his

ballet,]ewc (1913).,]ewc's often

fragm entary material, its freque nt changes of temp o, its nondevelopm ental for m , an d its

discontinuities m ade it a highly influential piece am on g the D arm stadt com posers (Stock-

hause n, Pie rre Boulez, H er be rt Eim ert, et al.) who were w orking self-consciously with

discontinuous time in the 1950s an d '60s. Am ong m ore recent m ultiple music are Edwin

Dug ger's Intermezzi (1969 ),a conscious attemp t to create multiple time in a non tonal idiom,

an d We're Late fr om L uka s Foss' Time Cycle (196 0). I am indebted to my s tudent Jo hn

Colligan for pointing ou t the multiple time in We're Late.



Critical Inquiry Spring

1981

547

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. 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 seem ar-

bitrary. 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 per-

formance to the next, perhaps within certain restraints.'

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 Schonberg 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 ex-

plained, 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. typical example of mobile form is Barney Childs tui for Cello 1 9 6 3 ? ) ,which

contains a nu mb er of f ragm ents to be read in any orde r by the per former . Also impor tan t

are Ear le Brown s Avail able Forms I 1 9 6 1 )and Stockhausen s Momente 1961-72) a n d Mixtur

1 9 6 4 ) .T h e latter is a particularly straightforward exam ple of a mobile form in mom ent

time.



5 8 Jonathan D. Kramer Ne w Temporalities in Music

performance. This ideal would indeed produce mobile multiple music.I7

However, the student compositions based specifically on this model none-

theless 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 un-

equivocally 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 de-

grees of discontinuity necessary for a successful moment form are dif-

ficult 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 W in d Instru-

ments 1 9 2 0 )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 s a moment form, albeit an early and impure example.Is

Its temporality belongs primarily to moment time because its sections

17. Perception of mobility on on e hea ring has perha ps been achieved in at least one

of Stockhausen's works, but for differe nt reasons. T h e time sense in

Zyk lw

(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. Edwa rd T. Cone has analyzed Symphonies in a ma nn er 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

suppor ts a moment- t ime hear ing of the work on a m iddleground level and a l inear hear ing

on the foreground and background levels. I am com fortable w ith this possibility, exce pt

that I d o not feel complete c losure at t he e nd (as Cone apparent ly does) , owing in large

part to the short, unpro long ed f inal tonic. Th is partial open -ende dnes s is quite ap pro -

priate in mom ent time. See Co ne, Stravinsky: T h e Progress of a Method, in Perspectives

on Schonberg and Stravi wky ,

ed . Benjamin Boretz and Co ne (New York, 1972), pp. 153-60,

and my Mom ent Form in Tw entieth Century Music, Mwical Quarterly 64, no. 2 (April

197 8): 181-87.



Critical Inqui7y Spring 19 81 5 4 9

are self-contained and because there is considerable discontinuity be-

tween them.Ig

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 andlor order of succession (despite its ap-

parent 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 mo-

ment 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 writ-

ten 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 nec-

essary 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

Oi se aw 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 Gray IstvPn 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.



55

Jonathan

D

Kramer New Temporalities i n Music

self-imposed boundaries is essential because any move outside these lim-

its would be perceived as a temporal articulation of considerable struc-

tural 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 undiffer-

entiated 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, im-

plication, 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

lattereZ2 nce 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'

ing

(1968)-at least as per form ed at Mills College in the late '60s.

Such music is dynamic a nd kinetic at the points whe re it redefines its world, and thus its

time se nse is not vertical.

22. One polemicist for the experimental in art argues that boredom is a necessary

an d positive com pone nt of the new art . See Dick Higgins, Boredom an d Danger,

foewk ombwhnw (New York, 1969).

23.

I

am indebted t o Don W alker for pointing ou t to me, somewha t inadvertently, the

necessity of a positive respon se t o what vertical music contains (as opposed to a negative

respon se conc ern ing such music's deficiencies ). I am also indebted to him for several

oth er perceptive com me nts on an earlier version of this article.



Critical Inquiry Spring 98 5 5

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. 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.24Other 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. T he 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 rela-

tionship 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 O n 1972i for solo cello, for example, each

event is carefully composed (by a statistically weighted computer program), but its rela-

tionship to any other event is left totally to chance.



55 Jonathan D. Kramer New Temporalities in Music

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. few

years ago, for example, I listened so often to the recorded (Mainstream

5005) realization of Cage s

Aria

(1958) performed simultaneously with

Fontana

ix

(1958) that I had quite literally memorized it. My knowledge

of what event was to follow lent a predictability to my listening experi-

ence: it seemed that event not only succeeded event but also that

implied 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 ex-

amples, could be heard as quite static. After all, it never leaves C major,

never leaves 414 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



Critical Inqui7y Spr ing

98

553

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 succes-

sion 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 (l951),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 W in d Instruments

an impure moment form, utilizes

moment time in the middleground as one section follows another with

considerable discontinuity. In the foreground, however, motivic, har-

monic, and voice-leading consistency produce continuity within the mo-

ments; 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-



554

Jonathan D Kramer New Temporalities in Music

directed linearity, is in a sense the opposite of the Stravinsky. It is non-

linear in the foreground (each note seems to have been generated sto-

chast i~al ly) ,~~inear 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 fun-

damental 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 de-

pendent on the nature of (or probabilities implied by) at least one pre-

vious 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

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 com positional process is rathe r com plex, altho ugh the au ral result

is still nonlinear in the fore gro und . See Xenakis, Formulized Mus ic trans. Christopher A.

Bu tchers (Bloo min gton, Ill., 19 71), pp . 79-109.

26. I am adap ting these ideas, with slight modification, from Chadabe. I have found

most useful his inform al discussions an d his From Simplicity to Complexity (pa pe r

delivere d at th e symposium Tim e in Music, Rhy thm, an d Percussion: East an d West,

Milwaukee, 9 March 1979). I am using choice he re as a me taphor. My interest is not in

the compositional act but in the perceptual act. If a composer consciously decides to opt

for a discontinuity so extrem e that i t could not have been forecast, the result m ight sou nd

nonline ar despite the compositional intention ality; if a random ized com positional proce-

dure produces stepwise adjacency of notes, we might well hear continuity despite the

compositional randomness.

T h e de pend ence 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 Le jaren A.

Ilil ler and Leonard Isaacson, Experimental Music (New York, 1959 ), pp . 22-35. For a brief

discussion o f the lim itations of app lyin g Ma rkov proc esses to musical analysis, see A. Wayne

Slawson's review o f

Computer Applications in Music Journal ofM usic T h eo ~y

2, no . 1 (Spr ing

1967): 149-51.



Critical Inquiry Spring

98 555

hierarchic levels up through the moment but not beyond. Vertical music

can be, paradoxically, totally nonlinear o r 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 ver-

tical 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 con-

siderable 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 progress-

ing 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 prob-

lematic for several reasons. First, the categories apply both to compo-

sitions and to listening modes, and these can be quite different; hence

the categories are not necessarily comparable. Second, distinctions be-

tween the varieties of temporality are not always readily made. For ex-

ample, 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 ~uccessively.~~

27. An ex am ple o f successive tem poralities is Messiaen s Cantkyodjayci

1948),

a well-

proportioned series of discrete blocks. Some of these blocks are clearly moments, but

other s are in motion toward goals fou nd in oth er, not necessarily ad jacent, sections. T h e

piece is not a pur e m om ent form b ut rat he r has elements of multiple time as well. In fact,

there is a recapitulation of the o penin g which so unds like a partially prep are d struc tural

downbeat , a gesture that would h app en in p ure l inear t ime.



6 Jonathan D Kramer New Temporalities i n Music

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 con-

temporary 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 s t r u c t ~ r e . ~ ~

Twentieth-century music has presented real challenges to our tra-

ditional ways of hearing. Critics often remark on experimentation that

has produced such formerly impossible compositional aesthetics as mo-

bile form, music in which the first or at least primary) act of composition

is the establishment of durational

proportion^,^^ 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 pre d i~ ta b le .~ ~o 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 prop osi ng a rigorous th eory of temporality. Rathe r,

I

am try ing

to suggest attitudes and modes o f unde rstand ing. T h e distinction is crucial. My emph asis

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 o n the categories themselves.

29. For a d iscussion of one type of precom posi t ion~ l ropor t ioning , see my Th e

Fibonacci Series in Twentieth-Century Music, Journal of usic T h e 9 17, no. 1 (Sprin g

1973): 118-32.

30. Process music is perhaps a desperate attempt to recapture linearity, or perhaps

it is conceived as ' 'n eo ~i ne ar it ~ comparable to the neomodality that often provides the

pitch language of trance pieces). But the listening experience is decidedly vertical.

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