The Musical "Culture of Time and Space"
The Culture of Time and Space: 1880-1918, by Stephen Kern, is a study of the changes in individual and societal perceptions of time and space in the years preceding and including World War I. Kern weaves an intricate fabric of ideas from contemporaneous architects, artists, politicians, authors, scientists, and philosophers. He concludes that the impatient ultimatums of the July Crisis of 1914, leading from the assassination of Archduke Ferdinand to the onset of the war, arose in part from a perception of greatly accelerated time, fostered by new technologies such as the telephone and telegraph. In addition, Kern asserts that the conflict was in many ways a Cubist war:
The psychological fragmentation experienced in no-man's-land during the war was but one of a series of shattered forms - national boundaries, political systems, social classes, family life, sexual relations, privacy, moral imperatives, religious convictions, human sensibilities.
Kern's multidimensional fabric is somewhat threadbare in the area of music. This article extends some of his ideas by relating them to music composed from 1900 to the present, and in addition it concludes by connecting them with the hierarchy of musical time presented by Jonathan D. Kramer.
Kern's book has three large divisions: time, space, and matters related to World War I. Those chapters concerning time include "The Nature of Time," "The Past," "The Present," and "The Future," after which a chapter on speed connects the sections on time and space. The chapters regarding space include "The Nature of Space," "Form," "Distance," and "Direction." Kern finishes his book with "The Temporality of the July Crisis," "The Cubist War," and a conclusion.
The first chapter considers numerous ideas, including public versus private time, Einstein and the theory of relativity, the relationship between the unconscious and time, the debate over whether time is atomistic or a flux, and the potential reversibility of time. This article examines these topics and also notions of positive negative space and time in connection with selected twentieth-century styles, composers, and pieces.
Kern initially presents the ideas of public and private time by showing their relationships to the telegraph, to precise military planning, and most especially to railroad schedules, which began to be coordinated according to Greenwich time in the year 1884. The private times of individual railroad stops had become so diverse by the late nineteenth century that some sort of coordination was necessary. The standardized public time established to align the schedules was adopted reluctantly at first; Kern details the gradual process of acceptance and alignment and demonstrates an increasing societal emphasis on public time and a corresponding decline in both the quantity and quality of individual private times. Some of the contemporaneous art and literature reveals a strong reaction against the authority of public time; Joyce, Proust, and Kafka enter into private, individual temporal worlds in Ulysses, Remembrance of Things Past, and The Trial. Public time is important in some styles of twentieth-century music; however, there has been a concurrent revolt against this standardization, and as a result the private times of individual composers and works are of increased significance in comparison to those of earlier generations.
This article's examination of musical public and private times begins with the Classical period. When temporal notions such as meter, rhythm, and proportion are integral components of a stylistic norm, this norm might be construed as representing the public time most characteristic of that music. Upon examining the music of Mozart, Haydn, early Beethoven, and other Classical composers, one sometimes considers how the expansion, contraction, or elision of regular phrases creates aberrations from normative four-bar phrases and eight-bar periods. In addition, the theorists at the time demonstrated how one might go about doing this. The alterations reflect a sort of "private time" evoked within the composition, conflicting with the "public" expectation of stylistic norms.
What is characterized here as the public time of stylistic norms continues into nineteenth-century music, where many compositions still exemplify the four- and eight-bar norms and theorists advocate them as models for both analysis and composition. This musical public time becomes less standardized in the later nineteenth century, particularly in the music of Wagner and his followers, and it is overcome by the private times of individual composers and styles in twentieth-century music. In addition to periodic structure, the public time considered here is related to common-practice tonal harmony, the chromatic domination and eventual collapse of which compelled composers to reconsider both tonal and temporal systems.
One way in which composers handled these decisions is by parodying public time, which may be categorized several ways: 1) deliberate irony or sarcasm; 2) brief quotations of earlier music; 3) quotation of an entire piece ("parody" in a manner like the parody mass); and 4) style parody, in which composers combine their ideas with some other (usually earlier) style.
The ironic, sarcastic type of parody is heard in works such as Parade by Satie, An American in Paris by Gershwin, or multi-media events of Laurie Anderson. The second type of parody, brief quotations of earlier music, is used in numerous twentieth-century pieces for a variety of reasons; just a few examples include the chorale sections from Berg's Violin Concerto, Schoenberg's Second String Quartet, Op. 10, movement II, and George Crumb's Ancient Voices of Children and Black Angels.
Parody of an entire composition or parts thereof, where the composer adds private touches to a previously composed, public object, is exemplified in Lucas Foss' Baroque Variations and in Stravinsky's Pulcinella and Le Baiser de la Fée. Many twentieth-century works include style parody, in which composers borrow the public time of earlier styles and superimpose their own ideas onto it; examples of this final type of parody include portions of Prokofiev's Classical Symphony, Berg's Wozzeck, Stravinsky's The Rake's Progress and Mass, and Bolcom's Ghost Rags.
What I am calling musical public time still exists in much twentieth-century music. Works by relatively rhythmically conservative composers such as Barber, Piston, Hanson, Persichetti, Rorem, Prokofiev, Hindemith, and Copland sometimes maintain an easily ascertained rhythmic and metric structure which evokes the public time of earlier stylistic periods. Works whose times are pre-compositionally determined, for example, multi-parametric serial works like Babbitt's Composition for Four Instruments, exhibit public times if the rhythmic structure is discernible. Jazz and rock often exemplify yet another variety of public time in repetitive patterns such as twelve-bar blues, improvisation over "I Got Rhythm" changes, or stereotypical progressions such as I - vi - IV - V in 1950s rock music. In addition, works which suggest timelessness to the Western ear - especially early minimalist pieces - exist in a non-teleological time which bears great similarities to public time conceptions in non-Western regions of the world. Continuing with Leonard Meyer's terminology, it appears safe to conclude that works which are less predictable and create and fulfill fewer expectations would be of a more private nature and take longer to be assimilated in the listener's mind than works in which a regular, stylistically predictable, more public time creates implications which are recognizably realized or refuted.
"Private time" in any work includes at least the temporal structure of the piece itself, that of the performer, and especially the qualities of time imposed on the piece by the listener. The temporal world of music is particularly fascinating because a work generally is not just an object, but a process through time which performers continually convey in different ways. In addition, an individual who reads a novel or views a work of art or sculpture has control over the time spent assimilating the work and determining meaning, while the time of most music moves forward regardless of the listener's level of comprehension. Thomas Clifton writes:
The responsive listener does not create the composition, but he constitutes it as meaningful for him...it is the listener's composition which counts for him. In short, order is constituted a priori by the listener, not imposed by the composer.
In a sense, there are as many works as there are listeners - both "private time" and experience differ for each listener, and sometimes change upon rehearing. Who has not returned after a period of some months or years to a Beethoven symphony or Bach fugue and heard it in a new light, with a different view of the structure of the piece? At the other extreme, works for which time should ideally be different upon rehearing, such as Cage's Aria with Fontana Mix, Stockhausen's Klavierstück XI, or Earle Brown's Available Forms I , become more predictable through repeated listening to the same recording. The process is complicated by the complexity of twentieth-century music, but the phenomenal world of the individual listener obviously influences the perception of any work.
The prodigious variety of twentieth-century musical styles is intimately related to the numerous new ideas of the time. For example, Kern states that the late-nineteenth-century theories of the physicist Hendrick Lorentz "looked forward to relativity by suggesting that time measurements are modified by motion," and that "there is a plurality of 'local times,' each dependent on the relative motion of the clock and observer." By 1916, Einstein had developed his theory of relativity to the point where "every reference body had its own particular time." When Kern adds: "Einstein had filled the universe with clocks each telling a different correct time," the rejection of Newtonian absolute time and analogies to music become more obvious. Polyrhythmic works and other pieces with the stratification of independent lines lie close to this relativity, but the best connection is to music by Elliott Carter, in which different lines have their own tempos. In the Second String Quartet, each line has its own character and temporal quality, and it is possible to listen to one line relative to the others. Each instrument is an individual musical clock, telling its own correct musical time yet integrated into the whole. Other Carter works, for example the Third Quartet, also exemplify this relativistic quality.
Many of the works of Ives conform to the paradigm of relativity, yet they also show some relationship with the unconscious. Freud's effort to penetrate the unconscious included experiments with free association, which in turn are reflected in the stream-of-consciousness literary style of the time, in works such as Joyce's Ulysses. Music of this era also exhibits some aspects of stream-of-consciousness; representative works include Debussy's Jeux and Soirées dans Granade or, in a different vein, Ives' Three Places in New England and Second Sonata for Violin and Piano, II ("The Revival"). Ives' music is especially appropriate to this analogy; his memories of town square concerts and parades are depicted in the juxtaposition of familiar melodic fragments in a sort of stream-of-consciousness style. In addition, Ives' music reflects public and private times in a unique way, in that his private memory and interpretation of events which transpired in a public time are incorporated into his works.
Philosophers and scientists working around the turn of the century argued about whether time was atomistic or a flux. Those who found time to be atomistic in nature cited Newton's calculus and even the mechanical ticks of the clock. William James and Henry Bergson were among those who argued for a flux. James coined the term "stream-of-consciousness," endeavoring to show continuous thought through this metaphor. Bergson defined his concept of "durée" through numerous metaphors, including a melody in which the notes dissolved or melted into one another. Impressionist and Cubist painters responded to these ideas, attempting to convey motion or the passage of time in works such as Nude Descending a Staircase by Duchamp.
Describing musical time as atomistic or a flux is an even more difficult matter. The problem is related to hierarchy: just how small must an "atom" be? How much music must occur before one hears a series of atoms as a flux? The individual notes in a melody do not literally dissolve into one another and thus the melody might be characterized as atomistic. Further, a stereotypical eight-bar period with antecedent and consequent phrases and a close on the tonic surely includes some aspects of musical flux, yet if it is put into a larger context it may be perceived as an atomistic closed unit. Another view might hold that the motive is the atom from which music is constructed. While these atomistic views of musical time are plausible, the idea of a thematic gesture - or even metaphors of musical motion such as Berry's reactive and anticipative impulses - present evidence of some sort of flux. In teaching theory and performance, once students comprehend the fundamentals of harmony, rhythm, and melody, one tries to discourage atomistic note-by-note interpretation, substituting notions of musical growth and direction to encourage more global understanding. Different twentieth-century styles exemplify varying points on an "atomistic-flux" continuum. The especially pointillistic works of Webern, Varèse, Cage, and others may sound atomistic, yet even they might be interpreted as points of sound on a background flux of silence - a notion examined later in this article. Works in which a quality of timelessness is evoked - Stockhausen's Stimmung, Terry Riley's Rainbow in Curved Air, early minimalist works by Glass and Reich - could still be viewed as atomistic in that individual notes and attacks create the seemingly timeless fabric. The notion of musical time in a flux, however, is more compelling in this music, in which past, present, and future are blurred and "vertical time" is created. It would appear that while painters were trying to depict motion and avoid stasis, composers were (and still are) striving for the opposite, endeavoring to negate impressions of forward-moving time and musical motion.
The potential reversibility of time was another fin-de-siècle topic of debate. Kern points out that "the cinema portrayed a variety of temporal phenomena that played with the uniformity and the irreversibility of time," and indicates that the first attempt at running film backwards took place in 1895. Whether or not this is possible in music depends in part upon the divisibility of musical and "clock" times. If the two are separable, then perhaps musical time may be reversed, even while clock time continues its inexorable march forward. Deep listening to reversed musical time is similar to deep viewing of reversed film: it may be possible to lose oneself in musical (or film) time and experience its reversal, even if clock time moves forward. It is undeniable that this powerful metaphor seemed to draw composers into the attempt to implant reversibility into their music. Webern's palindromes, used in works such as Symphonie, Op. 21, II, and in Piano Variations, Op. 27, I, are good examples of this fascination with the reversibility of time. A more powerful example is the film music from Act II of Berg's opera Lulu, which combines the reversibility of time in film (or, action) and in the music, resulting in a powerful impression of reversed time.
To sum up to this point, ideas such as public time and private time, relativity, the unconscious, time as atomistic or a flux, and the reversibility of time have been extracted from Kern's book and have been examined in terms of how they may be reflected in selected pieces or stylistic tendencies in twentieth-century music. Let us now examine how the concepts presented are evident in two compositions from different decades and by different composers: Stravinsky's L'Histoire du Soldat and Berio's Sinfonia, III. Stravinsky's L'Histoire du Soldat, composed in 1918, is directly related to parodied public time in that he borrows the public time of earlier styles and adds his own private touches to it. The parody begins immediately in "The Soldier's March," where the introductory three measures are an ironic, distorted version of a "typical" march introduction. The ostinato which begins at m.4 commences the public time of the march, onto which Stravinsky superimposes the private time of the changing ideas and lines. The relativity of the individual lines and the juxtaposition of different ideas create an image of multiple perspective similar to Picasso's paintings, yet the ostinato provides an underlying unity of borrowed public time.
The "Three Dances" exemplify a more straightforward style parody, borrowing the "public time" of the tango, waltz, and ragtime, yet they all include different private touches and surprises. The surprise in the tango begins immediately, as the written downbeat becomes an anacrusis when the stereotypical tango rhythm enters on beat two in the percussion. Throughout the tango, Stravinsky plays with the metric location of this pattern and with the distance between reiterations of it, taking a public time idea (most typically a regular two-measure unit, including a quarter rest after each statement) and altering it. The waltz, more straightforward metrically and rhythmically, borrows the meter and accompaniment of a typical waltz, and here it is the pitch (particularly in the melody) which is the private element. The irregular phrase structure is temporally "private," as are the surprises at several of the cadences (see the measures before rehearsal numbers 12 and 16). The ragtime, an early example of Stravinsky's fascination with jazz, is furthest removed from its stylistic model, juxtaposing sections which are rhythmically closer to the model (see rehearsal numbers 24, 31, 33, and 36) against those which diverge from it (see rehearsal numbers 27ff. and 34ff.).
Both "The Little Chorale" and "The Great Chorale" are additional examples of style parody. Here, Stravinsky pours new wine (the sonorities, counterpoint, and instrumentation) into old bottles (the borrowed public time of a chorale setting).
While the examples from L'Histoire exemplify style parody, the third movement of Luciano Berio's Sinfonia (1968) makes use of "public time" in a different way. Berio borrows the scherzo movement from Mahler's Second Symphony, establishing underlying continuity while portions of the text from Samuel Beckett's The Unnamable, other text quotations, and numerous musical quotations create extreme discontinuity. The combination of the Mahler and the quotations results in a special kind of private time which evokes the stream-of-consciousness: the abrupt juxtaposition of a variety of ideas and the ephemeral, almost subconscious recall of numerous musical fragments related in some way to the text. Berio writes:
Quotations and references were chosen not only for their real but also for their potential relation to Mahler. The juxtaposition of contrasting elements... can also be considered... a documentary on an objet trouvéJ recorded in the mind of the listener... One might describe the relationship between words and music as a kind of interpretation, almost a Traumdeutung, of that stream-of-consciousness-like flowing that is the most immediate expressive character of Mahler's movement. If I were to describe the presence of Mahler's "scherzo" in Sinfonia, the image that comes most spontaneously to mind is that of a river, going through a constantly changing landscape, sometimes going underground and emerging in another, altogether different, place...
The movement is a collage; Berio "assembles" the citations, expanding earlier composers' ideas of overlap (see, for example, the finale of Act I of Don Giovanni, where Mozart overlaps ideas in several different meters). The resulting texture is the agglomeration of the various lines and quotations; each of these lines has its own perceived tempo and character, creating a kind of musical relativity comparable in some ways to that of Elliott Carter discussed earlier.
The Stravinsky and Berio examples have more in common than might initially appear. Both contain surface discontinuities and non-developmental form (examples of "private time"), yet they also have underlying continuity created by the parodied public time: the style parody in "The Soldier's March," the three dances, and the chorales, and the parody of an entire composition in the Berio. They also exemplify the conflict between an atomistic conception of time and time-as-flux: the atomism is created by the juxtaposition of different ideas in the Stravinsky and by the numerous disjointed quotations in the Berio. The underlying flux in both works is created by the parodied public time: in the Stravinsky, it comes from the ostinato in "The Soldier's March" and from the continuity in the three dances; Berio conveys a flux by parodying Mahler. Both compositions contain the relativity of different lines and contrasting apparent meters, and both make interesting use of musical space, especially in the registral deployment of the various lines and quotations. This article continues with a brief digression about conceptions of space, followed by a concluding section concerning silence in music.
Kern discusses specific works where artists employ new conceptions of space, drawing upon such diverse ideas as Jacob von Uexküll's Umwelt und Innenwelt der Tiere, Einstein's field theory, and multiple perspective in painting. Von Uexküll's theory holds that each animal has its own surrounding world (Umwelt), and that its response to this Umwelt creates its special inner world (Innenwelt). Higher animals are able to mirror objects and spatial relations in the environment, and thus create a mirror or counterworld (Gegenwelt). The worlds vary with each animal and constitute different senses of space. J. T. Fraser has adapted these ideas into a hierarchical theory of time which is discussed later in this article.
As explained by Kern, Einstein's field theory disproved the idea that the electromagnetic field is to be regarded as a state of a material carrier. The field becomes an irreducible element of physical description. Everything is in movement throughout the field at the same time; space is full and dynamic. The universe is full of fields of energy in various states. Other scientists have presented the concept of a Brownian motion of countless particles moving in a gas or liquid, an idea discussed in a musical context by Leonard B. Meyer. Both the dynamic field and the Brownian motion are analogous to sound mass pieces by Varèse, Ligeti, Penderecki, and other composers. Varèse's blocks of sound (see Hyperprism, Ionisation, Arcana, and other works), attracting and repelling one another and recombining in various ways, depict fields of energy in various states, while Ligeti's mikropolyphonie (see Atmospheres, Lux Aeterna, and other pieces) is related to the Brownian metaphor, though his pitches and rhythms move less randomly than particles in a gas or liquid. A composition like Penderecki's Threnody to the Victims of Hiroshima would appear to be more random, given its greater freedoms of register and time; however, the quality of time heard in performance is only subtly different.
Special conceptions of space are a critical component of the art of the Cubists and of sculptures and architectural works created at this time. Fragmented discontinuities in paintings by Picasso, Braque, and others are well-known, as are comparisons of Picasso's spatial discontinuities and Stravinsky's temporal ones. The Cubists made use of multiple perspective and compound views of the same object, just as Schoenberg conceived of manipulations of the tone row as differing views of the same hat and Varèse made connections between musical structure and that of a crystal. Kern points out that many artists, stage designers, and sculptors of the early twentieth century were fascinated with positive negative space, in which negative (empty) space was surrounded by positive space in such a way that the previously empty area became an essential part of the work's meaning. Sculptures such as Woman Combing Her Hair by Alexander Archipenko, in which an arching arm frames the empty space that is the head, make use of positive negative space, while literary works by Mallarmé, William Carlos Williams, and others exemplify positive negative space on the page as well as positive negative time upon being read aloud. Kern is therefore positing three different categories of space (or time): positive, negative, and positive negative. Positive space includes substance and meaning, while negative space does not. Positive negative space is thus a special category: strictly speaking, there is no "substance" present, but the surrounding positive space gives this negative space meaning; thus, a label like "positive negative" is more appropriate than simply "negative."
Composers create positive negative time in music by using silence. A brief summary of three articles about silence in music is followed by a critical examination of Kern's notion of positive negative time.
Gisèle Brelet asserts that a background silence frames music, and in fact "always exists in music, actually or implicitly." This silence "protects music from all the exterior noises of the ordinary world." While Edward Cone and other writers have examined the role of the framing silence, the notion of an ever-present background silence may well be unique to this article. According to Brelet, this silence has a formal power, or power of determination, and may be "an obstacle breaking the forward movement of musical time." Expressive silences may be integrated into the form for punctuation purposes.
Thomas Clifton identifies three kinds of musical silences: temporal, spatial, and gestural. Temporal silences cut off a succession of events, and may be "hard-edged" as in rests in Mahler's Seventh Symphony and the accented rest in the development section of the first movement of the Eroica (see m. 280), or they may be "smooth," as in the sixth measure of Debussy's Prelude to the Afternoon of a Faun. Spatial silences include three subcategories: first, silences which highlight the arrival of another part or changed activity in one part (as in a line dropping out and reentering in a Bach fugue, or possibly, as Kern implies, as in Klangfarbenmelodie); second, large-scale connections (exemplified by the high A's in the introduction to the first movement of Beethoven's Seventh Symphony); and third, silences which create gaps or absences in registral space, going as far as disengaging silences like those at the end of Berg's Lyric Suite or Mahler's Ninth Symphony. Gestural silences are silences in motion, where melodic motion carries through the gaps written into the melody - these are determined only by listening, according to Clifton. His categories are a bit hazy and exhibit some overlap.
Zofia Lissa traces a dialectic of sound and silence through a multitude of styles and at various formal junctures, such as the pause before the onset of the second theme in sonata form or the silences between movements. She views Beethoven as using silences for suspense, while Chopin and Liszt make use of silences "bristling with expectancy." Lissa interprets silence in Impressionistic music as a "re-echo," in which the sound lingers in the memory until the next sound enters. In pointillistic twentieth-century works such as Webern's Pieces for Orchestra, Op. 10, no. 4 and Piano Variations, Op. 27, Lissa hears rests wrap around the sound figures. With the advent of electronic music and musique concrète, Lissa states that silences are used as a constructional element.
The notion of silences as a significant component in the structure and meaning of the work comes closest to Kern's conception of silence as positive negative time. In most works through the nineteenth century, the musical fabric was a continuum of sound, into which silences were incorporated as points of articulation, surprise, or for other reasons. Twentieth-century works, particularly those of the second Viennese school, alter the proportions of sound and silence to the point where there is a kinetic interplay between the sounds and silences. This interaction is important in compositions by Debussy and Schoenberg, as in Debussy's Prelude to the Afternoon of a Faun or Schoenberg's Sechs Kleine Klavierstücke, Op. 19. The proportion of silence to sound increases in music by Webern, Varèse, and Cage, to the extreme where in works such as Poème électronique by Varèse or Concerto for Piano and Orchestra (1951) by Cage, the fragments of sound appear to be tossed onto a background of silence, much in the way that Jackson Pollack threw paint onto a canvas. This analogy, however, points toward a contradiction in Kern's argument. The contradiction is related to meaning.
The meaning which the viewer or listener derives from the artwork does not generally come from the canvas or the background silence, but rather from the paint or the sound fragments - the positive space or time. The silences allow reflection and assimilation and influence the structure of a work, but generally the meaning is derived from the "positive" time or sound. In a sculpture like Archipenko's Woman Combing Her Hair, the negative space has meaning, but it is defined through the surrounding positive space. Similarly, if the silence has meaning, it is defined by the sound around it, even where there are far fewer sounds than silences. Kern finds important, meaningful silences in Webern's music, where isolated notes are surrounded by much silence, as in the opening of the Passacaglia, Op. 1.  Silences are important, but paradoxically, silence may well have more meaning where it frustrates an expectation (like the accented rest in the Eroica) where it is a more general background and one is not sure what to expect. Thus, negative space acquired more meaning (as defined by the surrounding positive space) in the early twentieth century, but negative time (or, silence) lost some of its meaning even while occurring more frequently, because there was less positive time (or, sound) to give it definition. Further, Kern states that the increased meaning of negative space levels the hierarchy of positive and negative space; what was simply negative space becomes positive negative space as its constituent function increases in importance. While this may be accurate, the assumption that the hierarchy of positive and negative time is leveled through increased meaning of negative time does not hold true if my idea of lost meaning is correct; positive time (sound) still has a more important role in creating meaning than does negative time (silence).
George Crumb is well known for his use of silence and for the quality of ritual time evoked in his works. His early composition Eleven Echoes of Autumn, 1965 (Echoes I) was completed in 1966, and although some consider it merely a study-piece for his Pulitzer Prize-winning Echoes of Time and the River (Echoes II), (1967), it includes interesting qualities of time at a variety of structural levels. The work is scored for violin, alto flute, clarinet, and piano, and it consists of eleven echi of varying lengths and instrumentation. At the foreground and middleground levels, time in this work is relatively discontinuous; however, the background level is unified by what Crumb calls a "larger expressive curve."
The pitch construction of Eleven Echoes is fairly simple: it includes what Crumb refers to as the "bell motif," which is a quintuplet figure consisting of one pitch then a reiterated pitch a whole step lower. The combination of the first two statements of the bell motif produces a (0, 2, 5, 7) tetrachord which is the basic set used throughout the work. In addition to the (0, 2, 5, 7) set, Crumb uses sets with direct intervallic relationships to it: the set (0, 1, 6, 7) is created by compressing the whole steps to half steps; the set (0, 1, 6), used in a typically Viennese trichord intervallic configuration, is a subset of (0, 1, 6, 7); finally, the whole-tone set (0, 2, 6, 8) is created by "expanding" the interior minor third of (0, 2, 5, 7) to a major third. These sets are used most frequently in the work; they contribute to time at the largest scale in that Crumb uses the more "diatonic" sets [(0, 2, 5, 7) and (0, 2, 6, 8)] at the opening and conclusion of the work, reserving the more "chromatic, dissonant" sets [(0, 1, 6, 7) and its subset (0, 1, 6)] for the climactic middle portion of the piece.
The idea of time is a critical component of the piece's overall shape. Crumb writes that the work is based in part upon the Federico García Lorca quote "...y los arcos rotos donde sufre el tiempo" ("...and the broken arches where time suffers"). Crumb finds numerous ways to make time "suffer" throughout the work; the most prominent technique is the use of long pauses within (and sometimes between) the various echi. In addition to the pauses, Crumb creates echoes (and thus the distortion of time) within a single instrument, between two instruments, and by using sympathetic vibrations. The piano creates its own echoes through the use of dynamics and register in echi one and four, while the alto flute and clarinet share in creating echoes in several of the echi. As he does in some of his other compositions, Crumb has the wind players play into the piano with the sustaining pedal depressed, thus taking advantage of the sympathetic vibrations produced. He uses this effect in echi four, eight, and nine; it literally creates a quality of "re-echo" in which the sound lingers. One might go so far as to state that the pauses and sympathetic vibrations do create some sense of positive negative time, where the silences contain meaning, if for nothing else than reflection and savoring the pitches, registers, and timbres used.
Crumb creates a variety of times at a higher structural level. The entire work is placed upon a background of silence, as the opening emerges out of silence while eco eleven gradually recedes into nothingness. Crumb creates groupings of echi by arranging that some be followed attaca by the next; they are echi 1, 2-4, 5-8, and 9-11. Echi 5-7 form the midpoint, and each is an accompanied cadenza (alto flute, violin, and clarinet respectively). The notation of the solo lines (many short staves rather than fewer long ones) as well as the accompaniment (circular notation which proceeds halfway clockwise then reverses itself counterclockwise) represents "the broken arches where time suffers." The climax of the work is eco eight, after which there is a gradual dissolution into silence. The overall arch shape is created through dynamics, grouping, register, rhythmic intensity, an overall pitch shape of diatonic-chromatic-diatonic, and even conceivably through lighting. One possibility given by the composer is:
A deep blue lighting at the beginning; then very gradually (almost imperceptibly) brightening until reaching a fiery red at the beginning of eco 8; then very gradually dimming until reaching total darkness at the beginning of eco 11.
The overall arch shape of the work is concluded by eco eleven, where the bell motif recurs in its original diatonic configuration. Even at this point, time is still distorted, as the pauses between statements of the bell motif continually increase in duration, leaving one unsure when or if the bell motif will be heard again. The composition merges with the background silence from which it began. Despite the distortion and the suspended moments it has suffered, time continues.
A great number of ideas have been considered; in particular, this article has examined the relationships between some twentieth-century music and public and private times, relativistic time, and positive negative space and time. A variety of new musical temporalities emerged in the twentieth-century; these temporalities are explored in this article and investigated in a different fashion in Kramer's book The Time of Music. At its conclusion (see pp. 394-97), Kramer summarizes J. T. Fraser's hierarchical theory of time, which received its impetus from von Uexküll's theories mentioned earlier in this paper. Kramer then draws analogies between Fraser's theory and his own ideas about musical times in twentieth-century music, as shown in Table 1.
Time Characteristics Musical Time
Atemporality no past, present, or future; Vertical time
no before or after
Prototemporality events not necessarily simultaneous; Moment time
temporal position not that important
Eotemporality direct causation, but one cannot Multiply-directed time
tell which is cause and which is effect;
succession is meaningful, but
direction is not
Biotemporality rudimentary consciousness; dream Non-directed
world; unconscious mind; linear time
Umwelt of animals
Nootemporality personal identity; free will; Linearity
Umwelt of man
Sociotemporality Umwelt of cultures and civilizations (see below)
The lower levels are more concerned with being - with the unchangeable, with the eternal - while the upper levels involve becoming, the changeable and the temporal.
Fraser postulates that time has evolved and progressed to higher levels; however, the levels are nested and the higher ones still contain the lower. If in fact nootemporality is the Umwelt of man and if Kramer's idea that the musical time associated with it is linearity is correct, then linearity would be the most "public" of musical times. Therefore, Kramer's assertion that twentieth-century composers are exploring lower levels of time might also be construed as an exploration of the many categories of private time presented in Kern's book and in this article.
Kramer also states that sociotemporality has little role in Fraser's theory and does not have a formal musical metaphor; this conclusion may underestimate the importance of sociotemporality. Fraser refers to it as the Umwelt of cultures and civilizations; its science is sociology. If in fact this is the case, would not its musical science be ethnomusicology? Further, might sociotemporality tie the other Umwelts together? If different cultures and civilizations emphasize the other five levels of temporality to varying degrees, then sociotemporality would be that public time which is the combination of the other levels. One dichotomy which comes to mind is that of circularity versus linearity. If the dominant metaphor in Eastern religions is circularity, while in Western religions it is linearity, would this not be reflected to some extent in their overall cultural approaches to time? Spirituality is a private, personal matter, yet even if one chooses not to participate in a given faith, the times evoked in the religions practiced by the majority may become "public" and influence the time perception of entire cultures and civilizations. Therefore, when composers explore levels of time other than those emphasized by their own cultural contexts (in particular, Western composers exploring Eastern qualities of time), they are working with different levels which are created in part by contrasting sociotemporalities. The resulting music begins to create a transcultural sociotemporality, in which the public times of various spiritualities and cultures are combined with the private times of individual composers and listeners in exciting and innovative ways.
Philip Alperson, "'Musical Time' and Music as an 'Art of Time'," Journal of Aesthetics and Art Criticism 38, no. 4 (Summer 1980): 407-17.
Peter Altman, Sinfonia von Luciano Berio: eine analytische Studie (Vienna: Universal Edition, 1977).
Luciano Berio, record liner notes for Berio, Sinfonia, recorded by the New York Philharmonic and Swingle Singers, Luciano Berio conducting, Columbia records MS 7268.
Wallace Berry, Structural Functions of Music (Englewood Cliffs: Prentice Hall, 1976.
Gisele Brelet, "Music and Silence," trans. Suzanne Langer in Reflections on Art, ed. Suzanne Langer (Baltimore: Johns Hopkins Press, 1958): 103-121.
Thomas Clifton, Music as Heard: A Study in Applied Phenomenology (New Haven: Yale University Press, 1983).
Thomas Clifton, "The Poetics of Musical Silence," Musical Quarterly 62, no. 2 (April 1976): 163-81.
George Crumb, record liner notes written for the Aeolian Chamber Players recording of Eleven Echoes: CRI recording number CRI 233 USD.
Stephen Kern, The Culture of Time and Space: 1880-1918 (Cambridge: Harvard University Press, 1983).
Marianne Kielian-Gilbert, "The Rhythms of Form: Correspondence and Analogy in Stravinsky's Designs", Music Theory Spectrum 9 (1987): 42-66.
Jonathan D. Kramer, The Time of Music (New York: Schirmer Books, 1988).
Zofia Lissa, "Aesthetic Functions of Silence and Rests in Music, " trans. Eugenia Tarska, Journal of Aesthetics and Art Criticism 22 (1964): 443-54.
Leonard B. Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956)
Leonard B. Meyer, Music, the Arts, and Ideas (Chicago: University of Chicago Press, 1967).
Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition (Cambridge and London: Harvard University Press, 1990).
 Philip Alperson examines the idea of separating musical time from other "clock" times in "'Musical Time' and Music as an 'Art of Time'," Journal of Aesthetics and Art Criticism 38, no. 4 (Summer 1980): 407-17. He concludes that music is an "art of time," but that it does not have its own separate "musical time." For a different perspective, see Kramer, The Time of Music, Chapter 1, especially pages 5-6. Regardless of one's position on this matter, one may still separate the public time of stylistic norms from the private, individual times of the composer, performer, and listener.
 For an elegant discussion of parody, borrowing, influence, and a variety of other topics see Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition (Cambridge and London: Harvard University Press, 1990).
(Englewood Cliffs: Prentice Hall, 1976).
 See Marianne Kielian-Gilbert, "The Rhythms of Form: Correspondence and Analogy in Stravinsky's Designs," Music Theory Spectrum 9 (1987): 42-66, for details on the motivic and temporal structure of "The Soldier's March."
 See Peter Altman, Sinfonia von Luciano Berio: eine analytische Studie (Vienna: Universal Edition, 1977) for further information on the movement, including a complete list of musical quotations and a detailed chart of the texts used.
Suzanne Langer (Baltimore: Johns Hopkins Press, 1958): 103-121.
 Kern examines changes in conceptions of form, demonstrating that the Cubists made an assault on closed form and tried to eliminate the frame. Further, certain Futurists and stage directors attempted to break down the separation between the stage and the audience, in a way much like Cage later endeavored to destroy this barrier in musical "performances." See Kern, The Culture of Time and Space, 196-201.
(April 1976): 163-81.
 Crumb uses the singular "eco" and the plural "echi" in discussing the piece on the score. These notes are derived from the liner notes written for the Aeolian Chamber Players recording of the work: CRI recording number CRI 233 USD. Crumb's spellings are adopted here, and all references are to these notes.