sign in sign up
<<
Home , Anton Webern, Gavin Bryars, Gruppen, John Cage, Julio Estrada, Kaija Saariaho

Maja Trochimczyk From Circles to Nets: Thornton School of University of Southern , California 90089-0851, USA On the Signification of [email protected] Spatial Sound Imagery in New Music

As Bas van Fraassen observes in his introduction to Escape. the philosophy of time and space, ‘‘with respect to The flight engenders a vertigo of multiple else- space, it is not easy to make a plausible prelimi- wheres. nary list of basic relations’’ (van Fraassen 1985). Here . . . There . . . (Dhomont 1991) And yet we try: the number of studies of spatial Espace/Escape brings together the immensity and topics has gradually increased with the ever- intimacy of the human experience of space. Sounds growing variety of thematic subcategories and from various acoustic environments, ranging from types of approaches. In the domain of music, theo- a bird’s cage (the flutter of wings) to an airport rists like to discuss ‘‘musical space,’’ usually equat- lobby (the muffled din of footsteps and conversa- ing it with a two-dimensional pitch-time space, not tions and the noise of the airplanes’ engines) are the space of (e.g., Kurth 1969, origi- juxtaposed with synthetic sonorities in complex, nally published 1931; Bernard 1983, 1987; Lerdahl evolving formations that defy description. This in- 1988; cf. Harley 1994a). In the area of electroacous- stance of contemporary musique concre`te draws tics, we deal with sound projection spaces and from the acoustic physicality of human life and composed spaces, the latter being integral to the from the exploration of spatial dimensions of compositions themselves. Still different types of sounds possible in acousmatic projection, ‘‘the di- spatial imagery are represented by sonorities or mensions of volume, of near and distance, of front hinted at by the works’ titles (e.g., Krzysztof and back, left and right’’ (Gue´rin 1991). Penderecki’s Dimensions of Time and , 1961; Witold Lutosławski’s Les espaces du som- meil, 1975; Kaija Saariaho’s Lichtbogen, 1985– Spatial Designs 1996; ’s Space Testing, 1977). In other words, there are a plurality of ‘‘spaces’’ Space may be experienced only in time, and time that might be associated with music. An insight only in space. It is important to note that music into this diversity of spaces is provided by Francis drawing the space of performance into the realm of Dhoˆ mont’s poetic program notes for his electro- meaningful elements, that is, ‘‘spatial or spatialized acoustic composition Espace/Escape (1989), which music,’’ is really ‘‘spatio-temporal’’ and not ‘‘spa- has the word ‘‘space’’ in its title and explores the tial.’’ The categories of spatialization may seem to associative and symbolic aspects of space and belong outside of time, but their realization is al- movement: ways temporal. For instance, the perceptual experi- ence of musical layers originating from different Space. spatial locations involves the awareness of their Open, intimate, confused spaces. Broken succession and simultaneity. Several factors have a spaces, whirling. bearing on the classification of musical-spatial de- Indecisive edges of the space. signs (see Table 1). Firstly, these designs are not Space-refuge, enclosed, maternal, space of rem- purely geometrical as they are realized in sound. iniscence and of associations. ‘‘Space’’ in music is neither empty, nor absolute, Tumult or murmur in the space of a thousand nor homogeneous; it is revealed through the spatial reflections. attributes of sound matter. Secondly, the human auditory perspective constitutes an essential ele- Journal, 25:4, pp. 39–56, Winter 2001 ment of spatial arrangements. If, for instance, ᭧ 2001 Massachusetts Institute of Technology. groups of musicians are scattered in the hall, their

Trochimczyk 39

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Table 1. General classification of spatial designs Acoustic environments Enclosed space of the concert hall Enclosed space of any other kind Open air (different acoustic backgrounds) Variable space ( performers and audiences) Private, virtual space (headphones) Sound-space types Real sound-space (with vocal-instrumental sound sources) Virtual sound-space (with electroacoustic sound sources) Mixed sound-space (with sound sources of both kinds) Categories of mobility Static performers and static audience Mobile performers with static audience Static performers with mobile audience Mobile performers and mobile audience

distribution among listeners is more important per- able for in which all conven- ceptually than their exact balance of and tions and limits are contested. At the other volume. The performance and perception of spatial- extreme, that is, in conventional concert music, ized music takes place within certain acoustic en- the spatial character of compositions in which the vironments, and the choice of these conditions musicians are placed traditionally on the stage may may be part of a composition. Moreover, even the be easily overlooked. Obviously, works in which same acoustic environment may be perceived from the is split into several separate ensem- different auditory perspectives that vary because of bles are spatialized. However, it may suffice to the mobility of performers and listeners. have a large number of divisi parts (as in Ligeti’s From the acoustic point of view, there is a differ- micropolyphony) to obtain a spatial texture, ex- ence if one listens to music in a concert hall, any tended and varied within the confines of the stage. other space, such as that of the home, during an In Ligeti’s micropolyphony, the sonorities are si- open-air concert, while changing one’s surroundings, multaneously ‘‘quasi-spatial’’ (i.e., they are extended or via headphones. If such an environment is speci- in pitch/time space, from the lowest to the highest fied by the who forbids the performance sounds played simultaneously), and they are ‘‘spa- of the music otherwise, it belongs to the composi- tial’’ (i.e., they are extended on the concert stage, re- tion. Examples of this type of spatialization may be sounding from a three-dimensional section of the found in works by John Tavener (the requirement of hall). When writing for orchestra on the stage and a at least 6 sec of reverberation for Ultimos Ritos, large number of performers, e.g., or 1972) and R. Murray Schafer (see Harley 1997b, , are actually using the perfor- 1998b). mance space to create sonorities that are spatially Another aspect of musical spatiality, the mobil- extended in a physical sense. (There is a perception ity of the performers or audiences, is frequently of the ‘‘width’’ of sound, as well as—for listeners lo- problematic. The wealth of possibilities created cated closer—its ‘‘depth’’.) This physical spatiality is here is limited by the theatrical character of the not indicated in the score of a work written for div- performer’s movement in music. When the impor- isi instrumentalists, as it is taken for granted. tance of the musicians’ actions overshadows that of Postwar avant-garde composers were preoccupied the sonorous results of these actions, music is with geometric abstraction (in an anti-romantic transformed into musical theatre. Therefore, the vein) and with suffusing such abstract designs with movement of the audience forms a category of spa- a secular mysticism (e.g., Xenakis 1971). The new tialization rarely employed in the concert hall. The sound material was imagined as objective and rigid noisy informality of mobile listeners is more suit- ‘‘matter’’ devoid of all mutability of emotion—

40 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Table 2. From point to sphere: positions of the performers forming simple geometric patterns, with representative compositions Point Any music for a centrally located, stationary soloist (e.g., an instrumentalist or singer) Line Segment ’s Car nos vignes sont en fleur (1981) for 12 voices in a linear arrangement on the stage Two Line Segments Two groups facing each other from a distance in ’s Hoketus (1975) Triangle Three instrumental ensembles in ’s of (1955–1957) or in ’s Alax (1985) Square Four choirs in Stockhausen’s Carre´ (1959–1960; see Figure 3); also a diamond shape, such as the three wind bands and a steel drum in Henry Brant’s Hidden Hemisphere (1992) Hexagon Six percussionists in Xenakis’s Persephassa (1969) Circle See the list in Table 3 Cube Julio Estrada’s Canto Naciente (1975–1978) for eight brass instruments Sphere Stockhausen’s (1970) for one performer, to be played inside the spherical pavilion in Osaka with electroacoustic sound projection in space

lines, blocks, volumes, and sound masses (Rochberg perceived as if it resounded from a point (i.e., as if 1963; Harley 1998a). Interestingly, Henry Brant, an it were purely temporal, with a spatial dimension American composer of ‘‘,’’ had little of zero), to the full three-dimensionality of sounds appreciation for such geometry in sound: surrounding the listeners from all sides. (Table 2 presents a selection of examples; for a study fully Ideas of that kind seem to me more an expres- based on the growth of dimensions ‘‘from point to sion of hope than of reality. . . . It is hard sphere,’’ see Harley 1993.) Because the point has no enough to make the sounds do what you want volume, it is bodiless; it may easily represent the ‘‘in sound’’ without saying that the sound situation in which the spatiality of music is irrele- should be shaped like a pretzel or something vant. The sphere symbolizes the opposite. Here, like that (Brant 1992; see Harley 1997a). music is perceived in the entirety of its spatial– Spatial designs based on sound location in the temporal presence surrounding the listeners with a performance space may be classified on the basis of multidirectional pattern of sounds. Note that the principles borrowed from the mathematical theory image of the sphere is an idealization implying a of dimensions. Engelking’s topological study re- stationary audience located within a spherical en- veals the multidimensionality of mathematical closure, or a single listener limited by a particular spaces, with the number of dimensions varying hearing range which extends equally in all direc- from zero (e.g., a point), through one (e.g., a line tions (Ihde 1976). The standard concert hall does segment), two (e.g., a square), three (e.g., a cube), not create conditions for such equidistant location and N, to an infinity of dimensions (Engelking of sound sources, and spatial imagery is usually 1977). However, the existence of fractal dimensions ‘‘fractal’’—that is, fragmented, non-linear, and not of various sizes in mathematics (e.g., a curved line easily described. that fills in a plane and has a fractional dimension A survey of the repertory of spatialized music re- between one and two; cf. Mandelbrot 1982) sug- veals the continuous hold of geometry on the imag- gests that spatial dimensions of a similar complex- inations of composers. The compositional use of ity may exist also in music. spatial distribution may be inspired by geographic The basic typology of musical-spatial designs re- or architectural shapes. In Charles Hoag’s Trom- flects the straightforward growth of the number of bonehenge (1980), for instance, 30 sur- dimensions from zero to three—from point to round the audience in a pattern imitating the sphere—from music without spatial characteristics, outline of the ruins at Stonehenge. Spatial designs

Trochimczyk 41

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 1. The circle as semiotic object.

the mystical (the sacred images of the Sun in many religions; the ‘‘mandala’’; the circular Host, or Eu- charist, in Roman Catholicism). The circle seen as a pure circumference divides the world into two non-homogeneous domains (inside and outside), and it may signify order, unity, hierarchy, and fo- cus (see Figure 1). The megalithic Stonehenge (Atkinson 1987) and the circles or ‘‘medicine may also be motivated by the intent to portray or wheels’’ made by the Indians of the Plains (e.g., evoke mythical, ritual, or imaginary spaces. The lat- Bighorn Medicine Wheel in Wyoming) are both ter option appears in ’s The Sinking of structured on a circular plan. Moreover, both sites the Titanic, a conceptual work-in-progress begun in have a marked point of focus in the center (serving 1969 (Bryars 1975). Bryars considers an impossible as a focus and an orientation point) and radial arms situation: what if the music, supposedly resounding connecting the center with the periphery. Thus, at the bottom of the North Atlantic Ocean for over both forms articulate the most complex spatial ar- 60 years, could have been refloated? Thus, the music rangement associated with the image of the cir- supposedly played by a band on board while the Ti- cle—one that may signify spiritual focus (center) tanic was sinking (performed by an ensemble of in- and hierarchical ordering (the circumference as the strumentalists) is surrounded with musical glosses border of ‘‘within’’ separating what is on the inside associated with memories of the survivors, the titles from the outside). The shape of the circle could of hymns played by the band, and so forth—- also be seen as non-emotive, scientific, abstract, formed, pre-recorded sounds heard from various loca- and pure, cleansed of all imperfections. Perhaps tions in space. The hymn played at the moment of this is one of the reasons of its attractiveness for the sinking undergoes timbral transformations that modernist composers. suggest four stages in its imaginary history: ‘‘as heard in the open air on the deck, as the ship sinks, as it Interestingly, the of renaissance remains stable on the bottom of the ocean, and in a canons often includes the geometric shape of the new state in the open air’’ after the ship’s raising circle (cf. Besseler and Gu¨ lke 1973). The four-part (Potter 1981). canon by Bartolome Ramos de Pareja (ca. 1440– The works by Hoag and Bryars mentioned here 1491) found in the manuscript from the Biblioteca draw from two basic types of geometric designs: the Nazionale Centrale in Florence provides the music circle and the net, respectively. In the remainder of for an illumination by Gherardo and Monte da Gio- this article, I will address these two types of geomet- vanni del Fora. In the design reproduced here as ric designs, each bearing a range of semiotic and sym- Figure 2, the images of the four winds (Oriens, Oc- bolic associations: the circle (and, by extension, the cides, Meridion, Septetrion) are placed at points-of- sphere) and the net (or web, of a greater spatial com- compass on the circle (the stave is circular) and plexity and multi-dimensionality). An indirect inspi- represent the singers and the entry-points of their ration for this study was provided by a reading of parts. Their positions form a diamond that supports Gaston Bachelard’s The Poetics of Space (Bachelard the musical circle of the canon. During a perfor- 1967/1969) and Henri Lefebvre’s The Production of mance (quite likely without an audience and for a Space (1991)—two vastly different studies of the personal enjoyment only), the musicians would meaning of humanly constructed (or imagined and sing while standing around the manuscript. There- described) spaces. fore, the notation simultaneously indicates the temporal circularity of the canon and the spatial Circles and Their Meanings circularity of the performers’ locations. The shape of the circle is continuous and topo- The circle has a variety of symbolic connotations, logically equivalent to a triangle, square, rectangle, ranging from the familiar (‘‘a circle of friends’’) to ellipse, or any other continuous, closed shape. The

42 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 2. Four-part canon zionale Centrale, MS. by Bartolome Ramos de Banco Rari 229, fol. C. Pareja (ca. 1440–1491, III.b). Florence, Biblioteca Na-

musicians, however, may only form ‘‘discrete’’ ar- living border around the audience, and all the lis- rangements, and composers have used various ap- teners are inside the circle, immersed in sound. proximations of the circle by placing several groups The number of compositions based on circular of performers symmetrically around the audience plans in performance space increased after World (see Table 3 for examples). For some reason the War II with the growing interest in the spatializa- composers have favored even numbers, using four, tion of time (discussed next) and the geometriza- six, eight, or twelve groups to suggest the shape of tion of sound; a sample is included in Table 3. the circle and to allow for the creation of various Time in music becomes ‘‘spatialized’’ when it is patterns of sound distribution and movement. No- notated and measured. Here, the condition of being tice that in these designs, the performers form a spatial is associated with being static and measur-

Trochimczyk 43

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 3. Rectangular per- formance plan of Stock- hausen’s Carre´ (1959– 1960).

ence may also create dramatic and expressive cli- maxes in ‘‘purely musical’’ compositions (e.g., Xenakis’s Nomos Gamma and Persephassa, dis- cussed in Harley 1994b). Finally, the idea of immers- ing the listeners in stationary, circular sound fields may have quasi-mystical overtones, as this design serves to evoke other-worldly stillness and to induce a state of contemplation (e.g., Stockhausen’s Carre´ and Schafer’s Credo, discussed below). These geo- metric patterns are endowed with a symbolic func- tion. Works with varied and unusual placements of performers are often meant to communicate some- thing, to convey a message through the articulation of sound in space. Notice that in the phrase ‘‘sound in space,’’ both nouns are in singular form, without any descriptive characterization. This is the domain of the ‘‘absolute’’ or ‘‘abstract’’ space (Lefebvre 1991). It is empty and non-inhabited by difference; it is emptied of the cultural plurality of the past, and ready for a new content, perhaps of a mystical na- ture. able; musical spatiality is considered to be identical In some spatial works, based on the framework with temporal stasis. According to Theodor of the circle, simplicity and uniformity of musical Adorno, the music of Debussy and Stravinsky material are accompanied by a ‘‘mystical’’ inten- (which often lacks development and direction) is tion of the composer who attempts to influence the inherently spatial (Adorno 1966; Adorno 1972). mental state of the listeners. Enveloped in sonori- Such music, constructed from static blocks of ties, surrounded by sounds, the audiences are led sounds, is analogous to painting. Adrono’s descrip- on a path to contemplation or even trance, result- tion of ‘‘withdrawal of time into space’’ prefigures ing from a confluence of musical and spatial fea- later conceptions of temporal stasis, including the tures. term ‘‘spatialization of time’’ used by European avant-garde composers such as Hans Eimert and Gyo¨ rgy Ligeti in reference to the music of Anton Karlheinz Stockhausen von Webern (see Eimert 1958, Ligeti 1960/65). These composers construed Webern’s compositions An early example of a ‘‘continuous’’ sound-space as consisting of configurations of points and blocks approximated by a square appears in Stockhausen’s of sound in a ‘‘pseudo-space’’ (a term from Eimert), Carre´ for four orchestras and choirs with four con- which is either flat as a surface (pitch/time) or ductors (1959–1960). The four groups of musicians three-dimensional. An important attribute of this are located at central points of the sides of a rectan- spatial image is the perceived stasis and rigidity of gular performance space (see Figure 3). Vocal and the musical building blocks; here time has lost its instrumental sonorities are integrated into one fluid, ever-changing character captured in the an- static sound world, realizing the composer’s wish cient Heraclitean metaphor of the ‘‘river.’’ that ‘‘this music should give a little inner stillness, The effect of surrounding listeners with sounds breath and concentration’’ (Stockhausen 1964). The may serve a programmatic purpose (e.g., the apoca- temporal stasis of Carre´ is a consequence of the lyptic of the Last Judgement in Berlioz’s music’s slow , the absence of meter, and the Requiem, Op. 5). Sound rotations around the audi- frequent use of long, motionless chords. It also

44 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Table 3. Circles: selected compositions Composer Composition Notes Kazimierz Serocki Continuum for six percussionists (1965– With optional designs including a circle 1966) around the audience Iannis Xenakis Terretektorh (1965–1966) for 88 performers Circular design on the plane (circumference, dispersed among the audience (see Figure interior) 5); Nomos Gamma (1967–1968) for 98 musicians dispersed among the audience Karlheinz Stockhausen Spiral (1970) for one performer for the Designs and movements within the interior spherical pavilion in Osaka; pieces with of the sphere rotating sounds, recorded with his ‘‘rotating loudspeaker system’’ Zina’s Circle from Sonic Meditations (1972) For any number of ‘‘meditating performers’’ placed in a circle, holding hands (voices and gestures) John Tavener Ultimos Ritos (1972; see Figure 6) With multilevel spatial designs including the cross and the circle; a circle of male singers facing the center, chanting a prayer R. Murray Schafer Credo from Apocalypsis (1976–1977; see For 12 choirs located on a circle, symbolic Figure 4) color robes, light effects, and four-channel tape; mystical text by Giordano Bruno Henry Brant Orbits (1979) For 80 trombones around the audience Charles Hoag Trombonehenge (1980) For 33 trombones surrounding the audience

results from the work’s . Carre´ con- figure of the square, the spatial extension of the sists of 101 self-sufficient moments and nine inter- choirs and their locations in the centers of each ludes, which, like the interludes in Gruppen for wall allow us to consider this ‘‘square’’ an approxi- three orchestras (Harley 1993), exploit various pat- mation of the circle. Both figures are topologically terns of sound rotation. The circular motion con- equivalent; moreover, the composer frequently in- nects the four groups in a clockwise or troduces circular patterns of movement. His idea of counter-clockwise direction. In addition, Carre´ surrounding the listeners with static sounds also presents a variety of spatial configurations, often relies on the metaphor of the circle. linking two or three of the distant ensembles in A similar diamond shape placing four instrumen- crisscrossing patterns. Considering the mysticism tal groups in a point of compass arrangement is of sustained sonorities in Carre´, it seems not acci- used in Henry Brant’s Hidden Hemisphere (1992; dental that Karlheinz Stockhausen’s drawings illus- see Harley 1997a). There is almost no attempt to trating the serialization of spatial location in his unify the music by shared textures, keys, or harmo- article ‘‘Musik im Raum’’ resemble the shapes of nies in this work; unlike Stockhausen, Brant does the sacred sites of the Plains Indians (i.e., a wheel not try to ‘‘square the circle.’’ with spokes) or a mandala (Stockhausen 1961; see Harley 1993, 1998a). His attempt to ‘‘square the circle’’ with four choirs resembles the model used R. Murray Schafer for the renaissance canon described above; the crea- tion of a virtual circle is only possible if the ensem- Another example of a work using an approximation bles play one after another and share musical of a circle by an even number of ensembles and material. connecting circular design with mysticism is While Stockhausen’s composition is based on the Credo, the second part of Apocalypsis (1976–1977)

Trochimczyk 45

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 4. The placement of choirs and color scheme for R. . Schafer’s Credo (1976–77).

The universe is ‘‘all that exists’’ (No. 1), it is ‘‘infi- nite in extent, immobile in time’’ (No. 2), it ‘‘has no parts yet it contains all parts. . . . It is formed yet it is formless. It is end yet unending’’ (No. 9). The universe ‘‘has no before, after or present. It has no up, down or position’’ (No. 10). In the universe, ‘‘point does not differ from circumference, finite from infinite, maximum from minimum. There- fore, the universe is all centre yet nowhere centre, and all circumference yet nowhere circumference’’ (No. 11). The universe is one: ‘‘one act, one form, one soul, one body, one being, the maximum and only’’ (No. 12). This image of unity and perfection is, perhaps, best approximated by a circle, which does not favor any of the points at its circumfer- ence. The music of Credo attempts to portray the calmness of heavenly bliss following the turmoil of the last moments of existence of this world. Ac- cordingly, it presents ‘‘motion within tranquility’’ and follows a simple overall dynamic pattern: all by Canadian composer R. Murray Schafer. This the invocations are sung forte, while the responses piece, crossing the border between music and thea- show a gradual dynamic increase. In addition, as ter, is ‘‘intended to be performed in a large church Schafer writes, ‘‘within each response the dynamics or cathedral, or failing this a large hall with a mini- should be exaggerated to create the impression of mum of four seconds of reverberation’’ (Schafer the sound shifting from to choir; this is a 1981). Credo is scored for 12 mixed choirs sur- structural feature of the work’’ (Schafer 1986). The rounding the audience, and it may be performed as invocations resound from a semicircle, and their an independent concert piece. It is very slow and positions gradually shift around the audience. They almost trance-like. As the composer explains: ‘‘I are rather brief, and apart from the gradual shift in wanted the musicians to surround the audience, location along the circle, do not contain many of they also describe patterns—like the cross or the the spatial effects which Schafer includes in the re- star—in the music’’ (Schafer 1992). In terms of spa- sponses. Here, minute dynamic fluctuations result tial design, Schafer replaces the Biblical model of the city of the saved described at the end of the from the use of a set of dynamic envelopes (pat- book of Revelation (i.e., the square or cube, with terns of crescendo and decrescendo) that depend on twelve gates symbolizing the twelve tribes of Is- the order and type of the consonants and vowels in rael) with a large circle formed by twelve choirs each syllable of the text. This dynamic variability around the audience (see Figure 4). enriches the texture of dense sound masses but is While retaining elements of St. John’s apocalyp- detrimental to the perception of sound movement tic vision, Schafer rejects his text describing the around the hall, requiring a specific type of overlap- city sheltering all the redeemed in the eternal pres- ping crescendi. (Schafer also used these patterns in ence of God, replacing it with a pantheistic creed North/White; cf. Harley 1997b, 1998b.) In Credo, by Giordano Bruno. The text of Credo is divided this effect is possible if the successive voices sing into twelve identical invocations (‘‘Lord God is the same syllable with a crescendo. Universe’’) and twelve responses that complete the All through Apocalypsis Part Two: Credo, the repeated, opening statements in a number of ways. voices blend with pre-recorded bell sounds. To cre-

46 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 ate an illusion of the immateriality and omnipres- concert hall into the spiritual domain of Christian- ence of these sounds, the loudspeakers are hidden ity. According to the composer’s biographer, behind the performers around the auditorium. (The Stephen Adams, ‘‘Schafer’s Jerusalem is surely a four-channel tape may be projected from more than heaven for the faithful only, for others would find four loudspeakers.) The composer intends to create it intolerable—a 46 minute expanse of nearly fea- a continuous, ‘‘uniform, wrap-around sound’’ that tureless, interwoven sound’’ (Adams 1983). would support and enrich the static sonorities of This motionless music also ‘‘touches the outer lim- the choirs but not compete with them. The sound its of the possible’’ in the domain of spatialization. material of the tape part consists of ‘‘filtered bells Schafer intends to create patterns of crosses, stars, from Salzburg Cathedral, recorded in 1975 by the and so on, using voices from certain choirs only. World Project’’ (Schafer 1986). The fil- The audibility of these patterns, perceivable on pa- tering is gradually released, and, at the conclusion per, is doubtful. Following Schafer, several other of this 46-min piece, the bells are heard in their composers attempted to link circular shapes with natural form and ‘‘surge forward to overwhelm the mystical themes and subjects, including Bronius choir.’’ Kutavicius, Adriana Ho¨ lszky, and John Tavener The presence of recorded sounds in the two parts (see Table 3). of Apocalypsis as well as many of Schafer’s other large-scale spatialized works may seem like a con- tradiction of his views. The composer has been Iannis Xenakis quite critical of the schizophrenic ‘‘split between an original sound and its electroacoustical trans- The complexity of the relationship between the mission or reproduction’’ underlying the depen- performers and the listeners increases when the or- dence of musical culture on electricity (Schafer chestra and the public are scattered on one spatial 1977). In an interview I conducted with him in plane. Here, as in circular arrangements, the audi- 1992, Schafer cited ecological reasons for his objec- ence is ‘‘inside’’ the music. Nonetheless, the musi- tion to loudspeakers: cians do not create a continuous border separating the audience, immersed in sounds, from the out- I object to amplification of sound, often to side world. In this arrangement, listeners have overpowering degrees that are threatening us unique aural perspectives based on their positions all with deafness. It also bothers me a great relative to each performer. This arrangement ap- deal when I think of the way that the whole pears in Xenakis’ Terretektorh and Nomos Gamma Western European tradition is plugging itself (cf. Harley 1994b, 1998c). In both of these large- into electricity, because the assumption that is scale compositions, the orchestra and the public being made is that there is always going to be a are placed within a circular performance space. constant supply of electricity. . . . I think that In Terretektorh for a large orchestra of 88 players if there was a real energy crisis so that there scattered among the audience (1965–1966), the in- was no more electricity our whole Western strumentalists are divided into eight groups, A to musical tradition would disappear. It would be H, filling out a circular performance space framed vaporized like a whiff. There would not be any by three percussionists placed in a triangular for- music left apart from what we still could play mation (see Figure 5; Harley 1993 and 1994b). This on acoustic instruments, which is less, and arrangement removes the psychological and audi- less, and less all the time (Schafer 1992). tory separation of the listener from the performers Yet he has used recorded sounds to realize his seated on stage. The proximity of the sound creates programmatic goals and to expand the virtual space a new aural experience strengthened by the move- of music. In Credo, the sounds of bells recorded at ment of sound masses in space and enhanced by the Salvator Mundi cathedral in have the the novelty of the sound itself. The musicians are same function: to take the listeners beyond the required to play, besides their normal instruments,

Trochimczyk 47

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 5. Formation of per- formers in Xenakis’s Terre- tektorh (1965–1966).

four percussion instruments each: wood-block, masses, rolling one against the other like siren-whistle, maracas, and whip. Here, according waves (Xenakis 1971). to the composer: The ‘‘sound masses . . . roll like waves’’ as a re- The orchestra is in the audience and the audi- sult of Xenakis’ technique of virtual sound move- ence in the orchestra. . . . The scattering of the ment that involves ensemble dispersion, dynamic musicians brings in a radically new kinetic shading, and temporal overlapping of sounds. Sta- conception of music. . . . The composition will tionary instrumental groups are placed around the thereby be entirely enriched . . . both in spatial audience and successively play sounds of the same dimension and in movement. The speeds and pitch and timbre with similar dynamic envelopes accelerations of the movement of the sounds (crescendo–decrescendo; see Harley 1993 and will be realized, including logarithmic or Ar- 1994b). The sound seems to rotate in space, gradu- chimedean spirals in time and geometrically ally shifting from one instrumental ensemble to . . . [as well as] ordered or disordered sonorous another. The perception of this effect is very frag-

48 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 ile; it depends on the position of the listener and and love’’ and places them in the two high, circular the quality of performance—that is, the placement galleries around the bottom of the cupola to repre- of the groups, the exact matching of pitch, timbre, sent the heavenly elevation of Christ descending to dynamics and so forth. This effect, first used in earth in the Eucharist. The Eucharist ‘‘descends’’ in Karlheinz Stockhausen’s Gruppen fu¨ r Drei Orches- response to an ardent prayer by twelve basses, ter (1955–1957; Harley 1993), appears also in his placed in a circle directly below the cupola and Carre´ for four orchestras and choirs (1959–1960), R. chanting a poem by St. John of the Cross. The sing- Murray Schafer’s Credo, and many other pieces. ers surround the instrumentalists who articulate So far, I have focused on circular designs that lo- the symbolic ‘‘descent’’ in the second part of the cate the audience within the circle. This is the tra- second movement, subtitled ‘‘El descenso de la Eu- ditional arrangement for spatialized sound caristia.’’ This descent takes the form of an alterna- projection in . Nonetheless, it tion between the elevated and floor-level is not the only option for creating circles in sound. instruments of the same timbre. Six trumpets, lo- The audience itself may also form the circle, for in- cated in the highest possible gallery surrounding stance, when they are both performers and listeners the central cupola of the building, and six recorders as in Pauline Oliveros’s Zina’s Circle from Sonic placed in a lower gallery play a slow sequence of Meditations (1972). Here, an unspecified number of chords three times before it starts to resound from performers (participants in a workshop) is asked to the ground, performed by trumpets and flutes lo- hold hands and squeeze them while uttering a sud- cated directly below the cupola (see Figure 6). den scream—passing the sound on, as it were, with These sections are interrupted by music from the the gesture. The screams travelling around the cir- timpani, trombones, and organ, instruments that cle provide a sonorous link between the partici- outline the shape of a cross on the horizontal pants; the simultaneous gestures and sounds are plane. the material of this meditation. In Ultimos Ritos, Tavener creates a rare musical instance of spatial motion in the vertical direction. At the same time, the interlocking designs of a ver- John Tavener tical descent and a horizontal cross represent a theological statement that the incarnation of The last option is one in which the listeners are lo- Christ (i.e., the living Eucharist) was completed by cated outside the circle and observe it from a dis- His crucifixion. Nonetheless, the auditory realiza- tance. In this case, the circular designs may be tion of such complex geometric designs, easily con- linked with other spatial forms. In the second veyed in musical notation, may be quite movement of John Tavener’s Ultimos Ritos (1972), problematic. In Tavener’s piece, for instance, a lis- dedicated to St. John of the Cross, the circle co- exists with the shape of the cross. Both images con- tener seated near the entrance to the church—at tribute to the religious of the music. the bottom of the cross, as it were—will recognize The contour of the cross, a standard floor plan in neither the circular arrangement of the distant many churches, provides the basic architectural de- singers, nor the shape of the cross outlined by the sign. Tavener writes, ‘‘the proportions of the work placement of the timpani. Thus, Tavener’s compo- are those of a cross, and so is the layout of the sition illustrates the perceptual fragility of spatial choirs and some of the instruments’’ (Tavener designs and the dependence of their symbolic inter- 1974). The circle is located around the central point pretation on notation (i.e., the graphic images of of the cross, where its arms join together; it also the cross and the circle included in the score). Si- denotes the location of the cupola above the sanc- multaneously, Ultimos Ritos reveals the complex- tuary in the cathedral. This circular design plays a ity of the coexistence of various aspects of very peculiar role in the music. The composer asso- spatialization in one work (e.g., the choice of the ciates the recorders and trumpets with ‘‘royalty acoustic environment of the church, the realization

Trochimczyk 49

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 6. Placement of per- formers in Tavener’s Ulti- mos Ritos (1972).

credited with the invention of this type of perfor- mance , thus describes the behavior of the audi- ence in ‘‘Diary: Audience 1966’’: An audience can sit quietly or make noises. People can whisper, talk, and even shout. An audience can sit still or it can get up and move around. People are people, not plants (Cage 1967). Cage’s multimedia not only allow but require the mobility of the audience witnessing simultaneous performances of independent musi- cal, theatrical, and visual works. In Musicircus (1967), Reunion (1968), and HPSCHD (1967–1969), the spectators are free to wander around and experi- ence various aspects of the whole event, or perceive one of its elements from different aural and visual perspectives. Their behavior results from the abun- of events to observe. The musical anarchy of HPSCHD and the audience’s anarchic behavior are of geometric images in music, and the location of consistent with Cage’s political preoccupations of performers in a three-dimensional space). the time. In this ‘‘five hour multi-media extrava- ganza’’ (Pritchett 1993), created by Cage in coopera- tion with , up to seven harpsichords Nets and Human Chaos play different music at the same time (works by Mozart, Mozart transformed by Cage, etc.). The Composers of contemporary concert music rarely harpsichords are accompanied by the simultaneous allow their audiences to wander around in their playback of up to 51 tapes, each presenting the mu- tightly controlled designs. In the words of Iannis sic in a different tuning system. The individual lay- Xenakis, the composer of Terretektorh and Nomos ers are almost inaudible in the total din of Gamma in which the audience was dispersed in be- simultaneous sonorities. tween the orchestra, on one circular plane: Cage’s chaos results from his concept of compos- The problem is that when people move around ing as being ‘‘non-intentional’’ and is, perhaps, the they cannot listen in the same way, they do most radical example of a musical use of a complex not concentrate on the music. They do not network of sonorities, consisting of numerous know how to pay attention while walking and sound sources and layers (see Andriessen in Tro- they do not notice the fact that when they chimczyk 2002a). Such plurality of elements is one change position they have a different aural per- of the characteristics of the spatial design of a net, spective caused by the difference in location. which may be described as providing only the ‘‘in- Besides, they are distractive, they annoy other side’’ (there is no circumference and no outside). people who are listening, when they move (Xe- The net, consisting of a potentially unlimited num- nakis 1994). ber of interconnected nodes, stands for chaos and complexity, but also for equality and the lack of hi- The listeners enjoy such freedom, though, during erarchy and centralized focus. Without a center, performances of conceptual works or multimedia the net does not have a super-structure; it is essen- events held in unusual locations: art galleries, mu- tially egalitarian in its nature and capable of infi- seums, outdoor spaces. , who is often nite expansion.

50 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Net-based designs underlie the chaotic happen- mitted to different cubicles or rooms ings of Cage and experiments with performance connected to each other. By walking through formats in which the traditional form of the con- the space each listener creates his own version cert has disappeared. In these ‘‘centerless’’ spatial of the piece (Krauze 1988). designs, musical performances can take place out- This work, known in Polish as Rzeka Podziemna doors or in unusual spaces, as in Brant’s Brand(t) and in English as Underground River, premie`red at aan de Amstel, a site-specific composition for four the 1987 Rencontres Internationales de la Musique boatloads of flutes floating through the canals of Contemporaine, in Metz, France. In La rive`re sou- Amsterdam and encountering multiple ensembles terraine, each of the seven pairs of loudspeakers dispersed throughout the city (1984). The informal, emits music performed on a different instrument outdoor performances often transform musical (transformed electronically), and one to three of works into theatrical actions or acoustic explora- these sources may be heard simultaneously. The tions (e.g., ’ series of Listen. Field listeners may dwell in some of the cubicles filled Trips thru Found Sound Environments of 1966– with music, return to ones already visited, or 1968). Here, the division between performer and in one of the intermediary spaces and enjoy the audience disappears, standard musical notation mixture of the neighboring musical layers. The du- gives way to written instructions, and the ‘‘supra- rations of individual segments depend on the dura- temporal’’ musical work is replaced with a process tion of the listeners’ presence in each cubicle, and or an action that cannot be repeated twice in the the dynamic proportions shift while they walk. same way. The increasing mobility of participants Therefore, what listeners hear depends on their di- in such ‘‘musical’’ situations is associated with pro- rection and speed of walking. Although the idea of found changes in the understanding of music, its a complex space consisting of many interconnected artifacts, and its social contexts. elements (i.e., an open network) provides the foun- Even without chaos encountered during such dation for Krauze’s spatial experiments, its roots egalitarian peregrinations of the public—implicit in are firmly planted in his modernist idea of the such musical experiments—music may reflect the ‘‘unitary composition’’ (kompozycja unistyczna) spatial shape of a net and, by doing so, reflect the inspired by the constructivist theory of a Polish growing awareness of the network-like structure of avant-garde painter, Władysław Strzemin¯ ski the physical and human worlds. Selected designs (Trochimczyk 2002b). Krauze’s ‘‘unitary’’ composi- by John Cage, , Henry Brant, Adriana tions, for example Piece for Orchestra No. 1 (1961), Ho¨ lszky, and Marta Ptaszyn¯ ska are listed in Table consist of static textures and exemplify the idea of 4; they provide instances of the heterogeneity of the musical form based on the absence of contrasts musical material (one of the conditions for a net- and changes. Gradually, the composer modified like design) and of the diversity of its interconnec- these ‘‘unitary’’ works into richer, more complex tions. compositions by the addition of spatial features In Zygmunt Krauze’s La rivie`re souterraine (i.e., the distribution of musicians or sound sources (1987), the public is invited to wander around a in performance space) and by the increased density specially designed architectural space (a series of of the material. cubicles connected in a labyrinthine pattern) and A link between the two designs discussed in this listen to music broadcast from several loudspeakers article—the musically unified circle and the net- placed at various points of the space (see Figure 7). work of contrasting elements—can be found in According to the composer, the architecture fulfils Krauze’s Feˆte galante et pastorale (1974–1975). ‘‘the role of an instrument’’ (Krauze 1988). The This composition is scored for 13 chamber ensem- composer describes his spatial compositions as con- bles and 13 tapes performing simultaneously in a sisting of: series of 26 halls of the Eggenberg Castle in Austria simultaneous performances of live and re- (Festival Steirischer Herbst). The halls are con- corded music with unlimited duration, trans- nected in a circular pattern so that the visitor may

Trochimczyk 51

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Table 4. Nets: selected compositions Composer Composition Notes Henry Brant Millennium II (1954) for ensemble A ‘‘spatial assembly’’ for 10 trumpets and 10 trombones placed along the walls of the hall, 8 horns, 2 , and 4 percussion players on the stage and a high voice located anywhere at a distance from the stage and the brass (preferably in a high balcony) Voyage Four (1964) for , 83 instrumentalists and one singer dispersed on several chimes, and timpani levels in the concert hall: on two balconies at the back (flutes and voice on the higher balcony, other woodwinds and strings beneath), on two side balconies (24 along the wall of one balcony and eight with eight along the wall of the other), under the overhang of the back balcony (low-pitched instruments: double basses, contrabassoons and ), on the stage (three separate groups: three trumpets with three trombones on the right, four horns on the left, ‘‘ 6’’ of keyboards and percussion in the center), high up above the stage (the location of the organ pipes) and in three places under vents in the floor John Cage Musicircus (1967); Reunion (1968); Audiences free to wander in the performance space with HPSCHD (1967–1969) a variety of events taking place simultaneously Marta Ptaszynska Space Mobile (1974) for two Increasingly dense material recorded and projected from percussionists and tape the stage Adriana Ho¨ lszky Die Wa¨ nde (1993–1995) Opera after Jean Genet’s Les Paravents and based on the idea of a ‘‘holographic multi-dimensional sound space’’ with ‘‘each image closed-in-itself’’ and separated from the others by the ‘‘composed-out screens’’ Pierre Boulez Re´pons (1981–1988) For six instrumental soloists (surrounding the audience), instrumental ensemble of 24 musicians (in the midst of the audience), and electroacoustic equipment to process and spatialize the sound (including two sets of six loudspeakers on the outskirts of the performance area; see Figure 8) Gavin Bryars The Sinking of the Titanic A conceptual work-in-progress begun in 1969 Zygmunt Krauze La rivie`re souterraine (1987) Electroacoustic installation on a complex spatial plan (see Figure 7)

walk around the whole building and experience a circle and the net coexist in a work of modernist music that ‘‘inhabits’’ the space. The musicians roots and experimental sensibility (terminology play in every other hall along the circular pattern, from Nyman 1974, also used by Nicholls 1990). and each of these spaces has its own distinct mu- Krauze’s other spatial works have been presented sic. The circularity of the audience’s movement in art galleries, not concert halls. In this setting, it and of the overall design of the architectural space is possible to consider constellations of loudspeak- is coupled with the non-uniformity and non- ers as unusual works of art (Raaijmakers, Bruyne`l, continuity of the sonorities that are placed and ex- and Struycken 1971). Here, musical sounds without perienced in this space. Thus, the elements of the definite temporal envelopes exist in space in a

52 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 7. Architectural space of Krauze’s La rivi- e`re souterraine (1987).

pons refers to a form of plainchant in which the so- loist (individual) alternates with the choir (collective). Boulez’s work explores various types of responsorial dialogues among the individual - ists and the ensemble, the instrumental sounds, and their electronic transformations. This interplay of acoustic and electroacoustic sonorities is only partly notated in the score. The audience surrounds the central instrumental ensemble and is, in turn, encircled by six soloists and two sets of six loud- speakers—one set for the amplified sounds of the soloists and one for the sounds processed electroni- cally (see Figure 8). The transformation, distribu- tion, and ‘‘spatialization’’ of sounds is computer- controlled. Only the soloists’ sounds are diffused (amplified or processed and dispersed into space by means of two sets of six loudspeakers surrounding the performance area). Spatial distribution of in- strumentalists and loudspeakers is an essential component of the work’s concept. Boulez thus describes his intention: ‘‘I do not want my audience to look at music from a distance quasi-objective, reified manner; they are continu- but to be involved and immersed in the music’’ ously present in the segments of space. Thus, elec- (Boulez 1992). The composer compares listening to troacoustic installations approximate the mode of his work with the lived experience of architecture. existence of Satie’s musique d’ameublement. In ad- The awareness of a building as an architectural dition, Krauze’s spatial music shares vital charac- work of art entails more than seeing it from the teristics of spatialized music as exemplified by Ives outside. One must be conscious of the interior to and Brant. This music consists of many simultane- walk through the different rooms, see their propor- ous layers separated in timbre, pitch material, and tions and qualities, and fully experience the archi- spatial location. The perceptual freedom of the tecture from a mobile point of view. This does not static listener in Brant’s music, for example, im- mean, though, that the audience should walk plies shifts of attention from one sound layer to an- around during the concert. Instead, Boulez proposes other. Krauze externalizes these shifts into motion listening to Re´pons several times, from different lo- in performance space filled with either live or re- cations. Only then can the liveliness and richness corded sound. of the spatial interactions between the various ele- Since Vare`se’s De´serts, the juxtaposition of in- ments of the music be fully experienced. strumental and electroacoustic sounds within one musical work has posed problems for composers. The mutual relationship of the two types of sonori- Conclusion ties may range from total opposition (as in De´serts) to smooth blending (e.g., Verblendungen for or- To conclude this overview of some implications of chestra and tape by Kaija Saariaho, composed 1982– spatial patterns and designs used by contemporary 1984). Pierre Boulez’s Re´pons (1981–1988) for six composers, I would like to pose some general ques- instrumental soloists, an instrumental ensemble of tions. Is a search for the mystical circle indicative 24 musicians, and live electronics creates a middle of a need to return to hierarchy and order after the ground between these extremes. The title of Re´- ‘‘fall’’ of and the failure of ? Can

Trochimczyk 53

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Figure 8. Placement of per- formers in Boulez’s Re´pons (1981–1988). LS and ls re- fer to two sets of loud- speakers.

circular, static, and trance-inducing patterns of man existence. Let me conclude this survey of sound provide an actual and lasting spiritual illu- some of these meanings and associations by stating mination, or are they just illusions of composers? that the avant-garde rejection of standard setting of Do chaotic and egalitarian networks of sounds and the concert hall for the sake of circular spaces and patterns frighten? Are they rejected owing to lack musician/audience placement patterns as well as of order, organization, and control? Finally, what the fascination with technology that could replace are the lasting artistic results of all this spatial ex- and surpass humans (i.e., the geometry of sound, perimentation, or was it all done only for the—by the precision of computer generated sound synthe- now irrevocably past—present? sis, and spatial sound projection) was not innocent. Numerous compositions explicitly devoted to It did, perhaps, express a hope that, as a result, the the subjects of sound in space have appeared since listeners would come and worship the novelty of the 1960s and continue to grow in number; several sound in space in quasi-Stravinskian ‘‘mystical cir- festivals dedicated to this theme have been orga- cles of the young girls’’ or ‘‘spring rounds.’’ nized (see Graham 1983; Giuliani 1988; Gelhaar 1991; Kupper 1988, 1991). Often, as recently in Santa Barbara at the Sound in Space Symposium, References the ‘‘sound’’ is as abstract as the ‘‘space’’ that ap- pears in the symposium’s title. Yet spatial designs [Editor’s note: In 2001 Maja Trochimczyk legally bear their meanings, the multitude of cultural asso- changed her name from “Maria Anna Harley” to ciations accumulated through the centuries of hu- honor her Polish parents, Henryka and Aleksy Tro-

54 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 chimczyk. The writings of M. A. Harley and M. Tro- 1950).’’ Canadian University Music Review 13:123– chimczyk have been authored by the same person.] 144. Adams, S. 1983. R. Murray Schafer. Toronto: University Harley, M. A. 1994a. Space and Spatialization in Con- of Toronto Press. temporary Music: History and Analysis, Ideas and Im- Adorno, T. W. 1966. ‘‘U¨ ber einige Relationen zwischen plementations. Ph.D. diss., McGill University. Musik und Malerei.’’ In Festschrift fu¨ r Daniel Henry Harley, M. A. 1994b.’’Spatial Sound Movement in the In- Kahnweiler. Stuttgart: Verlag Gerd Hatje. strumental Music of Iannis Xenakis.’’ Journal of New Adorno, T. W. 1972. Philosophie der neuen Musik. Music Research 23(3):291–314. Frankfurt am Main: Ullstein. Harley, M. A. 1997a. ‘‘An American in Space: Henry Atkinson, R. 1987. Stonehenge and Neighboring Monu- Brant’s ‘Spatial Music’.’’American Music 15(1):70–92. ments. London: English Heritage. Harley, M. A. 1997b. ‘‘Ritual und Klanglandschaft: Zur Bachelard, G. 1967/1969. The Poetics of Space, trans. M. Musik von R. Murray Schafer.’’ MusikTexte 67/68 Jolas. Boston: Beacon Press, 1969. (January):23–34. Bernard, J. W. 1983. ‘‘Spatial Sets in Recent Music of Harley, M. A. 1998a. ‘‘Spatiality of Sound and Stream Elliot Carter.’’ Music Analysis 2:5–34. Segregation in 20th-Century Instrumental Music.’’ Or- Bernard, J. W. 1987. The Music of Edgard Vare`se. New ganized Sound 3(2):147–166. Haven: Yale University Press. Harley, M. A. 1998b. ‘‘Canadian Identity, Deep Ecology Besseler, H., and P. Gu¨ lke. 1973. Schriftbild der Mehrs- and R. Murray Schafer’s The Princess of the Stars.’’ In timmigen Musik. Leipzig: VEB Deutscher Verlag fu¨r H. Jarviluoma and R. M. Schafer, eds. Soundscape Musik. Yearbook. Tampere, : University of Tampere, Boulez, P. 1992. ‘‘Space and Spatialization in Music: In- pp. 119–142. terview with Maria Harley.’’ Unpublished interview, Harley, M. A. 1998c. S¯ wiat Xenakisa. Special issue of Po- tape transcript, . lish Musicological Quarterly / Muzyka 43(4). Brant, H. 1992. Unpublished interview with the author, Hoag, C. 1980. Trombonehenge for 30 Trombones. Bryn , tape transcript. Mawr, Pennsylvania: Theodore Presser. Bryars, G. 1975. ‘‘The Sinking of the Titanic. Composer’s Ihde, D. 1976. Listening and Voice: A Phenomenology of Notes.’’ Soundings 9. Sound. Athens, Ohio: Ohio University Press. Cage, J. 1967. ‘‘Diary: Audience 1966.’’ In A Year from Krauze, Z. 1988. La Rivie`re souterraine. Architecture so- Monday. Middetown, Connecticut: Wesleyan Univer- nore. Program notes from the 31st Festival of Contem- sity Press, pp. 50–51. porary Music, September 1988, ‘‘Warsaw Autumn,’’ Dhomont, F. 1991. ‘‘Espace/Escape.’’ Cycle de l’errance. Warsaw, Poland. Sound recording. Montreal: Diffusion iMe´dia IMED Kupper, L. 1988. ‘‘Space Perception in the Computer 9607. Age.’’ In F. Dhomont, ed. L’Espace du Son I. Revue Eimert, H. 1958. ‘‘A change of focus.’’ In No. d’Esthe´tique Musicale. Ohain, Belgium: Musiques et 2, . Bryn Mawr, Pennsylvania: Theodore Recherches, pp. 58–61. Presser. Kupper, L. 1991. ‘‘The Well-Tempered Space Sound In- Engelking, R. 1977. Teoria wymiaru (Dimension Theory). strument. A New Musical Instrument.’’ In F. Warsaw: PWN. Dhomont, ed. L’Espace du Son II. Revue d’Esthe´tique Gelhaar, R. 1991. ‘‘Sound-Space: An Interactive Musical Musicale. Ohain, Belgium: Musiques et Recherches, Environment.’’ In S. Montague, ed. Live Electronics. pp. 92–98. London: Harwood Academic Publishers. Kurth, E. 1969. Musikpsychologie. Hildesheim: Georg Giuliani, R. 1988. ‘‘Festival Spaziomusica 1987 Cagliari Olms Verlag. 29 –28 XI 1987.’’ Rivista di Musicologia Italiana Lefebvre, H. 1991. The Production of Space, trans. D. 22:118–120. Nicholson-Smith. Cambridge: Blackwell Publishers. Graham, D. 1983. Pavilions. Catalogue of the exhibition Lehrdahl, F. 1988. ‘‘Tonal Pitch Space.’’ Music Percep- 12 March-17 April at the Kunsthalle, . Three in- tion 5(3):315–349. stallations presented at the Kunsthalle, Bern. Ligeti, Gyo¨ rgy. 1960/65. “Metamorphoses of Musical Guerin, F. 1991. ‘‘Un Espace Mental Favoriser.’’ L’Espace Form,” Die Reihe no. 7, 1965 (originally in German, du Son II. Ohain: Musiques et Recherches. 1960). Harley, M. A. 1993. ‘‘From Point to Sphere: Spatial Orga- Mandelbrot, B. 1982. The Fractal Geometry of Nature. nization of Sound in Contemporary Music (after New York: W.H. Freeman.

Trochimczyk 55

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021 Nicholls, D. 1990. American Experimental Music, 1890– Schafer, R. M. 1992. Conversation with the author. 19 1940. Cambridge: Cambridge University Press. October. Nyman, M. 1974. Experimental Music: Cage and Be- Stockhausen, K. 1961. ‘‘Music in Space.’’ Die Reihe 5:67– yond. London: Studio Vista. 82. Potter, K. 1981. ‘‘Just the Tip of the Iceberg: Some As- Stockhausen, K. 1964. Carre´. London: . pects of Gavin Bryars’ Music.’’ Contact 22:4–15. Tavener, J. 1972. Ultimos Ritos. En Honor de San Juan Pritchett, J. 1993. The Music of John Cage. Cambridge: de la Cruz. London: J. & W. Chester Ltd. Cambridge University Press. Tavener, J. 1974. ‘‘Notes about Ultimos Ritos.’’ Unpub- Raaijmakers, D., T. Bruyne`l, and P. Struycken. 1971. lished typescript. Sound—Sight. Three Audiovisual Projects. Installa- Trochimczyk, M. 2002. Sound Constructions: Number, tions presented at the Stedelijk Museum, Amsterdam, Image and Space in Contemporary Polish Music. 5 March–18 April 1971. van Fraassen, B. C. 1985. An Introduction to the Philoso- Rochberg, G. 1963. ‘‘The New Image of Music.’’ Perspec- phy of Time and Space. New York: Columbia Univer- tives of New Music 2(1):1–10. sity Press. Schafer, R. M. 1977. The Tuning of the World. New Xenakis, Iannis. 1971. Formalized music. Bloomington: York: Knopf. Indiana University Press. Schafer, R. M . 1981. Apocalypsis. Part 1: John’s Vision. Xenakis, I. 1994. ‘‘Musique, espace, et spatialisation: En- Toronto: Arcana Editions. tretien de Iannis Xenakis avec Maria Harley.’’ Circuit. Schafer, R. M. 1986. Apocalypsis. Part Two: Credo. Ban- Revue Nord-Americaine de Musique du XXe Sie`cle croft, Ontario: Arcana Editions. 5(2):9–20.

56 Computer Music Journal

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/01489260152815288 by guest on 28 September 2021