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Appropriating an architectural design tool formusical endsMichael Fowler aa Spatial Information Architecture Laboratory, RMIT University, AustraliaVersion of record first published: 04 Jan 2012.
To cite this article: Michael Fowler (2011): Appropriating an architectural design tool for musical ends,Digital Creativity, 22:4, 275-287
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Appropriating anarchitectural design toolfor musical endsMichael Fowler
Spatial Information Architecture Laboratory, RMIT University, Australia
Abstract
NURBS (non-uniform rational b-spline) modelling hasbecome a ubiquitous tool within architectural designpraxis. In this article I examine three projects thatutilise NURBS modelling as a means for which amusical system’s inherent spatiality is visualised.There are numerous precedents for which architecturalform is a derivation of a musical system, or a musicalsystem is proportionally informed by architectonicgesture. I propose in this article three NURBS modellingmethodologies: for the spatial analysis of KarlheinzStockhausen’s sound projection geometries in Pole fur2; for a spatial realisation of John Cage’s indeterminatework Variations III; and for the generation of a surfacemanifold informed by musically derived soundscapedata from the Japanese garden Kyu Furukawa Teien.Rather than seeking to translate music into inhabitablearchitecture, or architectonic form into music, I high-light an approach that produces an interstitial territorybetween discourses on architecture and music analysis.
Keywords: graphic music, NURBS modelling, sounds-cape studies, architecture
1 Connecting music and architecture
There is a rich body of work that seeks to unite thespatial aesthetics of architecture and music inmyriad ways (Martin 1994). Architects such asStephen Holl (1994), Garth Ancher (2007), YagoConde (2000) and Yoryia Manolopoulou (2005)have each drawn on specific musical scores or per-formances as a means to generate novel architec-tural forms, while Bernard Tschumi’s iconicManhattan Transcripts (1981) contains numerousreferences to graphic music notation as catalyst topush the limits of functionality in the traditionalarchitectural diagram. Holl’s Stretto House usesBela Bartok’s Music for Strings Percussion andCeleste for a translation of proportional, numericand textural combinations into architectonicgesture, while Conde and Manolopoulou openlysample graphic score-based elements of JohnCage’s indeterminate work Fontana Mix (Cage1958). Ancher’s approach explores the intangiblequalities of Miles Davis’s jazz–rock fusion eraperformances as a departure point for an architec-tural design process as spatial translation mechan-ism. But this movement of ideas betweendisciplines has flowed both ways (Forsyth 1985),and ostensibly appears as far back as the fifteenthcentury. Warren (1973) and Trachtenberg (2001)identify Guillaume Dufay’s 1436 motet Nuperrostrum flores as containing an elegant manifes-tation of the proportions of the newly completedFlorence Cathedral dome of Filippo Brunelleschi,while Claudio Monteverdi’s later well-known
Digital Creativity2011, Vol. 22, No. 4, pp. 275–287
ISSN 1462-6268 # 2011 Taylor & Francishttp://dx.doi.org/10.1080/14626268.2011.622286http://www.tandfonline.com
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early Baroque masterpiece Vespro della BeataVergine 1610 makes extensive use of the balconiesat St Mark’s Basilica for floating brass choireffects that articulate the work’s musical structurein spatial terms. Goethe’s infamous observationthat ‘architecture is music frozen’ (Goethe andWood 1901) has provided a legacy to notabletwentieth-century exemplars of architect/compo-ser Iannis Xenakis. His collaborative work withLe Corbusier at the Phillips Pavilion of the Brus-sels World Fair in 1958 finds a manifestation ofthe pavilion’s hyperbolic paraboloids in theorchestral work Metastasis—for which his laterPolytopes series equally explore architectonicconcepts as structural generators within music(Serken 2007, Kanach 2008).
In this article I will explore my own generativemethodologies in which an architectural design toolhas provided a novel spatial dimension to processesof musical realisation, analysis and composition. Ioutline here three projects that explore the nexusbetween music space and architectural spacethrough the utilisation of NURBS (non-uniformrational b-spline) modelling, predicated for themost part on a music-centric approach. As a com-monly used design tool, NURBS modelling isnow ubiquitous in architectural design offices forcomplex form generation, material rendering,design communication, and surface analysis (Szala-paj 2005). In particular, I have used the softwareRhinoceros3D as a means for visualising spatialitywithin musical systems and event soundscapes. Theprojects I discuss here were developed during anAustralian Research Council funded post-doc atthe Spatial Information Architecture Laboratory atRMIT University, Melbourne, Australia. Having aresearch background in twentieth-century musicanalysis and contemporary electro–acoustic per-formance practice gives my adaptation of atypical architectural modelling tool a particularproclivity, though my intentions are that theresults be informative between disciplines.
As a digital design tool, Rhinoceros3D is com-monly used to seamlessly connect the constructionand analysis of three-dimensional form to the rapidprototyping processes of printing physical models.Instead of focussing on the tool as a technology in
itself, here, I explore its utilitarian strengths inmapping spatial information from a musicalcontext. This article highlights my use of Rhino-ceros3D in relation to generating a spatial analysisof sound projection geometries prescribed in thescore of Karlheinz Stockhausen’s Pole fur 2(Stockhausen 1975), developing a three-dimen-sional realisation of John Cage’s indeterminategraphic work Variations III (Cage 1963), and inconstructing a surface manifold from musicallyderived data from the soundscape of Kyu Furu-kawa Teien, a Japanese garden located in Tokyo,Japan. As such, the methodology I have developedis one that quantitatively interrogates musical dataderived either from an extant score or extantsoundscape. In its original musical context, thedata is meaningful as a series of linked elementsthat enable musical production to proceed viainterpretation, composition or performance. I useRhinoceros3D as a means to visualise the inherentspatiality and architectonic potential of thismusical data, providing a domain to map andtrack its spatial fluctuations. Whereas traditional3-D modelling within architectural praxis is con-cerned with the development of functional formfor a given architectural program, the methodologyoutlined in this paper produces proto-architecturalmodels. By proto-architectural I mean that theirform is without an architectural function, theirstructure is not predicated on their intended useas an inhabitable space, and they remain withoutgrounding to a particular site and therefore donot respond to a site context or embody any fixedscale. In this sense, the works modelled here arearchitectonic mappings of musical data embodiedwithin a typical architectural presentation frame-work, though concurrently they act as spatialstudies of musically derived data.
2 NURBS modelling for spatialanalysis in Pole fur 2
Karlheinz Stockhausen composed Pole fur 2 forthe Osaka World’s Fair, 1970. Collaborating withthe architect Fritz Bornemann, acoustician FritzWinckel and engineer Max Mengeringhausen,the German pavilion at Osaka was most notable
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for the striking blue geodesic dome that housed thespherical auditorium (the only visible architec-tonic feature sitting above ground at the site).Inside the auditorium, over fifty loudspeakerswere embedded in the walls in six concentricrings above and below the seated audience. Loud-speaker layers could be controlled via a sphericalsensor or a rotation mill at the control desk, andallowed any geometric combination of loudspea-ker groups to be utilised (for example, as circular,spiral or diagonal fields/trajectories). Stockhausenspecifically composed Pole fur 2 for the capabili-ties of the auditorium, providing a sound projec-tion score in which the electro–acoustic soundsignals of two musicians were to be movedthroughout the interior of the space (Figure 1).
The graphic nature of the sound projectionscore is mirrored in the score for the performingmusicians, in which Stockhausen only providesindications about the thematic transformation andimitation of short wave (SW) radio signals thateach musician obtains from a portable radio.Like the performing score, which uses thesymbols of + and – to indicate the relative stateat any one time of four musical parameters(volume, rhythm, register and duration), the pro-jection score also uses + and – to signify theextremities of the loudspeaker walls to use. Line-work and hatching indicate to the sound projec-tionist various degrees of inclusion of the sixindividual loudspeaker layers, with occasionalsound signal trajectories requiring dynamic move-ment up and down the sound walls in each hemi-sphere in quick succession. The entire pieceunfolds and develops then as a series of strikingaural architectures in which varying changes inthe density, surface area, movement and locationof each musician’s sound signal (which is limitedto a pre-defined hemisphere) comes to define thework’s spatial auditory form.
How, then, to visualise this spatial develop-ment in the sound projection geometries whileconcurrently accounting for the three-dimensionalinterior? Traditionally, music theory and analysishas abstracted thematic material and musicalforms into a series of relational structures thatbecome examined and understood through tech-
niques that graphically represent meta-informationsuch as Schenkerian analysis (Schenker 1969) orKlumenhouwer networks (Lewin 1990). In thecase of the sound projection score of Pole fur 2,Stockhausen’s spatial proclivities may on thesurface seem to be self-evident within the notationitself, but the projection score is really an abstrac-tion because it points to a three-dimensional datasetvia two-dimensional representational means. Likea traditional architectural section or elevationdrawing, the sound projection score captures onlytwo of the object’s three dimensions and belies theintrinsic connection that the structure of the audi-torium holds for the sound projection geometries.
In an effort to visualise the flux and spatialcharacter of Stockhausen’s sound projection geo-metries, I have used NURBS modelling to mapthe pattern of sound projection in Pole fur 2against a template of the interior of the sphericalauditorium. By including time as a function ofthe articulation of the musical form and unfoldingof the work, changes in the model’s surface tracethe ebb and flow of spatial information inherentin the projection score. Figure 2 documents theprocess. Here, the auditorium section shows thesix discrete loudspeaker layers. As each player isdesignated a hemisphere to which the sound pro-jectionist directs their signal through, a sectiontemplate—in which the six layers articulate thediameter of the auditorium—is used as a guide inan explosion in the x axis (representing time).Stockhausen articulates Pole into sections called‘Moments’ for which collections of ‘Moments’can be performed separately from the largerwork (Figure 2 shows one such performablesection, Moments 1–9). By directly transcribingthe original sound projection score into thesection template (Figure 2, B), the two–dimen-sional linework of the score is spatialisedthrough the unfolding moments. Using a processcalled lofting1 (Figure 2, C), the linework of thespatialised projection score becomes the structuralbasis for a self-intersecting surface or manifoldthat maps the changes in the range, surface areaand continuity of the original sound projectionscore’s geometry. Rather than a rudimentarymapping of the projection score into three-dimen-
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Figure 1. Karlheinz Stockhausen, Pole fur 2 excerpt, Moments 9–11. The sound projection score is located directly beneath theperforming musician’s score and has indications regarding which layer of loudspeakers are to be activated (2 indicates lowest level,+ for the most upper level). Additionally, the hatching notation directs the sound projectionist to open loudspeaker layers as pro-portional groups (gradually increasing the soundwall surface area).Source: # Stockhausen Foundation for Music, 51515 Kurten, Germany (http://www. stockhausen.org).
Figure 2. Surface generation methodology in Pole fur 2. From the Osaka Auditorium section, six layers of loudspeakers are abstractedinto fixed points on its circumference, thus providing an auditorium-section template. A: Each auditorium-section template (containinghemispheres I & II) articulates Stockhausen’s designation for the start point of Moments, indicated as M1, M2, etc. B: The original soundprojection score is then spatialised through these auditorium-section templates. C: Finally, through NURBS lofting, a surface tracks thespatialisation of the sound projection geometries. Image#M. D. Fowler 2011. Reproduced with kind permission of the copyright holder.
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sions, the use of lofting in Rhonceros3D producesunexpected inconsistencies and diversions whichpushes the digital models outside of the purelyfunctionalist limit of spatial analyses of Stockhau-sen’s design scheme. Though the intention of theNURBS modelling in this case is for a qualitativeunderstanding of how the sections of Poleconstruct particular spatial identities, there is no
doubt that the visual aesthetic of the models com-municates an architectonic grounding in tangiblespace (Figure 3 and 4).
The sound projection NURBS modellingrevealed Stockhausen’s design to be predicatedon two expected states (poles) of surface complex-ity. These states are fluid within sections, however,and occur both as a:
Figure 3. NURBS model of Moments 12–19, Pole fur 2 showing original sound projection score, elevation, front and perspectiveviewpoints. Image # M. D. Fowler 2011. Reproduced with kind permission of the copyright holder.
Figure 4. NURBS model surface detail of Moment 30–35, Pole fur 2. Image # M. D. Fowler 2011. Reproduced with kindpermission of the copyright holder.
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. complex—an embellished, fragmented, discon-tinuous state;
. simplex—a planar, flowing, continuous state.A further examination of these distinct formaltypologies revealed a localised set of surfacecharacteristics. By tracing the surface articulationsin the models, three discernable parameters wereused to describe the two states of a surfacethrough its:. manifold (degree of surface uniformity/inter-
section);. volume (the flux of void spaces);. envelope (the degree of topological variation).
The NURBS modelling and a tracking ofthe morphology and typology of the modelsbetween performable sections of Pole fur 2enabled an analytical design schema for thework to be established with regard to the architec-tonic flux in the surface manifold, which inevitablycorresponds to Stockhausen’s variations in soundprojection geometries between sections (Figure 5).
3 NURBS modelling for spatialrealisation in Variations III
Unlike Stockhausen’s championing of music aspotential three-dimensional architectonic object,John Cage’s spatial aesthetic always predicatedthe undetermined and unforeseen as valuableagents for structural articulation of compositionalform. The relationship Cage had to indeterminateprocesses in composition was diverse. Whetherthe originate was acquired from the Chineseoracle I-Ching, through coin tossing, AndrewCulver’s computer program tic for random
number generation, or the simple observation ofimperfections in a blank manuscript paper, eachgenerative process sought to embody aleatoric prin-ciples. Similarly diverse were the various media towhich such processes were applied, includingmusical or theatrical works, print-making andpoetry/writing. This diversity of expression invarious media and Cage’s united methodologicalstance of embracing indeterminate processes wasa point of inquiry for my own interrogation intohis 1963 graphic work Variations III.
Like all the works in his Variations series(which number I–VIII) the number of performersrealising the score is freely chosen. In contrast toStockhausen’s prescriptive graphic notation usedin Pole fur 2, Cage’s Variations III employs trans-parent sheets as utilitarian tool. The score itselfconsists of forty-two small circles printed onloose individual transparent sheets which mustbe randomly arranged as an overlapping andjuxtaposed conglomerate (Figure 6). From thismeta-score, any individual circle is nominatedthat overlaps at least one other circle. Theseinstances of overlapping circles are what Cagerefers to as ‘interpenetrating variables’ (Cage1963). The number of overlapping circles onthe nominated circle in question is then mappedto a corresponding action chosen by the performer(musical, theatrical or otherwise, Cage is aspecificregarding the definition of ‘action’). Any numberof repetitions concerning recounting, the nomina-tion of other circles for examination, or the re-combination of the circles is permitted to obtainan extended interpretation or storable dataset.This meta-score is in essence a utility for the pro-duction of a notation for Variations III—howeverelaborate or traditional its graphic nomenclaturebecomes is left to the imagination of theinterpreter(s). Cage’s own realisations includedthe mapping of common, everyday gestures andactions to the circle juxtaposition dataset includ-ing: smoking a cigarette; thinking; drinking aglass of water; and writing a letter; all of whichwere notated as handwritten instructions on asingle sheet of paper (Fetterman 1996, p. 201).The possibilities for the compositional form,notation and thematic content of the work, then,
Figure 5. Complete Moments of Pole fur 2 grouped as sections(S) indicating typological equivalence between six developedNURBS models: S1 ¼ Moments 1–8; S2 ¼ Moments 9–11;S3 ¼ Moments 12–18; S4 ¼ Moments 19–21; S5 ¼Moments 22–28; S6 ¼ Moment 29; S7 ¼ Moments 30–35.Image # M. D. Fowler 2011. Reproduced with kind per-mission of the copyright holder.
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are seemingly unbounded and limited only bythe inventiveness of the performer/interpreter.Given the several commercially available record-ings of the work explore it as an indeterminateessay in the theatrics of aleatoric musical struc-tures led my own realisation to eschew neither amusical performance nor a sound-log of actions.The question that was foremost in my mind waswhat might Variations III become when read as adirective for generating three-dimensional form?Given that Cage has no specific stipulations onthe temporal scale of the work, nor if the workneeds to be presented in real-time, as a pre-realisedtape piece, video work or in another visual mediapoints to an openness in Cage’s acceptance ofVariations III as meta-score: the identity of thework remains indeterminate, even in relation tothe very fabric of its final embodied form.
Both Manolopoulou (2005) and Conde (2000)have explored, in not too dissimilar ways, howCage’s earlier, yet similar indeterminate workFontana Mix (1958) might be used as an architec-tural design schema or spatial tool for an interven-tion in the built environment. Both architectsidentify the multi-configurable graphic elements
in the score of Fontana Mix in which transparenciesof differing curved and straight lines, points, and agrid offer a seemingly shared notational spacebetween architectural drafting and music compo-sition. Neither designer’s use of Fontana Mixthough attempts to usurp the actual directionsCage stipulates for a realisation of the work, inwhich the measurement (using any metric)between juxtaposed elements located on the trans-parencies provides a dataset (interpreted as timebracket) for assigning controlled actions to.Instead, both focus on using individual elementsof the score as a layering device placed onto sitein an effort to generate and extrude new interactionsand spatial forms within the extant landscape.
My own realisation of Variations III differsfrom the Conde and Manolopoulou’s precedentprimarily in the approach I take to Cage’s inde-terminate notation. Whereas Conde and Manolo-poulou quite literally take elements from FontanaMix as self-referential pattern-generating deviceswithout recourse to Fontana Mix’s realisationdirective, I attempt to directly incorporate Cage’sdirectives outlined in Variations III. Though thereis an inevitable shift from the legacy of the
Figure 6. Typical Variations III score juxtaposition. Image#M. D. Fowler 2011. Reproduced with kind permission of the copyright holder.
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score’s original performance context into a proto-architectural context (i.e. a site-less, program aspe-cific one), like any of Cage’s open-ended works,the goal is to apply rigor in the face of a freedomof unrestricted modes of execution (Pritchett1993). Figure 7 documents my realisation process.
A typical score of overlapping circles providesthe basis for any realisation. By digitising this scoreand importing it into Rhinoceros3D the centrepoints of the circles can be pinpointed. Thesecentre points can then be read as a point-cloud inplan, a mapping in itself of the origin of ‘interpene-trating variables’ that each circle represents in theoriginal score. The homogeneity of the point-cloud in the z axis is challenged through elevatingeach point according to the interrogation of analready established dataset obtained as per Cage’sinstructions for counting any given circle and itsoverlapping circles (Figure 7, I). This processthus produces a varied topography to the point-cloud that is an iterative function of Cage’s instruc-tions. Figure 7 (II and III) shows two generatedNURBS open polylines. The first open polylineconnects points of equal elevation; the second isa continuous trajectory through the entire point-cloud. From these polylines, applying a closedloft surface-generating algorithm in Rhinoceros3D
produces the surfaces, S1 and S2. The obviousvariability within each surface’s geometry high-lights the indeterminacy prevalent within evenone multiple realisation of the fixed point-cloud.In Figure 8, a third surface is produced from adifferent point-cloud using straight closed poly-lines to generate the loft, while Figure 9 uses yetanother point-cloud conglomerate again with asingle curved polyline and closed loft.
That countless further explorations, derivationsand variations on this particular methodology forspatial form generation in Variations III existonly seems to highlight the vast nature of thework’s interpretive domain. Though NURBS mod-elling is used here as a means to materialise indi-vidual object-interpretations (analogous to singleperformances), I envisage a host of other method-ologies that might capture spatial modularity andmalleable variability within a single model.
4 NURBS modelling for architectoniccomposition: Kyu Furukawa Teienshusaku
In 2006 I became involved in an interdisciplinaryresearch project to map soundscape data from aJapanese garden in Tokyo (Fowler and Harvey
Figure 7. Surface generation methodology in Variations III. From the juxtaposed circles of the original score, a point-cloud directlytranslates x, y coordinates. I: control-points are elevated in the z axis according to a stored database of observed “interpenetratingvariables.” II: open polylines that stratify the point-cloud through connecting equal heights produces surface S1 through closedlofting. III: a single open polyline produces surface S2 through closed lofting. Image # M. D. Fowler 2011. Reproduced withkind permission of the copyright holder.
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2006). The scope of the project was to gathersoundscape data and to make it available tosound designers and architects through variousvisualisation techniques. Our sampling site wasthe Japanese garden at Kyu Furukawa Teien inTokyo’s northern Kita-ku ward. The garden datesfrom the Taisho period (1912–1926) and wasdesigned by Kyoto master gardener Niwashi-Ueji (1860–1933) and includes a traditional Japa-nese teahouse and Western-style house designedby Josiah Condor. Within the 30,780m2 of KyuFurukawa Teien, there are two large water fea-tures: a pond at the southern end of the garden—shinjiike, which is modelled in the shape of theChinese ideogram for heart—as well as a largewaterfall called ootaki that feeds the pond fromits northern aspect. The drop of the ootaki isaround 10m, and provides the garden with a
soundscape whose constancy and balance isheard around the perimeter of shinjiike.
Three sites were identified as recording capturepoints at Kyu Furukawa Teien. Given the con-stancy of the sound of falling water emanatingfrom the ootaki, the presence of various birdspecies within the garden’s plantings, and humanvisitor’s traversal around the circuitous path onthe edge of shinjiike, sampling sites were estab-lished at the base of the ootaki, at a smallviewing area on the southern side of shinjiike,and at the karetaki (dry waterfall) on the pond’swestern edge (see Figure 10). Using a multi-channel recording array, captured recordings ofthe soundscape were subjected to frequency analy-sis using the open-source audio program PureData, for which equal tempered pitch informationwas extracted and stored. It was envisaged that this
Figure 8. NURBS model of Variations III developed using single straight closed polyline and closed loft. Image # M. D. Fowler2011. Reproduced with kind permission of the copyright holder.
Figure 9. NURBS model of Variations III developed using single curved closed polyline and closed loft. Image # M. D. Fowler2011. Reproduced with kind permission of the copyright holder.
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pitch information be later used as a compositionaltool kit for sound designers interested in compos-ing works generated from auditory conditionswithin a Japanese garden. Using the Forte (1973)pitch-class2 series classification terminology, thethree sample site recordings revealed similaritiesin pitch content.
That there were three distinct pitch-class setsoperating in the recordings taken from thevarious sites also presented a case for the use ofthis information in developing an architectonicstudy or shusaku (another objective of theproject). This process is documented in Figure 11.In an effort to incorporate spatial elementsinherent in the site, as well as musically deriveddata from the soundscape, shinjiike was conceptu-alised as a ‘pitch-pond’ that fed the three samplessites with data. Using Rhinoceros3D, control-points populated the confines of the general areaof the pond and were randomly elevated througheleven different height functions that corre-sponded to the range of Forte’s (1973) modulotwelve pitch-class series classification system:3
this means that the values of individual pitch-classes recorded at each site can be spatially articu-
lated. According to the pitch-class constituentsinherent in each site’s defining series means thatvarious trajectories can be composed to traversethe pitch-pond and inscribe these values withNURBS polylines. When three possible trajec-tories are defined, they can be combined todefine the cross-section curves of a closed lofted,thus enabling the development of a surface. Likethe process of defining trajectories through theVariations III point-cloud, a vast number of trajec-tories may be nominated for defining the pitch-class values for each sample site’s pitch-classseries. Figure 12 documents three variations inproto-architectural form—S1, S2, S3—that aremappings from three possible grouped trajectoriesof closed polylines for each sample site’s pitch-class series.
5 Conclusions
Each of the projects explored here haveattempted to use NURBS modelling as a meansto project musical data into a spatialised context.There is obviously, to some extent, a subjectivecompositional approach to each of the spatial
Figure 10. Map of Kyu Furukawa Teien, Kita-ku Tokyo Japan. A: ootaki. B: shinjiike. C: karetaki. Image # M. D. Fowler 2011.Reproduced with kind permission of the copyright holder.
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methodologies I have used, though I see my rolenot as composer or designer per se. The processof form generation in the Kyu Furukawa Teienshusaku is perhaps the natural bookend to a conti-nuum that locates the spatial visualisation ofStockhausen’s sound projection geometries inPole fur 2 at its opposite end. Both seek to rep-resent structural trajectories as the basis for anarchitectonic mapping. In the case of Pole fur 2
these are prescribed by Stockhausen’s spatialsound design plan, whereas in Kyu FurukawaTeien shusaku they are a conceptualisation ofmusically derived characteristics of the extantsoundscape of the garden. Sitting between thesebookends is Cage’s Variations III which, likemany of the composer’s indeterminate works ofthe 1960s, requires a highly determined and sub-jective realisation methodology that need not
Figure 11. Surface generation methodology in Kyu Furukawa Teien shusaku. Each recording site is marked by a Forte (1973) pitch-class series name and set of values. A: ootaki ( ) 8–9 {0, 1, 2, 5, 6, 7, 8, 11}. B: shinjiike ( ) 9–3 {0, 1, 2, 3, 4, 5, 6, 8, 9}. C:karetaki ( ) 8–5 {0, 1, 2, 3, 7, 8, 9, 11}. I: shinjiike is conceptualized as ‘pitch-pond’ for which control-points populate the areaand are randomly elevated through eleven discrete values. II: Three closed polylines track each value of the pitchclass elements for A,B and C by a trajectory through the ‘pitch-pond’ control-points that produces a structure for the closed lofted surface S1. III: Threealternate closed polylines produces surface S2. IV: Three more alternate closed polylines produces surface S3. Image # M. D.Fowler 2011. Reproduced with kind permission of the copyright holder.
Figure 12. Three NURBS modelling solutions of Kyu Furukawa Teien shusaku showing surfaces S1, S2, and S3, in front andperspective viewpoints. Image # M. D. Fowler 2011. Reproduced with kind permission of the copyright holder.
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reference Cage’s own performance practice of thework.
The impact of the completely digital nature ofNURBS modelling on these projects points in mymind towards a novel spatial territory in which atypical architectural design tool has opened up anew way of visualising spatiality within a givenmusical system. For architect Marcus Novak thepotential of contemporary digital tools to generatevirtual environments produces a new type ofspace in which architecture and music co-existsas ‘archimusic’ (Novak 1994). His concept ofthe ‘dataworld’ is one in which composition isfacilitated through the utilisation of algorithmsthat generate music and architectonic form simul-taneously. Though I would hesitate to describemy own application of NURBS modelling as atype of ‘archimusic,’ the decontextualisation ofthe extracted musical data and its subsequentrestratification produces models that sit outsideof time in a like manner to any traditionalmusical score, yet embody architectonic formand gesture. Novak’s contemporary, architectGreg Lynn, has also championed 3-D computermodelling and animation as a way to manipulateform outside of the boundaries and perceivedrestraints of traditional architectural design draft-ing. For Lynn, the lure of radicalising architecturalform through real-time software manipulationstems from his desire to counter architecture’s ded-ication to permanence and the inert:
By collapsing the plan and elevation into asingle three-dimensional form, the computermodel encourages architects to break out oforthogonal, right-angled space. Instead theycan manipulate all dimensions at once. Spacebecomes as plastic as a hunk of Silly Putty(Waters 2003, p. 67).
Perhaps in an analogous fashion to Lynn’sapproach, the NURBS methodology I have usedhas attempted to move beyond the traditionaltwo-dimensional nature of music notation in aneffort to examine the consequences of extendingits graphic nomenclature to embrace architecturalspatiality. But the results, unlike true architecturalmodels, are non-representational with regard to
scale or site. That they are purposely withoutscale also points to their generic quality as archi-tectonic forms designed not as inhabitable spacesbut contemplative objects occupying a threshold.Sitting thus as models of spatial flux or mappingsof spatialised musical data makes them distinctlyproto-architectural. But their nature as interstitialobjects between functional architectural formand discrete analytic visualisations also creates apotential for them to move beyond the nexusthey occupy. I envisage that they could readilyinform architectural praxis as ontological investi-gations into form generation, or equally provideinsights into other methodologies for examiningspatial predilections within musical systemsusing spatial design tools. That the contemporarydiscourse on the nexus between architecture andmusic has tended to focus on design method-ologies for the translation of one into the otherhas also provided a strong impetus for my explora-tion of NURBS. I contend that the work describedhere seeks not to translate musical concepts or thequalities of musical performances into tangiblearchitecture in the manner of Goethe’s notion ofarchitecture as a frozen music, but instead intro-duce architectonic concepts, spatial analysis andform-generating methodologies into the sphereof musical composition and analysis. In doing soI am seeking a means to communicate ideasbetween the disciplines via a spatial languagethat is ideally comprehensible by both. I envisagesuch an interstitial territory as one developed forinterdisciplinary dialogue in which disciplinespecific tools are re-imaged and usurped toprovide novel insights into spatial composition—be it within the tangible boundaries of architecturaldesign or the intangible realm of music analysisand soundspace composition.
Notes1 The process of lofting in Rhincoeros3D involves
creating a surface as a function of a number ofselected cross-section curves. The surface connectseach cross-section in a linear manner producing aplanar topology for which closed or open cross-section curves determines the volume/surface areaof the resultant form.
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2 A pitch-class is the infinite set of pitches separatedby whole octaves. The pitch-class D#, for example,refers to all D#s in all registers.
3 In this system the eleven semitones of the equallytempered octave are mapped to integers: e.g. thetrichord (A, A#, B) can be expressed as {0, 1, 2}where A ¼ 0, A# ¼ 1, B ¼ 2. Forte also names allpossible combinations of three to eleven elementseries such that the nomenclature 3–1 ¼ {0, 1, 2},3–2 ¼ {0, 1, 3}, etc.
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Dr Michael Fowler’s research focuses on auralarchitecture as an intersection between musictheory, soundscape studies and architectural mod-elling. In 2009 he completed an AustralianResearch Council funded post-doc at the SpatialInformation Architecture Laboratory at RMITUniversity, Melbourne, Australia.
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