Peter Abstract ChristensenThis Advanced Study Report documents the process and outcomes of a digital design project with the aim of translating music into architecture. Parametric software has been used to generate 48 virtual forms derived from the preludes and fugues of Book I of The Well-Tempered Clavier (bwv 846The report discusses composer of the relationship 869), by the Baroque the history Johan Sebastian between music and Bach (16851750). architecture in the Western tradition, and its relevance to contemporary thought and practice. The report includes a description of the process of translation, and an analysis of the virtual forms that have been generated.

Spatial Polyphony Virtual Architecture Generated from the Music of J.S. Bach

Advanced Study Report Faculty of Architecture, University of Sydney 2007

ContentsAcronyms ............................................................................................. .............7 Acknowledgements .............................................................................. .............7 Figures and capte 1 Introduction ....................................................................................9 Tables ............................................................................................8 1.1 Aims and Objectives .................................................................9 1.2 Motivation and Significance......................................................9 1.3 Process.................................................................................... 10 capte 2 Literature Review........................................................................... 11 2.1 Historical Context: A Rich Tradition..................................... 11 2.2 Contemporary Context: Literal and Metaphorical Approaches ..................................... 12 2.3 Architecture as Frozen Music ............................................... 12 2.4 The Architectural Music of Bach.......................................... 13 2.5 Digital Architecture ................................................................ 14 2.6 Enhancing Creativity .............................................................. 14 capte 3 Process ........................................................................................... 16 3.1 Background............................................................................ 16 3.2 Description............................................................................. 16 3.2.1 Step 1: MIDI (music) .................................................... 17 3.2.2 Step 2: ASCII (text) ...................................................... 17 3.2.3 Step 3: EXCEL (numerals) ............................................ 18 3.2.4 CATIA (form)............................................................... 19 3.3 Wavelength and Pitch......................................................... 20 capte 4 Virtual translations of the 48 preludes and fugues from The Well-Tempered Clavier, Book 4.1 Prelude No. 1 in C Major, I ................................................... 24 bwv 846 ....................................... 25 4.2 Fugue No. 1 in C Major, bwv 846 ......................................... 26 4.3 Prelude No. 2 in C Minor, bwv 847....................................... 27 4.4 Fugue No. 2 in C Minor, bwv 847......................................... 28 4.5 Prelude No. 3 in C-sharp Major, bwv 848 ............................. 29 4.6 Fugue No. 3 in C-sharp Major, bwv 848 ............................... 30 4.7 Prelude No. 4 in C-sharp Minor, bwv 849............................. 31 4.8 Fugue No. 4 in C-sharp Minor, bwv 849............................... 32 4.9 Prelude No. 5 in D Major, bwv 850 ....................................... 33 4.10 Fugue No. 5 in D Major, bwv 850 ......................................... 34 4.11 Prelude No. 6 in D Minor, bwv 851....................................... 35 4.12 Fugue No. 6 in D Minor, bwv 851......................................... 36 4.13 Prelude No. 7 in E-flat Major, bwv 852.................................. 37 4.14 Fugue No. 7 in E-flat Major, bwv 852.................................... 38 4.15 Prelude No. 8 in E-flat Minor, bwv 853 ................................. 39 4.16 Fugue No. 8 in D-sharp Minor, bwv 853............................... 40 4.17 Prelude No. 9 in E Major, bwv 854........................................ 41 4.18 Fugue No. 9 in E Major, bwv 854 .......................................... 42 4.19 Prelude No. 10 in E Minor, bwv 855...................................... 43 4.20 Fugue No. 10 in E Minor, bwv 855........................................ 44 4.21 Prelude No. 11 in F Major, bwv 856 ...................................... 45 4.22 Fugue No. 11 in F Major, bwv 856 ........................................ 46 4.23 Prelude No. 12 in F Minor, bwv 857...................................... 47 4.24 Fugue No. 12 in F Minor, bwv 857........................................ 48 4.25 Prelude No. 13 in F-sharp major, bwv 858 ............................ 49 4.26 Fugue No. 13 in F-sharp major, bwv 858............................... 50 4.27 Prelude No. 14 in F-sharp minor, bwv 859 ............................ 51 4.28 Fugue No. 14 in F-sharp minor, bwv 859 .............................. 52 4.29 Prelude No. 15 in G major, bwv 860...................................... 53 4.30 Fugue No. 15 in G major, bwv 860........................................ 54 4.31 Prelude No. 16 in G minor, bwv 861 ..................................... 55 4.32 Fugue No. 16 in G minor, bwv 861 ....................................... 56 4.33 Prelude No. 17 in A-flat major, bwv 862................................ 57 4.34 Fugue No. 17 in A-flat major, bwv 862 .................................. 58 4.35 Prelude No. 18 in G-sharp minor, bwv 863 ........................... 59 4.36 Fugue No. 18 in G-sharp minor, bwv 863 ............................. 60 4.37 Prelude No. 19 in A major, bwv 864 ...................................... 61 4.38 Fugue No. 19 in A major, bwv 864 ........................................ 62 4.39 Prelude No. 20 in A minor, bwv 865...................................... 63 4.40 Fugue No. 20 in A minor, bwv 865........................................ 64

4.41 4.42 4.43 4.44 4.45 4.46 4.47 4.48

Prelude No. 21 in B-flat major, bwv 866................................ 65 Fugue No. 21 in B-flat major, bwv 866 .................................. 66 Prelude No. 22 in B-flat minor, bwv 867 ............................... 67 Fugue No. 22 in B-flat minor, bwv 867 ................................. 68 Prelude No. 23 in B major, bwv 868 ...................................... 69 Fugue No. 23 in B major, bwv 868 ........................................ 70 Prelude No. 24 in B minor, bwv 869...................................... 71 Fugue No. 24 in B minor, bwv 869........................................ 72

capte 5 Analysis and Interpretation ............................................................ 5.1 The 48 Virtual Forms ............................................................. 73 73 5.1.1 A Family of Forms......................................................... 73 5.1.2 The Shape of Music ...................................................... 73 5.1.3 Digital process............................................................... 74 5.1.4 Orientation ................................................................... 74 5.1.5 Symmetry ...................................................................... 74 5.1.6 Harmony....................................................................... 74 5.2 Other Work ........................................................................... 75 5.2.1 Physical Model .............................................................. 75 5.2.2 Fly-through movie ........................................................ 75 5.2.3 Flash animation............................................................. 77 capte 6 Conclusion..................................................................................... 78 6.1 Limitations.............................................................................. 78 6.2 Potential for Development...................................................... 78 Apparatus.............................................................................................. .......... 79

Figures and Tablesfue 1.1: Johan Sebastian

Bach .................................................................... 10 fue 2.1: Pages from Ten Books on Architecture by Vitruvius..................... 12 fue 2.2: Description of proportions from Albertis De re aedificatoria......... 12

compositional principles from serial music ..................................... 13fue 2.3: Sketch for the Phillips Pavilion, based on

fue 2.4: Daniel Libeskinds Jewish Museum, a conceptual translation of music .................................................. 13 fue 2.5: Steven Holls Stretto House, a literal translation of music............... 13 fue 2.6: Wood and cardboard replica of for a Bach Monument................................................................... 14 Neugeborens design fue 2.7: Painting by Kandinsky ................................................................... 14 fue 2.8: Virtual space generated from Beethovens Ode to Joy................... 15 fue 2.9: CAD model translation of The Avalanches Flight Tonight.......... 15 fue 3.1: ASCII text file................................................................................ 19 fue 3.2: The data converted to numerical format in Excel.......................... 20 fue 3.3: The highest and lowest notes are equally balanced ....................... 22 fue 3.4: A visual representation of the five octave range used by Bach....... 25 fue 5.1: Asymetrical arrangement ................................................................ 76 fue 5.2: End view of virtual form generated from Fugue No. 1................... 77 fue 5.3: Physical model of Fugue Figure 3.1: ASCII text No.1 ....................................................... 77 fue 5.4: Screen shots file ................................................................................ 18 Figure 3.2: from a fly-through animation of Fugue No. 1 ........... 78 The data converted to numerical format in Excel .......................... 19 Figure 3.4: A visual representation of the five octave range used by Bach ....... 23 tae process tae tae 3.4:Mapping 3.1: Summary of 16 tae the 3.2: File 20 betweenmusicand .................................................................. 3.3: ofparameters

Design Tables.................................................................................. 18 Structure...................................................................................

space .......................... 21 tae 3.5: Bachs keyboard, showing each notes actual and notional value... 22

ASCII American Standard Code for A standard computer code for Information Interchange

Acronyms

representing alpha-numeric characters (Macquarie Dictionary) CAD Computer Aided Design MIDI Musical Instrument An industry standard protocol for Digital Interface converting music performance

information (note names, durations, dynamics, etc.) into digital data streams for storage, transmission, or playback (Macquarie Dictionary) MP3 Moving Pictures 3 A digital audio file in which the audio signal is compressed by removing the parts of the signal not heard by the human ear. Derived from MPEG (Moving Pictures Expert Group) (Macquarie Dictionary) WAV

Acknowledgements

capte 1

IntroductionThis chapter describes the aims and objectives of the project, as well as its significance and the motivation for undertaking it. A short summary of the process is also given. 1.1 Aims and Objectives The aim of this digital design project is the translation of music into architecture. For centuries, architects have puzzled over the relationshipbetween musical and architectural The project is concerned with the structure to form.This project uses the latest technologyof music, this ancient conundrum. explorenot the sound produced by a particular performance. The musical score is the starting point, providing the blueprint from which virtual Spatial Polyphony refers to a representation, in forms are generated. space, of the rich structure of Baroque music, as exemplified in the fugues of Johan Sebastian Bach (1685-1750). A fugue is a complex musical game in which two or more melodic lines are woven together to form a harmonised whole. This type of music is known as polyphony (literally, many sounds) and Bach is regarded is to translate a A key objective of the project as its greatest exponent. of works by Bach, in its entirety. This collection enables the generation of a family of forms, which aids comparison and improves the depth of The Well-Tempered analysis possible. Clavier (bwv 846-893) is a famous collection of keyboard pieces by Bach. With each of its two volumes containing preludes and fugues written in all 24 keys, it is a veritable compendium of contrapuntal keyboard music To make the translation of a large number of (Stegemann 1993). pieces feasible, a process with a high degree of automation has been developed. This process is described in detail in chapter 3. 1.2 Motivation and Significance This project is motivated by the desire to use new technology to shine light on anoldproblem.The long history of musical analogy in architecture, and the close formal links between the two art forms, testify to the significance of the relationship.ffd8ffe000104a46494600010201009700 960000ffe205384943435f50524f46494c4 5000101000005286170706c022000006d 6e74725247422058595a2007d20005000 d000c00000000616373704150504c0000 00006170706c000000000000000000000 000000000000000f6d6000100000000d32 d6170706c000000000000000000000000 000000000000000000000000000000000 000000000000000000000000000000000 00000d7258595a0000012000000014675 8595a00000134000000146258595a0000 014800000014777470740000015c00000 01463686164000001700000002c725452 430000019c0000000e675452430000019 c0000000e625452430000019c0000000e 64657363000001ac0000003f6370727400 0002540000004876636774000001ec000 000306e64696e0000021c000000386473 636d0000029c0000028c58595a2000000 0000000744b00003e1d000003cb58595a Figure 1.1: Johan 200000000000005a730000aca60000172 Sebastian Bach 658595a20000000000000281800001557 (www.imagesonline.bl.uk) 0000b83358595a20000000000000f35200 010000000116cf73663332000000000001 0c42000005defffff326000007920000fd91 fffffba2fffffda3000003dc0000c06c637572 76000000000000000101cd00006465736 3000000000000001447656e6572696320 5247422050726f66696c65000000000000 0000000000144765

The idea of translating music into architecture is not new. During the Renaissance, musical theories of harmony formed the basis of the proportional systems used by architects such as Palladio and Alberti (Wittkower 1973).More recently, the contemporary architects Steven Holl and Daniel Libeskind have sought to make translations of music ina Bauhaus studentliterally or In 1928 their work, either named Heinrich metaphorically (Harvey to design a sculpture based Neugeboren attempted 1998). on a fugue by Bach (Wingler 1969). By his own admission, Neugeborens attempt met with limited success. In the 21st century, the advent of digital design and the notion of virtual space have opened up new avenues to explore the problem. This project continues Neugeborens work, using the latest digital tools to make a virtual translation of Bachs music. 1.3 Process The process of translation is entirely digital, beginning and ending withelectronic representations of music.The raw material is not The procedure is divided rather computerhuman performance, but into four main steps, described in music. programmeddetail in chapter 3. The process begins by extracting the information stored in electronic music files. The data is then imported into a spreadsheet application, where it is converted from text into numerical format. Lastly, parametric software is used to link the numerical information based on a set of virtual A parametric model is to 3-dimensional forms. parameters, or variables, which can be changed at any time. Unlike a conventional CAD model, which is more or less static once it has been created, a parametric model is a dynamic entity; a set of relationships defined by various parameters. Music and architecture can be seen as systems of variables. Parametric software is used to make a mapping between these two systems; the musical variables of time and pitch are mapped onto the spatial variables of length, width and height. The resulting forms are virtual representations of the information contained within the music.

capte 2

Literature ReviewThe studies reviewed in this chapter testify to a strong tradition of musical analogy in architecture. The reciprocal values shared by architecture and music are discussed, and the chapter argues for the validity of a literal, or formal, approach to the translation of music into architecture. 2.1 Historical Context: A Rich Tradition There is a long and well-documented tradition of musical analogy in architecture.The two arts are mentioned together in the earliest architectural treatises as well as contemporary sources. A wide variety of approaches to expressing the reciprocal relationship are documented, ranging from the indirect use of underlying principles or Architecture to music have translations from one philosophies,anddirect, literal shared strong links since antiquity, other. discipline to thewhen both were considered branches of the mathematical sciences, along with astronomy and geometry (Ham 2005,p139). At this time, an understanding of music, among other disciplines, was considered indispensable to the architect. Figure 2.1 shows pages from the earliest surviving Western architectural treatise, Ten Books on Architecture, in which the Roman Let him be educated, skilful with the pencil, architect Vitruvius states, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists and be acquainted with astronomy and the theory of The inclusive nature of architecture led to an the heavens. (Vitruvius 1999) interest in the underlying principles of other fields of study, including music. Rudolph Wittkowers Architectural Principles in the Age of Humanism describes the proportional systems used by architects such as Palladio and Alberti during the Renaissance (Figure 2.2). Based on the principles of musical harmony established by Pythagoras in Ancient Greece, they were grounded in the belief that the same universal principles of beauty are manifest in art, architecture and music (Wittkower 1973,p117).ffd8ffe000104a4649460001020100c900 c90000ffe20c584943435f50524f46494c4 500010100000c484c696e6f021000006d6 e74725247422058595a2007ce00020009 000600310000616373704d53465400000 000494543207352474200000000000000 00000000000000f6d6000100000000d32d 485020200000000000000000000000000 000000000000000000000000000000000 000000000000000000000000000000000 ffd8ffe000104a4649460001 000116370727400000150000000336465 0201008100810000ffe20c58 7363000001840000006c7774707400000 Architecture and music have 4943435f50524f46494c4500 1f000000014626b7074000002040000001 shared strong links since 47258595a00000218000000146758595a 010100000c484c696e6f0210 antiquity, when both were 0000022c000000146258595a000002400 considered branches of the 00006d6e747252474220585 0000014646d6e64000002540000007064 mathematical 6d6464000002c40000008876756564000 95a2007ce000200090006003 0034c0000008676696577000003d40000 10000616373704d53465400 00246c756d69000003f8000000146d6561 00000049454320735247420 730000040c00000024746563680000043 00000000c725452430000043c0000080c6 00000000000000000000000 75452430000043c0000080c6254524300 0000f6d6000100000000d32d 00043c0000080c7465787400000000436f 707972696768742028632920313939382 48502020000000000000000 04865776c6574742d5061636b61726420 00000000000000000000000 436f6d70616e7900006465736300000000 000000127352474220494543363139363 00000000000000000000000 62d322e31000000000000000000000012 00000000000000000000000 735247422049454336313936362d322e3 00000000001163707274000 100000000000000000000000000000000 0000000000000000000000 00150000000336465736300

0001840000006c777470740 00001f000000014626b70740 0000204000000147258595a 00000218000000146758595 a0000022c00000014625859 5a0000024000000014646d6 e640000025400000070646d 6464000002c400000088767 565640000034c0000008676 696577000003d4000000246 c756d69000003f8000000146 d6561730000040c00000024 74656368000004300000000 c725452430000043c0000080 c675452430000043c0000080 c625452430000043c0000080 c7465787400000000436f707 97269676874202863292031 393938204865776c6574742 d5061636b61726420436f6d7 0616e790000646573630000 00000000001273524742204 9454336313936362d322e31 00000000000000000000001 27352474220494543363139 36362d322e3100000000000 00000000000000000000000 00000000000000000000

Broad translations of musical principles into architecture continued in the 20th Century.As radical newideas developed in both disciplines, cross-fertilisation was encouraged by new developments in media and technology. Aesthetics of Total Serialism, by Marcus Bandur, documents the collaboration between Le Corbusier and the composer Iannis Xenakis on the Phillips Pavilion at the 1958 Brussells World Fair (Figure 2.3). The design of the pavilion referred to the principles and techniques of serial music, and the interior incorporated a multimedia show of lights, projected images and specially composed music (Bandur 2.2 Contemporary Context: Literal 2001,p74). and Metaphorical Approaches Architects have used music in their work both literally and metaphorically. Opinions vary as to the In The Emancipation of the validity of each approach. Dissonance, Michael Harvey describes Daniel Libeskinds Jewish Museum Berlin (19892001), based on the opera Moses und Aron, by the composer Arnold Schoenberg (Figure 2.4). Harvey argues that the building is successful because it avoids making a literal translation of the music, instead exploring the underlying philosophical concerns of the composer (Harvey 1998,p1). Harvey contrasts Libeskinds building with Steven Holls Stretto House (1990-92), which explores musical ideas of overlapping found in a composition by Bla Bartk (Figure 2.5). The author faults this project for its literal approach, commentators consider the literal However, not all and claims the architect has a flawed understanding of theArchitecture as a approach to be unsound. In music. Translation of Music, Elizabeth Martin describes the Stretto House positively as a study into the inherent multi-layered nature of architecture (Martin 1994,p55). The literal approach is further illustrated by Martins project, Epicyclarium, a translation of a piece of graphic music into architectural form (Martin 1994). 2.3 Architecture as Frozen Music Literal translations of music into architecture are founded on the formal parallels between each discipline. In Architecture and Music, Alexander Walton discusses the reciprocal values shared by the two arts, with an emphasis on technique rather than atmosphere (Walton 1934). The author declares architecture and music to be the two most formal arts (Walton 1934). He asserts that architecture and music share an underlying

structural logic; as architecture divides space according to proportion, so music divides time according to rhythm.

Figure 2.3: Sketch for the Phillips Pavilion, based on compositional principles from serial music (Bandur 2001,p67)

ffd8ffe000104a46494600010201009500 950000ffe20c584943435f50524f46494c4 500010100000c484c696e6f021000006d6 e74725247422058595a2007ce00020009 000600310000616373704d53465400000 000494543207352474200000000000000 00000000000000f6d6000100000000d32d 485020200000000000000000000000000 000000000000000000000000000000000 000000000000000000000000000000000 000116370727400000150000000336465 7363000001840000006c7774707400000 1f000000014626b7074000002040000001 47258595a00000218000000146758595a 0000022c000000146258595a000002400 0000014646d6e64000002540000007064 6d6464000002c40000008876756564000 0034c0000008676696577000003d40000 00246c756d69000003f8000000146d6561 730000040c00000024746563680000043 00000000c725452430000043c0000080c6 75452430000043c0000080c6254524300 00043c0000080c7465787400000000436f 707972696768742028632920313939382 04865776c6574742d5061636b61726420 436f6d70616e7900006465736300000000 000000127352474220494543363139363 Figure 2.4: Daniel 62d322e31000000000000000000000012 Libeskinds Jewish 735247422049454336313936362d322e3 Museum, a conceptual 100000000000000000000000000000000 translation of music 0000000000000000000000 (http://www.pbs.org) ffd8ffe000104a46494600010201009500 950000ffe20c584943435f50524f46494c4 500010100000c484c696e6f021000006d6 e74725247422058595a2007ce00020009 000600310000616373704d53465400000 000494543207352474200000000000000 00000000000000f6d6000100000000d32d Figure 2.5: Steven Holls 485020200000000000000000000000000 Stretto House, a literal 000000000000000000000000000000000 translation of music (Martin, 000000000000000000000000000000000 1994,p57) 000116370727400000150000000336465 7363000001840000006c7774707400000 1f000000014626b7074000002040000001 47258595a00000218000000146758595a 0000022c000000146258595a000002400 0000014646d6e64000002540000007064 6d6464000002c40000008876756564000 0034c0000008676696577000003d40000 00246c756d69000003f8000000146d6561 730000040c00000024746563680000043 00000000c725452430000043c0000080c6 75452430000043c0000080c6254524300 00043c0000080c7465787400000000436f 707972696768742028632920313939382 04865776c6574742d5061636b61726420 436f6d70616e7900006465736300000000 000000127352474220494543363139363 62d322e31000000000000000000000012 735247422049454336313936362d322e3 100000000000000000000000000000000 0000000000000000000000

Waltons book includes a discussion of counterpoint and harmony the horizontal and vertical aspects of music. Counterpoint, consisting of different melodic lines running independently in the same horizontal direction, is likened to the faade of a Renaissance palazzo, with its horizontal bands ofwindows.Bycontrast,harmony,with its vertical Waltons comparisons between architecture and arrangement of notes into chords, is equated with music seem slightly idealised; there are the verticality of a Gothic cathedral (Walton exceptions to every rule. Nevertheless, the use of 1934). spatial terms such as horizontal and vertical to describe music, supports the notion that significant formal parallels exist between the two disciplines. 2.4 The Architectural Music of Bach The polyphony of a Bach fugue is an ideal example of the integration of the horizontal and vertical aspects of music. A fugue is a complex musical game in which two or more melodic lines, or voices, arewoventogethertoformaharmonisedwhole.The challenge of writing a fugue is to preserve the The overtly each voice while a fugue is ideal identities of structural form of arranging them in inspiration that they produce his book, Bauhaus, such a wayfor architecture. In pleasing harmonies Hans played together. when Maria Wingler documents a student project to design a sculptural monument to the composer in 1928 (Wingler, p440-441). The sculpture, based on a graphic representation of a Bach fugue, is very literal in its approach (Figure 2.6). The monuments designer, Heinrich Neugeboren, explained at the time that he was not concerned with an emotionally personal reinterpretation, but Neugeboren scientifically exact synaesthetic ideas rather with a was inspired by the transformation of the theRussian painter,Kandinsky,whowas into another system (Wingler, p440-441). thenateacherat the Bauhaus (Wingler 1969). Kandinsky saw a great affinity between painting and music, especially in terms of colour (Figure 2.7). In his theoretical work Concerning the Spiritual in Art, Kandinsky writes, colour is the keyboard, the eyes are the hammers, the soul is Colour is with the strings (Dchting 1996). the pianonowhere to be seen in Neugeborens sculpture. His experimental work is concerned with representing the construction of the music (Wingler, p440-441). Each of the three forms in the model represents a voice from the fugue; as the music rises and falls, so too does the sculpture.

ffd8ffe000104a46494600010 201009100910000ffe20c5849 43435f50524f46494c4500010 100000c484c696e6f02100000 6d6e74725247422058595a20 07ce00020009000600310000 616373704d53465400000000 494543207352474200000000 00000000000000000000f6d6 ffd8ffe000104a46494600010201009000 000100000000d32d48502020 900000ffe20c584943435f50524f46494c4 500010100000c484c696e6f021000006d6 000000000000000000000000 e74725247422058595a2007ce00020009 000000000000000000000000 000600310000616373704d53465400000 000494543207352474200000000000000 000000000000000000000000 00000000000000f6d6000100000000d32d 000000000000000000000011 485020200000000000000000000000000 000000000000000000000000000000000 637072740000015000000033 000000000000000000000000000000000 64657363000001840000006c 000116370727400000150000000336465 77747074000001f000000014 7363000001840000006c7774707400000 1f000000014626b7074000002040000001 626b70740000020400000014 47258595a00000218000000146758595a 7258595a0000021800000014 0000022c000000146258595a000002400 0000014646d6e64000002540000007064 6758595a0000022c00000014 6d6464000002c40000008876756564000 Figure 2.6: Wood and 6258595a0000024000000014 0034c0000008676696577000003d40000 cardboard replica of 646d6e640000025400000070 00246c756d69000003f8000000146d6561 Neugeborens design for a 730000040c00000024746563680000043 Bach Monument. The low 646d6464000002c400000088 00000000c725452430000043c0000080c6 form on the left represents 767565640000034c00000086 75452430000043c0000080c6254524300 the bass. (Wingler, p441) 00043c0000080c7465787400000000436f 76696577000003d400000024 707972696768742028632920313939382 6c756d69000003f800000014 04865776c6574742d5061636b61726420 436f6d70616e7900006465736300000000 6d6561730000040c00000024 000000127352474220494543363139363 74656368000004300000000c 62d322e31000000000000000000000012 725452430000043c0000080c 735247422049454336313936362d322e3 100000000000000000000000000000000 675452430000043c0000080c 0000000000000000000000 625452430000043c0000080c 7465787400000000436f7079 726967687420286329203139 3938204865776c6574742d50 61636b61726420436f6d7061 6e7900006465736300000000 000000127352474220494543 36313936362d322e31000000 000000000000000012735247 422049454336313936362d32 2e3100000000000000000000 000000000000000000000000 0000000000

However, Neugeboren admits that his creation is flawed. The bass, deep and powerful when heard, seems insignificant in the sculpture. Its lesser stature allows it to be smothered by the towering monumentality of the soprano (Wingler, p440441). 2.5 Digital Architecture Neugeborens scientifically exact translation, while limited by the technology available at the time, is strikingly similar in spirit to contemporary digital design practice.An example is the process known as Data Representation Architecture, where architectural form is generated using data In Real and Virtual Spaces Generated by Music, from a source external to architecture. Music is Adrian Levy source of data. one possibledescribes the procedure whereby sounds (car horn, water) and melodies (Beethovens Ode to Joy) are translated into architectural form (Figure 2.8). Sampled sounds are converted to data, which is then manipulated to generate geometries. Musical parameters (frequency, duration and loudness) are mapped onto spatial parameters (x, y and z coordinates of points in space). This process creates a number of virtual surfaces, to which colour, light and texture Data Representation Architecture is an example of are added at the designers discretion (Levy in parametric design, a profound development 2003,p380). which promises to extend the architecture computer from a simple tool used for representation into a powerful instrument capable of generation (Menges 2005,p63). However, the role of the architect as data manipulator is crucial in this process. The human operator of the machine is the mediator between raw data and outcome, and must exercise judgement in the selection of the Enhancing Creativityof the system itself. 2.6 data and the design Issues of authorship are growing more relevant, especially in the educational context, where the use of advanced digital design techniques is Digital processes can be used in becoming increasingly common. architectural education to challenge notions of what architecture is and to enhance students creativity. In The Musitecture Game students explore the relationship between music and architecture using a process similar to Data Representation Architecture. Digital representations of architectural form are created directly from musical compositions using parameters such as dynamics, tempo, meter and rhythm (Figure 2.9). Diverse musical

sources are used, ranging from jazz and pop, to indy and heavy metal (Ham 2005,p142).

Figure 2.8: Virtual space generated from Beethovens Ode to Joy (Levy 2003,p384)

ffd8ffe000104a46494600010201009600 960000ffe20c584943435f50524f46494c4 500010100000c484c696e6f021000006d6 e74725247422058595a2007ce00020009 000600310000616373704d53465400000 000494543207352474200000000000000 00000000000000f6d6000100000000d32d 485020200000000000000000000000000 000000000000000000000000000000000 000000000000000000000000000000000 000116370727400000150000000336465 7363000001840000006c7774707400000 1f000000014626b7074000002040000001 47258595a00000218000000146758595a 0000022c000000146258595a000002400 0000014646d6e64000002540000007064 6d6464000002c40000008876756564000 ffd8ffe000104a46494600010201009600 0034c0000008676696577000003d40000 960000ffe20c584943435f50524f46494c4 00246c756d69000003f8000000146d6561 500010100000c484c696e6f021000006d6 730000040c00000024746563680000043 e74725247422058595a2007ce00020009 00000000c725452430000043c0000080c6 000600310000616373704d53465400000 75452430000043c0000080c6254524300 000494543207352474200000000000000 00043c0000080c7465787400000000436f 00000000000000f6d6000100000000d32d 707972696768742028632920313939382 485020200000000000000000000000000 Figure 2.9: CAD model 04865776c6574742d5061636b61726420 000000000000000000000000000000000 translation of The 436f6d70616e7900006465736300000000 000000000000000000000000000000000 Avalanches Flight Tonight 000000127352474220494543363139363 000116370727400000150000000336465 (Ham 2005,p142) 62d322e31000000000000000000000012 7363000001840000006c7774707400000 735247422049454336313936362d322e3 1f000000014626b7074000002040000001 100000000000000000000000000000000 47258595a00000218000000146758595a 0000000000000000000000 0000022c000000146258595a000002400 0000014646d6e64000002540000007064 6d6464000002c40000008876756564000 0034c0000008676696577000003d40000 00246c756d69000003f8000000146d6561 730000040c00000024746563680000043 00000000c725452430000043c0000080c6 75452430000043c0000080c6254524300 00043c0000080c7465787400000000436f 707972696768742028632920313939382 04865776c6574742d5061636b61726420 436f6d70616e7900006465736300000000 000000127352474220494543363139363 62d322e31000000000000000000000012 735247422049454336313936362d322e3 100000000000000000000000000000000 0000000000000000000000

One of the lessons students learn from The Musitecture Game is that extra-architectural sources such as music can inform architectural design. The process of translation from one medium to another can enhance creativity and lead to solutions or forms that would otherwise not emerge. Steven Holls description of the As boundaries between disciplines collapse, Stretto House illustrates this point: new channels suggesting thought and development open up A move away from compartmentalizing and mental closing is a move toward an open future. (Holl 1994,p59) This project seeks to break down the boundaries which surround architecture, in the hope of discovering new connections. Architecture and music have a strong shared tradition, indicated by the wealth of literature on the subject. The advent of digital design technologies and the emergence of the notion of virtual space have opened up new avenues for the exploration of this relationship.

capte 3

ProcessThis chapter describes the process used to generate the virtual forms documented in this report.After a brief background summary, each step is described in detail. 3.1 Background The music of Johan Sebastian Bach is known for its sense of completeness.The composer wrote collections of works which seem to exhaust the potential of the instrument or the compositional form. Examples include The Brandenburg Concertos, suites for solo cello, violin and lute, as The as the English Clavier (bwv846857) is well Well-TemperedSuites, French Suites and no exception. the of its two Partitas for Eachkeyboard. volumes contains preludes and fugues written in all 24 keys available in the tuning system know as welltemperament. Bach seems to have been intent on demonstrating the flexibility and adaptability of In order tuning system which had just been the new to preserve this sense of wholeness, and out of respectforthecollectionas a developed. workofartinitself,it has been decided to translate one of the volumes in its entirety 48 preludes and fugues. This has the added benefit of allowing comparison between a number of different pieces of similar structure, and the parametric software In order to make the to such a task. chosen is well-suited translation of a large number of pieces feasible, a high degree of automation has been built into the process. To this end, scripts have been used which were either created by the author or by others. 3.2 Description The translation process begins and ends with electronic representations of music.The raw materialfor the process is not a human performance, but a set of instructions for a Table The process consists of four main steps (see computer. step represents a different 3.1). Each Table 3.1: Summary the same data. manifestation of of the processMIDI > ASCII > EXCEL > CATIA music text numbers Form

3.2.1 Step 1: MIDI (music) The process begins with electronic music, in the form of MIDI files. MIDI (Musical Instrument Digital Interface) is the standard format for computer Unlike other music. programmedformats such as .wav or .mp3, a MIDI file is not a sound file. It is simply a set of instructions which tells a device, such as a synthesiser or a desktop computer, which sounds to play and when. It is an ideal source of data for this project as it provides lists of values which can Each MIDI file contains a number of tracks, be used later in the parametric software. which correspond to the different parts played simultaneously in each prelude or fugue. Each part Using MIDI is known asa great deal of time, as the of a fugue files saves a voice.* music would otherwise have to be manually transcribed. 3.2.2 Step 2: ASCII (text) The MIDI files are converted into ASCII text files using a script. The resulting file contains a list of all the notes in the MIDI file, providing information on the variables associated with each note (Figure 3.1). These variables are: Pitch:The note to be played, expressed as a roman character (C, C#, D, E, etc) Position:The location of each note in the musical sequence, expressed as a fraction Duration: The length of each note in time, expressed as a fraction Velocity: A quality of the note analogous to hard or soft, expressed as a decimal number Tempo:The speed of the music, expressed as a decimal number

ffd8ffe000104a46494600010201009600960000ffe20c584943435f50524f46494c4500010100000c48 4c696e6f021000006d6e74725247422058595a2007ce00020009000600310000616373704d5346540 000000049454320735247420000000000000000000000000000f6d6000100000000d32d4850202000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000001163707274000001500000003364657363000001840000006c77747074000001f0000 00014626b707400000204000000147258595a00000218000000146758595a0000022c000000146258 595a0000024000000014646d6e640000025400000070646d6464000002c4000000887675656400000 34c0000008676696577000003d4000000246c756d69000003f8000000146d6561730000040c000000 2474656368000004300000000c725452430000043c0000080c675452430000043c0000080c6254524 30000043c0000080c7465787400000000436f70797269676874202863292031393938204865776c65 74742d5061636b61726420436f6d70616e79000064657363000000000000001273524742204945433 6313936362d322e31000000000000000000000012735247422049454336313936362d322e3100000 0000000000000000000000000000000000000000000000000

Figure 3.1: ASCII text file

3.2.3 Step 3: EXCEL (numerals) In this step the data is reformatted into numerical form. The parameters in the text files is divided displayed The information in the ASCII text files are into as roman characters (pitch) or to the voices in different tracks, corresponding fractions (position and duration). These formats are unsuited to the each piece. parametric software, which can only read numerals, so the data must be converted from text into decimal numbers (Figure 3.2). This step is For each track of a macro Table 3.2: Design Tables automated using each MIDI file, five Excel files in Microsoft Excel. are created. These design tables enable DESIGN TABLE associations to be made between the musical MUSICAL PARAMETER SPATIAL PARAMETER and spatial parameters (Table 3.2).

DT_offset.xls The location of each note in the musical sequence The location of each block in the spatial sequence DT_duration.xls The length of each note in time The length of each block in space DT_frequency.xls A value derived from the pitch of the note The height of each block DT_wavelength.xls A value derived from the pitch of the note The width of each block * For the sake of convenience, the DT_note number.xls term voice will be used from now The though preludes the track on to refer to all musical parts, even number of notes inoften dont The number of blocks in the form contain voices.

In addition, a sixth Excel file is created, containing the complete information for each MIDI file in numerical and text format.

ffd8ffe000104a46494600010201009400930000ffe205384943435f50524f46494c45000101000005286170706c0220 00006d6e74725247422058595a2007d20005000d000c00000000616373704150504c000000006170706c0000000000 00000000000000000000000000f6d6000100000000d32d6170706c0000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000d7258595a00000120000000146758595a000001 34000000146258595a0000014800000014777470740000015c0000001463686164000001700000002c725452430000 019c0000000e675452430000019c0000000e625452430000019c0000000e64657363000001ac0000003f63707274000 002540000004876636774000001ec000000306e64696e0000021c000000386473636d0000029c0000028c58595a200 00000000000744b00003e1d000003cb58595a200000000000005a730000aca60000172658595a20000000000000281 8000015570000b83358595a20000000000000f35200010000000116cf736633320000000000010c42000005defffff326 000007920000fd91fffffba2fffffda3000003dc0000c06c63757276000000000000000101cd00006465736300000000000 0001447656e65726963205247422050726f66696c650000000000000000000000144765

Figure 3.2: The data converted to numerical format in Excel

3.2.4 CATIA (form) This is the final step of the process where the virtual forms are created.The parametric software application, Digital Project, is used.This is part of Two suiteof Catia file are created Catia. a largertypes of applications known as (Table 3.3): CATPart: For each voice, contains the musical notes CATProduct: For each prelude or fugue, contains CATPart files

Each CATPart template contains links to the five Excel design tables mentioned in Step 3. Before the templates are used, these links are broken. This allows each template to be re-linked to a For set voice, the appropriate template is neweachof design tables. selected, and copied into the folder which contains the design tables for that voice. Once the template is opened, it is automatically linked to these new design tables. At this stage the CATpart file is updated to reflect the new parameters. Any This step is completed for each voice of then unused pads at the end are deleted and each the prelude or saved as a new file. template isfugue. This results in the creation of a CATpart file for each voice. These files are then imported into a new CATProduct file, which represents the prelude or fugue in question. The structure of the Catia files corresponds to the structure of the music (Table 3.3). Table 3.3: FileStructure MUSICAL STRUCTURE FILE STRUCTURE Prelude/Fugue > Voice 1 > Voice 2 Prelude/Fugue.CATProduct > Voice_1.CATPart > Voice_2.CATPart ? ? > Voice n > Voice_n.CATPart

Each musical note is represented in the CATPart file by an extruded rectangle, referred to as a pad. The dimensions of the rectangle are determined by the pitch of the note, and the depth As each voice contains a different number of of the extrusion is determined by the length of the notes, note. each CATPart file contains a unique number of pads. Several CATPart templates are used, each containing a different number of pads: 200, 300, 400, 500, 600, 700 and 800. The template which most closely approximates the number of notes in the voice is used. For example, if a voice contains 232 notes, then the template containing 300 pads is used.

The problem of the third dimension has been resolved by dividing pitch into two parameters, notionally referred to as frequency and wavelength. Added to time, these form the three musical parameters needed (Table 3.4). Table 3.4:MUSICAL PARAMETERS SPATIAL PARAMETERS Mapping of parameters between music and space Time Length Pitch Frequency Height Wavelength Width

The pitch of a note is determined by its frequency and wavelength. These two values are locked in a reciprocal relationship; one is the inverse of the other. A rectangle also has two dimensions height and width. Therefore, it seems appropriate to use frequency and wavelength to determine the The actual of the rectangle which represents dimensionsfrequency and wavelength are not each used, note. as the values are two extreme (too great in the case of frequency and too small in the case of wavelength). Instead, an indexing system has In Bachs day, been devised. the typical keyboard contained less notes than it does today. A survey of all the preludes and fugues in Book I of The WellTempered Clavier reveals that a total of 64 notes are used, ranging from A three octaves below middle C, to C three octaves above. Each note in 3.3 Wavelength and Pitch the series has been given two index numbers, One two from 1numbers determine project hasand rangingthe main challenges of this the height The of index to 64, depending on where that been falls (Table 3.5). rectanglesthe two principle note finding extruded represent that make up the width of the a way to dimensions of When alltimenotes are in 3virtual forms. music the and pitch dimensional space. When mapping parameters superimposed, a diamond form emerges. This from one system onto another,range of The Wellrepresents the complete tonal it is imperative that both systems (Figure 3.4).is that the voices in One advantage of have the same number of Tempered Clavier this system Additional parameters such can as in and timbre parameters, so that a matchas volumethe work by the bass are not disadvantaged, be made have been investigated, but found (Figure betweeneach.Therefore a chapter 2to beparameter Neugeboren described in third musical unsuitable. Timbre is is needed. system,thelowest nature of the 2.6).Inthisdetermined by the and highest notes particular instrument used in a the same are represented by forms with performance, as Figure 3.3: The highest and lowest well as the acoustics3.3). notes areand vertical dimensions, but in the horizontal equally balanced respectively (Figure of the space. As noted earlier, however, directionsthis project is not concerned with the Regarding volume, it should be noted that Bachs performance of music, but its essential structure. score gives no indication for how loud or soft each prelude and fugue of The Well-Tempered Clavier should be played, leaving it up to the discretion of the performer. Volume, therefore, does not seem to be an integral part of this music.

ffd8ffe000104a4649460001020100c800c80000ffe20c584943435f50524f4649 4c4500010100000c484c696e6f021000006d6e74725247422058595a2007ce00 020009000600310000616373704d5346540000000049454320735247420000 000000000000000000000000f6d6000100000000d32d4850202000000000000 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000011637072740000015000000033646573630000018 40000006c77747074000001f000000014626b70740000020400000014725859 5a00000218000000146758595a0000022c000000146258595a0000024000000 014646d6e640000025400000070646d6464000002c400000088767565640000 034c0000008676696577000003d4000000246c756d69000003f8000000146d6 561730000040c0000002474656368000004300000000c725452430000043c00 00080c675452430000043c0000080c625452430000043c0000080c746578740 0000000436f70797269676874202863292031393938204865776c6574742d50 61636b61726420436f6d70616e7900006465736300000000000000127352474 22049454336313936362d322e31000000000000000000000012735247422049 454336313936362d322e3100000000000000000000000000000000000000000 0000000000000

Figure 3.3: A visual representation of the five octave range used by Bach

ffd8ffe000104a46494600010201004800480000ffe20c584943435f50524f46494c4500010100000c484c696e6f02100000 6d6e74725247422058595a2007ce00020009000600310000616373704d53465400000000494543207352474200000000 00000000000000000000f6d6000100000000d32d48502020000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000001163707274000001500000003364657363000001840000006c 77747074000001f000000014626b707400000204000000147258595a00000218000000146758595a0000022c00000014 6258595a0000024000000014646d6e640000025400000070646d6464000002c400000088767565640000034c00000086 76696577000003d4000000246c756d69000003f8000000146d6561730000040c0000002474656368000004300000000c7 25452430000043c0000080c675452430000043c0000080c625452430000043c0000080c7465787400000000436f707972 69676874202863292031393938204865776c6574742d5061636b61726420436f6d70616e790000646573630000000000 000012735247422049454336313936362d322e31000000000000000000000012735247422049454336313936362d322e 31000000000000000000000000000000000000000000000000000000

capte 4

Virtual translations of the 48 preludes and fugues from The Well-Tempered Clavier, Book IThis chapter presents the outcomes of the project. The 48 virtual forms are presented in a consistent way in order to aid comparison. Each virtual form is represented on one page by one perspective and four orthographic views: start, end, top and Sandwiched between the views represent the side. The start and end top and side views is a scale bar. This represents the length of each beginning and ending of each piece of music. piece, measured in bars. The major ticks of the scale represent the bars, while the minor ticks The scale is necessary as in each bar. show the number of beatsall the preludes and fugues have been scaledtothesamelength.Thishas beendone toaidcomparison.It should be noted that the score for The Well-Tempered Clavier has no instructions regarding tempo, so time is open to interpretation.

4.1 Prelude No. 1 in C Major, bwv 846

4.2 Fugue No. 1 in C Major, bwv 846

4.3 Prelude No. 2 in C Minor, bwv 847

4.4 Fugue No. 2 in C Minor, bwv 847

4.5 Prelude No. 3 in C-sharp Major, bwv 848

4.6 Fugue No. 3 in C-sharp Major, bwv 848

4.7 Prelude No. 4 in C-sharp Minor, bwv 849

4.8 Fugue No. 4 in C-sharp Minor, bwv 849

4.9 Prelude No. 5 in D Major, bwv 850

4.10 Fugue No. 5 in D Major, bwv 850

4.11 Prelude No. 6 in D Minor, bwv 851

4.12 Fugue No. 6 in D Minor, bwv 851

4.13 Prelude No. 7 in E-flat Major, bwv 852

4.14 Fugue No. 7 in E-flat Major, bwv 852

4.15 Prelude No. 8 in E-flat Minor, bwv 853

4.16 Fugue No. 8 in D-sharp Minor, bwv 853

4.17 Prelude No. 9 in E Major, bwv 854

4.18 Fugue No. 9 in E Major, bwv 854

4.19 Prelude No. 10 in E Minor, bwv 855

4.20 Fugue No. 10 in E Minor, bwv 855

4.21 Prelude No. 11 in F Major, bwv 856

4.22 Fugue No. 11 in F Major, bwv 856

4.23 Prelude No. 12 in F Minor, bwv 857

4.24 Fugue No. 12 in F Minor, bwv 857

4.25 Prelude No. 13 in F-sharp major, bwv 858

4.26 Fugue No. 13 in F-sharp major, bwv 858

4.27 Prelude No. 14 in F-sharp minor, bwv 859

4.28 Fugue No. 14 in F-sharp minor, bwv 859

4.29 Prelude No. 15 in G major, bwv 860

4.30 Fugue No. 15 in G major, bwv 860

4.31 Prelude No. 16 in G minor, bwv 861

4.32 Fugue No. 16 in G minor, bwv 861

4.33 Prelude No. 17 in A-flat major, bwv 862

4.34 Fugue No. 17 in A-flat major, bwv 862

4.35 Prelude No. 18 in G-sharp minor, bwv 863

4.36 Fugue No. 18 in G-sharp minor, bwv 863

4.37 Prelude No. 19 in A major, bwv 864

4.38 Fugue No. 19 in A major, bwv 864

4.39 Prelude No. 20 in A minor, bwv 865

4.40 Fugue No. 20 in A minor, bwv 865

4.41 Prelude No. 21 in B-flat major, bwv 866

4.42 Fugue No. 21 in B-flat major, bwv 866

4.43 Prelude No. 22 in B-flat minor, bwv 867

4.44 Fugue No. 22 in B-flat minor, bwv 867

4.45 Prelude No. 23 in B major, bwv 868

4.46 Fugue No. 23 in B major, bwv 868

4.47 Prelude No. 24 in B minor, bwv 869

4.48 Fugue No. 24 in B minor, bwv 869

capte 5

Analysis and InterpretationThe purpose of this chapter is to analyse and interpret the 48 virtual forms which are documented in the previous chapter. It also looks at other work done as part of this project, including the production of a physical model and two animations. 5.1 The 48 Virtual Forms 5.1.1 A Family of Forms The Well-Tempered Clavier is a compendium of contrapuntal keyboard music. Each prelude and fugue can be appreciated in isolation, but when the 48 are seen as a whole they take on far greater Each piece has been presented in the same significance. format in order to aidcomparison.Inthis way,differences andsimilarities are emphasised. The works illustrated in Chapter 4 can be seen as 48 instances of one parametric form. This ideal form has been determined by decisions made by the author. These decisions include not only which musical parameter to map onto which spatial parameter, but also the use of rectangular forms To a significant degree, then, as shapes of rather than other shapes suchthe circles or the virtual forms are determined by the system used, triangles. not the music. However, the consistent use of the same system to generate all 48 forms means that comparison within the set will reveal the unique identity of each prelude and fugue. 5.1.2 The Shape of Music The spatial representation allows one to see the whole piece of music simultaneously. At a glance, one can compare the beginning to theendor the middle.This is not possible when Musical notation also music. listening to the actualallows such time-independent comparisons to be made, yet written music also has limitations. The symbols used in musical notation are a system of code, a language which must be learnt in order to be understood. In the words of Henrich Neugeboren, the empty and filled notes heads merely signify length of the notes, without showing them (Wingler 1969). Like Neugeboren, this project seeks to reveal the construction of Bachs music in a direct way which can be understood by anyone.

The formal translations reveal the shape of each piece in its entirety. In Prelude No. 1, for example, the music begins in a high register and steadily moves down towards its resolution. This is represented by the height of the forms diminishing fromvirtual forms (sidebe contrastedwidth one The left to right can view) as the with increases (top view). illustrate facts about the music. For another to instance, the preludes tend to be more rhythmically regular than the fugues. This is shown in the virtual forms, which are simpler and feature more regular formal patterns. The fugues, on the other hand, are much more complex, as they Subject, countersubject, include a number of voices. This greater staircases complexity can be seen easily in the forms. 5.1.3 Digital process It is interesting to note that the MIDI files are programmed rather than performed. In fact, at no stage of this project has a performer been involved. 5.1.4 Orientation Each piece has been arranged in space horizontally. This reflects the horizontal linear nature of the music and leaves the forms open to This is only one possible interpretation. They could multiple readings. also be shown vertically like towers (insert image). The horizontal arrangement was chosen to avoid the obvious architectural connotations which would arise with a vertical, tower-like arrangement. The forms reside in virtual space, so they are free from the restrictions of real space, such as gravity. In this sense, the forms are pure crystallisations of 5.1.5 Symmetry The virtual forms display a high the music. degree of symmetry: 2-fold in the side views and 4-foldin theend views.This is theresult of a conscious decision to avoid any unnecessary eccentricity, which would distract from the pure Figure the music. form of5.1 shows the end view of an arrangement which was used in the developmental stage of the project. The final arrangement, shown in Figure 5.2, produces a more rounded and complete form. This arrangement is also intended to be reminiscent of the manner in which sound waves travel in all directions from their source. 5.1.6 Harmony Polyphonic music has a horizontal and vertical dimension.The voices move horizontally and harmonise vertically. Although they have a degree of freedom the voices are not completely independent of one another, they are interdependent.They must harmonise in order for the system to be meaningful.

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The virtual translations show this relationship between verticalityand horizontality. The start andendviews ofeach form show the vertical aspect of the music. In Figure 5.2, five rectangles overlap to create a crucifix-like form. Each rectangle represents a different note. When heard, these five notes combine to form the final chord which provides resolution at the conclusion The start and end views of the virtual is thus a of the fugue. The 2-dimensional shapeforms bear a striking resemblance of harmony. visual representation to the crucifix plan of churches common for most ofthehistoryofChristianity.This isentirelyappropriate,as Bach was a deeply religious man who dedicated his music to the glory of God. However, the similarity is not intentional, it is merely a piece of serendipity which has more to do with the way the system has been set up than 5.2 Other Work the spirit of Bachs music. This sections describes additional work done as a part of this project, including the production of a physical model and two animations. 5.2.1 Physical Model A physical model of Fugue No. 1 was produced for the exhibition, Disparallel Spaces, held during June 2007 at theTin Sheds Gallery, Faculty of Architecture, University of Sydney (Figure 5.3). The model was constructed from 430 pieces of laser cut plywood 1mm in thickness. Each plywood piece represents a semi-quaver; 16 of which make up a bar. 5.2.2 Fly-through movie The fly-through movie shown in Figure 5.4 was produced to give a senseof what it might be like to beinsideoneof theforms.The Quicktime movie was produced in VectorWorks. One of the limitations of this project is its emphasis on the forms as sculptural objects rather than spaces which can be experienced internally; architecture is as much about the interior as it is about the exterior. However, the fly-through movie reveals a rich spatial experience inside the virtual forms.

Figure 5.4: Screen shots from a fly-through animation of Fugue No. 1

ffd8ffe000104a46494600010201009600960000ffe20c584943435f50524f46494c4500010100000c484c696e6f02100000 6d6e74725247422058595a2007ce00020009000600310000616373704d53465400000000494543207352474200000000 00000000000000000000f6d6000100000000d32d485020200000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000001163707274000001500000003364657363000001840000006c7 7747074000001f000000014626b707400000204000000147258595a00000218000000146758595a0000022c0000001462 58595a0000024000000014646d6e640000025400000070646d6464000002c400000088767565640000034c00000086766 96577000003d4000000246c756d69000003f8000000146d6561730000040c0000002474656368000004300000000c7254 52430000043c0000080c675452430000043c0000080c625452430000043c0000080c7465787400000000436f707972696 76874202863292031393938204865776c6574742d5061636b61726420436f6d70616e7900006465736300000000000000 12735247422049454336313936362d322e31000000000000000000000012735247422049454336313936362d322e3100 0000000000000000000000000000000000000000000000000000

5.2.3 Flash animation A second animation was also produced for the exhibition Disparallel Spaces.The purpose of this animation is not to explore the interior of the form, but to explain the relationship between the Unlike the fly-through movie, the Flash animation different voices. includes the sounds produced by the MIDI file for Fugue No. 1, from which the forms are generated. In this animation, each note is delineated with a separate rectangle, in order to help the viewer understand the relationship between the music and the forms. Each voice is coloured differently in order to render the contrapuntal structure of the music more apparent.

capte 6

ConclusionThis chapter discusses the project, its limitations, and possible avenues for further exploration.

The purpose of this project is to explore the relationship between musical structure and architectural structure by translating preludes and fugues by Johan Sebastian Bach into virtual spatial form.The project has successfully translated BookI ofBachs Well-Tempered Clavier using a combination of software applications,and relying on parametricdesign.The 48 virtual forms that have been generated are a family of forms and reveal a wealth of information about the musical pieces they embody. Freezing the music in a single moment allows one to see the shape of the entire piece simultaneously, something which is not 6.1 Limitations possible when listening to a performance. Exterior not interior Western music/architecture 6.2 Potential for Development Pop music Interior Book II?

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