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Iannis Xenakis:
Trained as an Engineer;
worked as an engineer and architect with Le Corbusier;
wrote music, and designed ‘Polytopes’ – installations that combined
light and sound to make fully immersible environments.
Writings : 1963
Xenakis’ Concept:
To become a new kind of ‘Artist / Conceptor’
Knowledgeable and inventive in Mathematics,
Logic, Physics, Chemistry, Biology, Genetics,
Palentology, Human Sciences and History:
Knowledge based on, guided by, and oriented
toward forms and architecture
music and architecture : 1971
Le Corbusier Years
1947 - 1959 (Age : 25 - 37)
Xenakis’ role at La Tourette?
La Tourette: Designed as a Dominican Convent at Evaux
Today: Centre Thomas More
La Tourette: windows based on musical spacing: formal movement through shadow/light
Links between Music and Mathematics
Musicians and Analytical Geometry
Xenakis and probability calculation
1970’s Construction of the
Analog digital computer @
CEMAMu
(Center for mathematical and automated musical
studies, founded by Xenakis)
Computer: allows use of an electrolytic surface + a pen
linked to a computer and speakers -
Ability to transform drawings into sound
(compare to Frank Gehry’s use of CATIA to create 3-
Dimensional forms by tracing a pen over a phsyical model)
Music:
Sound and Number
Acoustics and Mathematics
Cite Radieuse: Marseilles Housing Block
1945 - 1953
Xenakis’ role : Calculation of Structural Members
Collaborators include artist: (color consultation)
Cite Radieuse Rooftop Nursery construction
Xenakis collaboration - 1953 - 54
Chandigarh
1951 - 60
High Court, Chandigarh: 1950 – 55
Xenakis Role: Structural Design
Assembly Building, Chandigarh, India
1951 – 62
Hyperbolic ‘Dome’ for the Assembly lets ceremonial light enter the Assembly
Chamber @ Equinox and Winter Solstice
Chandigarh Assembly: Xenakis Contributions:
‘Undulating Glass Panes’
Assembly Building ‘Plug’ form (concrete – just 6” thick)
The techniques developed with this construction carried over to Xenakis’s
design of Philips Pavilion
1951 - 59
Hyperbolic Paraboloid form: Assembly Chamber (note LC and Xenakis’ use of
mathematics and physics in design concepts – the Plug relates to shape of
Nuclear Power Reactor cone)
Chandigarh Assembly : Building Model: Assembly was Centerpiece of
LC”s Design for Chandigarh, India
Tower of Shadows: (Arch of the Equinox’s) – LC and Xenakis studied the
trajectory of the sun for several LC projects, including the Chandigarh
Assembly Cone
Tower of Shadows: An architectural sculpture designed with LC to
demonastrate the virtue of the ‘brise-Soliel’.
The Tower of shadows created a permanently shaded space
LC also planned to construct a ‘Arch of the Equinoxes’ – to demonstrate the
path of the sun during the Equinoxes in Chandigarh. The ‘Arch of the Equinoxes’
sculpture project was never built
Firminy : 1955 - 61
Firminy : Youth and Cultural Center including classrooms, 2 theaters, a
library and informal meeting and exhibition spaces. Main element:
Grandstand
1955 – 61
Firminy Cultural Center: Details
End elevation; Entry Ramp;
Window Detail
Philips Pavilion: 1956 - 58
Musical Architectural Influences:
Messiaen
Hermann Scherchen : Melos (Periodical) (writings on music)
Music of: India, Laos, Vietnam, Java, China, Japan
(Xenakis was ahead of his time: world music)
Musique concrete (samples)
Xenakis’ Musical accomplishments:
Metastaseis (first original score)
Phillips Pavilion: 1958 :
Development of Polytopes
Philips Pavilion: Hyperbolic Paraboloid
Influences on design:
Mathematics, Music, Physics, Computational Design
Formal Diagram for Philips Pavilion Plan
Philips Pavilion: ‘Built Sound’
Xenakis’ ‘Electronic Poem’ - 2 – minute concert (Metastasis) between
Varese’s Poeme Electronique: 8 minutes
Investigations linking Stochastic Systems to Architecture and Sound
1950 - 2001
Housing project in Reze near Nantes: 1950 - 54
Façade Studies for rooftop Kindergarden
Window patterns inspired by Gregorian neumes, with window distribution
Following a ‘stochastic’ pattern
What is ‘stochastic’? What is a ‘Neume’?
Xenakis, Le Corbusier, and Stochastic Pattern:
Stochastic pattern in windows, Rooftop Kindergarden at the Housing
Project in Reze, near Nantes (former slide)
This window pattern repeated in several Le Corbusier projects,
And has also been used in projects by other prominent architects
What is Stochastic? (from Greek = to aim, or guess) - an adjective that refers
to systems whose behavior is non-deterministic, and not intermittent
(random).
Stochas is Greek for Stick; the pattern of arrows striking around a stick stuck in
a Greek hillside by an Archer in practice is the epitome of what is stochastic.
Any kind of time development which is analyzable in terms of probability is
stochastic.
Mathematical Theory: based on the theory of probability
Artificial Intelligence: using probalistic methods to solve problems, ie:
stoastic neural networks.
Natural Science: the model of gas filling a chamber, even though individual
particles of the gas will be moving in non-deterministic patterns
Physics: the Monte Carlo method: Random methods of computation and
experiment to create simulations for: the Manhattan Project (hydrogen
bomb).
Ronchamp: Use of Stochastic Window Patterns
Sanaa application of Stochastic Pattern
(borrowing from Le Corbusier/ Xenakis)
Neumes Translated into Architectural and Musical
Form
Gregorian Chant Pattern: Gregorian Neume
Xenakis used Neumes to create Window Patterns (Nimes);
and also as a compositional device for sound compositions
Le Corbusier, Xenakis, and Neumes:
Gregorian Neume
What is a Neume? The basic element of Western and Eastern systems of
musical notation. From the Greek word for breath: pneuma.
The earliest known Neumes: Aramaic origin - used to notate inflections in
quasi-emmelic recitation of Christian holy scriptures (chants).
They resemble a similar system - for the recitation of the Qur’an
In the 9th Century: Neumes became shorthand mnemonic aids for the
proper melodic recitation of chant. Neumatic recitation was first developed
in the Eastern Roman Empire (today’s southern Turkey, Syria, Lebanon, and
Israel).
Ronchamp: Windows placed as a ‘Neume’, or Neumatic notation of a Chant
Polytopes and Diatopes
Diatope or Polytope:
Galactic movement made visible
Diatope / Polytope purpose:
To resolve unsolvable problems related to architecture & the
Mediocrity of Concert Halls not related to Music of our Time
ie: the frontal position created by most concert halls
Diatope: eliminate the inconveniences created by collective
listening (concert hall) through immersion
Diatope at Beauberg (@ Centre Pompidou)
Diatope de Beauberg:
Polytope de Cluny: Light constructions with Sound
Polytopes : 1950 - 1985
Immersive Environments created through Light and Sound:
Polytope de Cluny
Further Readings:
Toru Takemitsu & Mathematical Structure in Music
Robin Evans: The Trouble with Numbers
Graphic depictions of Landscape and Landscape
Urbanism, presented to UC Students, Spring 2013
Sound Studies and Landscape Urbanism by
Victoria Meyers architect, hMa
Sound Sections by UC students, Victoria Meyers
Sound Seminar, 2013
Flood Plain Image
Trash Track, courtesy of MIT Planning
SIEESS Diagram: Courtesy: Harvard
Galway County Plan: Courtesy Galway Planning Dept.
Galway County Plan : Courtesy of Galway Planning Dept.
Urban Land Institute: Deployable Modular Landscapes
Michael Van Valkenburgh: Campus Plan
MVVA: Parks Diagram
MVVA: Park Design Diagram
Sound Studies and Landscape Urbanism
by Victoria Meyers architect, hMa
hMa: Won Buddhist Site Plan
Geometry and Movement: The Choreography of Spirals
The Concept of ‘Edge’ - as interpreted through Infinity: Infinite Bleed of Edge
Thru Screens
Sound Sections by UC students,
Victoria Meyers architect
Sound Seminar
Course topic: study of sound urbanism/ sound ecoloty
using the city of Cincinnati as a case study to investigate how
changing demographics and changes to industry and labor force
factors influence sound in the city
Presented at UC, Spring 2013
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city
Victoria Meyers architect:  Sound Urbanism/ Sound Ecology:  Sound Sections from Cincinnati;  Urban Design studies for the post-Industrial city

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Victoria Meyers architect: Sound Urbanism/ Sound Ecology: Sound Sections from Cincinnati; Urban Design studies for the post-Industrial city

  • 1. Iannis Xenakis: Trained as an Engineer; worked as an engineer and architect with Le Corbusier; wrote music, and designed ‘Polytopes’ – installations that combined light and sound to make fully immersible environments. Writings : 1963
  • 2. Xenakis’ Concept: To become a new kind of ‘Artist / Conceptor’ Knowledgeable and inventive in Mathematics, Logic, Physics, Chemistry, Biology, Genetics, Palentology, Human Sciences and History: Knowledge based on, guided by, and oriented toward forms and architecture music and architecture : 1971
  • 3. Le Corbusier Years 1947 - 1959 (Age : 25 - 37)
  • 4. Xenakis’ role at La Tourette? La Tourette: Designed as a Dominican Convent at Evaux Today: Centre Thomas More
  • 5. La Tourette: windows based on musical spacing: formal movement through shadow/light
  • 6. Links between Music and Mathematics Musicians and Analytical Geometry Xenakis and probability calculation 1970’s Construction of the Analog digital computer @ CEMAMu (Center for mathematical and automated musical studies, founded by Xenakis) Computer: allows use of an electrolytic surface + a pen linked to a computer and speakers - Ability to transform drawings into sound (compare to Frank Gehry’s use of CATIA to create 3- Dimensional forms by tracing a pen over a phsyical model) Music: Sound and Number Acoustics and Mathematics
  • 7. Cite Radieuse: Marseilles Housing Block 1945 - 1953
  • 8. Xenakis’ role : Calculation of Structural Members Collaborators include artist: (color consultation)
  • 9. Cite Radieuse Rooftop Nursery construction Xenakis collaboration - 1953 - 54
  • 11. High Court, Chandigarh: 1950 – 55 Xenakis Role: Structural Design
  • 12. Assembly Building, Chandigarh, India 1951 – 62 Hyperbolic ‘Dome’ for the Assembly lets ceremonial light enter the Assembly Chamber @ Equinox and Winter Solstice
  • 13. Chandigarh Assembly: Xenakis Contributions: ‘Undulating Glass Panes’ Assembly Building ‘Plug’ form (concrete – just 6” thick) The techniques developed with this construction carried over to Xenakis’s design of Philips Pavilion 1951 - 59
  • 14. Hyperbolic Paraboloid form: Assembly Chamber (note LC and Xenakis’ use of mathematics and physics in design concepts – the Plug relates to shape of Nuclear Power Reactor cone) Chandigarh Assembly : Building Model: Assembly was Centerpiece of LC”s Design for Chandigarh, India
  • 15. Tower of Shadows: (Arch of the Equinox’s) – LC and Xenakis studied the trajectory of the sun for several LC projects, including the Chandigarh Assembly Cone
  • 16. Tower of Shadows: An architectural sculpture designed with LC to demonastrate the virtue of the ‘brise-Soliel’. The Tower of shadows created a permanently shaded space LC also planned to construct a ‘Arch of the Equinoxes’ – to demonstrate the path of the sun during the Equinoxes in Chandigarh. The ‘Arch of the Equinoxes’ sculpture project was never built
  • 18. Firminy : Youth and Cultural Center including classrooms, 2 theaters, a library and informal meeting and exhibition spaces. Main element: Grandstand 1955 – 61
  • 19. Firminy Cultural Center: Details End elevation; Entry Ramp; Window Detail
  • 21. Musical Architectural Influences: Messiaen Hermann Scherchen : Melos (Periodical) (writings on music) Music of: India, Laos, Vietnam, Java, China, Japan (Xenakis was ahead of his time: world music) Musique concrete (samples) Xenakis’ Musical accomplishments: Metastaseis (first original score)
  • 22. Phillips Pavilion: 1958 : Development of Polytopes
  • 23. Philips Pavilion: Hyperbolic Paraboloid Influences on design: Mathematics, Music, Physics, Computational Design
  • 24. Formal Diagram for Philips Pavilion Plan
  • 25. Philips Pavilion: ‘Built Sound’ Xenakis’ ‘Electronic Poem’ - 2 – minute concert (Metastasis) between Varese’s Poeme Electronique: 8 minutes
  • 26. Investigations linking Stochastic Systems to Architecture and Sound 1950 - 2001
  • 27. Housing project in Reze near Nantes: 1950 - 54 Façade Studies for rooftop Kindergarden Window patterns inspired by Gregorian neumes, with window distribution Following a ‘stochastic’ pattern What is ‘stochastic’? What is a ‘Neume’? Xenakis, Le Corbusier, and Stochastic Pattern:
  • 28. Stochastic pattern in windows, Rooftop Kindergarden at the Housing Project in Reze, near Nantes (former slide) This window pattern repeated in several Le Corbusier projects, And has also been used in projects by other prominent architects
  • 29. What is Stochastic? (from Greek = to aim, or guess) - an adjective that refers to systems whose behavior is non-deterministic, and not intermittent (random). Stochas is Greek for Stick; the pattern of arrows striking around a stick stuck in a Greek hillside by an Archer in practice is the epitome of what is stochastic. Any kind of time development which is analyzable in terms of probability is stochastic. Mathematical Theory: based on the theory of probability Artificial Intelligence: using probalistic methods to solve problems, ie: stoastic neural networks. Natural Science: the model of gas filling a chamber, even though individual particles of the gas will be moving in non-deterministic patterns Physics: the Monte Carlo method: Random methods of computation and experiment to create simulations for: the Manhattan Project (hydrogen bomb).
  • 30. Ronchamp: Use of Stochastic Window Patterns
  • 31. Sanaa application of Stochastic Pattern (borrowing from Le Corbusier/ Xenakis)
  • 32. Neumes Translated into Architectural and Musical Form
  • 33. Gregorian Chant Pattern: Gregorian Neume Xenakis used Neumes to create Window Patterns (Nimes); and also as a compositional device for sound compositions Le Corbusier, Xenakis, and Neumes:
  • 35. What is a Neume? The basic element of Western and Eastern systems of musical notation. From the Greek word for breath: pneuma. The earliest known Neumes: Aramaic origin - used to notate inflections in quasi-emmelic recitation of Christian holy scriptures (chants). They resemble a similar system - for the recitation of the Qur’an In the 9th Century: Neumes became shorthand mnemonic aids for the proper melodic recitation of chant. Neumatic recitation was first developed in the Eastern Roman Empire (today’s southern Turkey, Syria, Lebanon, and Israel). Ronchamp: Windows placed as a ‘Neume’, or Neumatic notation of a Chant
  • 37. Diatope or Polytope: Galactic movement made visible Diatope / Polytope purpose: To resolve unsolvable problems related to architecture & the Mediocrity of Concert Halls not related to Music of our Time ie: the frontal position created by most concert halls Diatope: eliminate the inconveniences created by collective listening (concert hall) through immersion Diatope at Beauberg (@ Centre Pompidou)
  • 39. Polytope de Cluny: Light constructions with Sound
  • 40. Polytopes : 1950 - 1985 Immersive Environments created through Light and Sound: Polytope de Cluny
  • 41. Further Readings: Toru Takemitsu & Mathematical Structure in Music
  • 42. Robin Evans: The Trouble with Numbers
  • 43. Graphic depictions of Landscape and Landscape Urbanism, presented to UC Students, Spring 2013 Sound Studies and Landscape Urbanism by Victoria Meyers architect, hMa Sound Sections by UC students, Victoria Meyers Sound Seminar, 2013
  • 45. Trash Track, courtesy of MIT Planning
  • 47. Galway County Plan: Courtesy Galway Planning Dept.
  • 48. Galway County Plan : Courtesy of Galway Planning Dept.
  • 49. Urban Land Institute: Deployable Modular Landscapes
  • 52. MVVA: Park Design Diagram
  • 53. Sound Studies and Landscape Urbanism by Victoria Meyers architect, hMa
  • 54. hMa: Won Buddhist Site Plan
  • 55. Geometry and Movement: The Choreography of Spirals
  • 56. The Concept of ‘Edge’ - as interpreted through Infinity: Infinite Bleed of Edge Thru Screens
  • 57. Sound Sections by UC students, Victoria Meyers architect Sound Seminar Course topic: study of sound urbanism/ sound ecoloty using the city of Cincinnati as a case study to investigate how changing demographics and changes to industry and labor force factors influence sound in the city Presented at UC, Spring 2013