NHABITING SOUNDSCAPE
Architecture
of the unseen world
Matteo Melioli
The Bartlett Faculty of the Built Environment
matteomelioli@yahoo.co.uk
Abstract
In 'Space', the
object - or architecture - is generated by a cumulative process of information
(geometrical transformations, visual sequences, sound structure…) directly
related to the psychological and physiological user’s frames. Each interaction
transforms the visible environment in a dynamic, elastic and multidirectional
imaginary space. The relationship between the object-space system (geometrical
and phenomenological determinate) and the body-mental projection system
(subjective view /aural decoded data ) induces new modes of perception strictly
connected to the inner spatial geometry and its physical reflecting (aural and
lighting) phenomena.
Sound as well
light reveals cryptic information about the space via echo and reverberations.
Those non linear physical process articulate the space along a dynamic and
continuous medium and the geometrical space suggested by echo and reverberation not longer deals with
Euclidean but with Multidimensional spaces. In this work, the conception of
'Space' explores structurally and visually the dynamic process engaged in a huge
architectural volume (the Byzantine Saint Mark’s basilica in Venice) by reflections of the acoustic rays produced
by a polyphonic song and the following transcription of reflections phenomena
into geometric parameters and shapes.
This process
enhances how the same acoustic phenomena distorts the architectural space
creating “ghost-spaces”. These “unreal” spaces will exist even beyond the
physical limits of real architecture. As a consequence this doubling process
will destroy the spatial identity (perceptive level) as well as the centrality role
of the subject (existential level). The space and the Ego will dissolve into a
new geometrical and psychological pattern, mutable, dynamic and elastic.
Introduction
In space, the image of an
object or architecture is built
through the accumulation of information (geometrical, visual, aural). The
strength of this process is such to create spaces which are imaginary, elastic
and open to saundry directions; spaces existing beyond those really perceived
and geometrically described by the Euclidean systems of geometry.
Our perceptive apparata
have such a degree of sensitivity to be able to grasp, for example, small
variations in light and sound, and, on the basis of these variations, elaborate
a mental image of space, translating data such as volume and strength,
brightness or reverberation period into parameters of distance, extension and
depth.
Sound and light, perhaps
due to their unsubstantiality, are, in fact, able to reach the essence of a
space that is revealed through the reflexion of its light and sound. This paper
explores the mechanisms — both physical and psychological — through which these
reflexions induce our mental apparatus to deform the real image of a space, and
analyses how and why these transformations generate imaginary architectures existing
beyond the boundaries of the real ones.
Geometry as frozen music [1]
Music and light are
partly a matter of solid geometry, in the sense that sounds and rays of light
propagate according to definite geometrical patterns. Athanasius Kircher during
the 17th century wrote that “(…) sound is a geometrical emanation of its
source,” stating, in other words, that the Euclidean theories were at the heart
of the acoustic phenomena, and that it was possible to plot (through bundles of
radial straight lines) the route taken by sound waves.
Left: Athanasius Kircher, Musurgia Universalis (1650), tome II,
fol. 264, Iconismus XV. Middle: Athanasius Kircher, Musurgia Universali (1650)s,
tome II, fol. 303. Iconismus XVII. Right: Athanasius Kircher, optical studies.
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Another reason for
investigating musical sound in terms of architectural geometry “has to do with
the spaces within which sounds are produced and heard. A basilica, legislative
chamber or concert hall, designed to reinforce and clarify musical and spoken
sound, can be thought as an enlarged version of a musical instrument’s
resonator, or even of the human voice box. “Architectural acoustics” is a
modern discipline, but the subject itself goes back into antiquity. The Greeks
and Romans built indoor theatres for music known as “odeia”[1]. The spaces
presumably sought to channel and amplify the performers’ music and speech. As
to outdoor structures, where the audiences were usually much larger, Vitruvius
discusses the use of strategically placed sound resonators or boosters
(Vitruvius, De Architectura, 5.5.1). Presumably when speakers and singers
sounded those pitches, their notes were amplified or perhaps transmitted to a
different part of the audience. The 16th century, while almost always quoting
Vitruvius, embarked on its own elaborations of these ideas. The French natural
philosopher and musical theorist Marin Mersenne [10] [11] begins his treatise Harmonicorum
Libri (1636) with a short illustrated essay on architectural acoustics,
maintaining that “sonic rays” (radios sonoros) are projected in conical form.
The rays bounce off inclined planes and can be mapped onto screens using
reflectors shaped like half-ellipses or parabolas. The reflectors focus and
project sounds by locating the speaker or player at one ellipse’s two foci.
Additionally, Kircher’s Musurgia Universalis (1650) is a landmark in the
history of acoustic theory. He is particularly concerned with echoes and
reverberations, writing about caves and classical buildings where strange,
elaborated echoes can be heard, and about how echoes may be bounced onward for
long periods of time. Kircher also reinforces the analogies, so common in the
late Renaissance period, between music and light. According to him, sound —
especially musical sound — is the ape of the light: sonus lucis simia est. He
diagrams the geometries of the linea actionis phonicae, the line of ray
of “phonic action”. For Kircher, acoustics — like optics —is a matter of
spherical and conic sections. Following this method in its essence, we will
start by considering the acoustic geometry of a wide volume like the one of a
Byzantine church, St. Mark’s in Venice. Built in the 10th century, the church
is of the Greek-cross plan, with transepts of the same length and vaults of the
same height, ideally tending towards a circular space. Moreover, the whole
church typology seems to repeat, almost in a fractal fashion, the same basic
circularity, traceable (in decreasing scale) in the domes, vaults, apses, and
even in the columns themselves.
Left: Venice and St.
Mark’s basin. Middle: Interior of the
basilica with the two choirs. Right: Basilica Plan
The sections also display
in quantity what the ratio is among the radia of the respective circumferences
that, following Fibonacci’s sequence, draw a parallel with the cochlis
progression of the human aural apparatus [2]. There is, therefore, in St.
Mark’s basilica, the intangible but consistant presence of an acoustic design,
at times conscious, at times unconscious, that certainly influenced the
centuries-old development of this building. The church, in fact, for the
characteristics of its geometrical space and the kind of material covering it,[2] behaves like a huge sounding box,
amplifying the resonance of sounds, and extending the period of their echo.
During the 16th century, composers like Giovanni Gabrieli [8]
[9] and
Claudio Monteverdi wrote the “Sonatas in Echo” which, exploiting the peculiar
acoustics of the basilica, produced sophisticated effects of sound distorsion,
such as the protraction of the echo, or the harmonic overlapping of a note with
the reverberation of the previous one. In those same years, the practice of the
salmi spezzati (‘divided or split psalms’) was introduced, which consists of arranging
the choir on two different lofts, opposing one another from the two sides of
the nave.[3] Whereas the choir’s splitting, in
the field of acoustic phenomena, doubles the echo’s depth, the same phenomenon,
in the field of sound perception, manifests itself in the image of an elastic
space, deep, dilated beyond the visual spacial boundaries of the church.
Hearing the echo of a sound expanding from side to side is as if the image of
the basilica, with its columns and mosaics, transformed slowly into something
similar to the sonority of the hollow belly of a grotto. Particular sounds,
exalted by the acoustics of the building, have the power of evoking, so to
speak, the idea of a space exceedingly wide, accelerating our imagination in a
race towards infinity.
Acoustic Geometry
Euclidean
Patterns in Aural Phenomena
The “Sonatas in Echo”
imitate an acoustic phenomenon — i.e. the echo — that works through definite
physical mechanisms which follow (Marsenne and Kircher) geometrical Euclidean
patterns. But how do these mechanisms work exactly, and how can they, in the
last resort, lead to the distortion of spacial perception? Let’s move in time
and space, and imagine ourselves walking down into the tube, hearing a train
arrive from a distance. Thinking we understand from which side of the corridor
the train is coming, we are surprised to find that the sound heard from the
left actually comes from the train arriving from the right. The reflection
inside the tunnel “deceives” our perception, driving it to represent the
existence of a train where no train actually exists, and the deception lasts
till our sight is able to verify the real train as it arrives
Reflected
standing waves. The moment of overlapping is called interference, and it
represents the sum of the single wave fronts.
opposite our expectation.
The walls, like mirrors, reflect the sound rays, projecting their real source —
the train — beyond the wall, giving us the impression that the sound is coming
from an “imaginary” train (or a “ghost” train) that exists only by virtue of
the reflecting wall. In Euclidean geometry, this phenomenon is well represented
by conic reversal projections, and the example of the train in the tube
demonstrates how Kircher’s acoustic geometry can faithfully represent the
reality of sound phenomena. Going back to St. Mark’s, let’s consider the
acoustic geometry of the basilica’s internal space; that is, let’s imagine
placing the sound sources on the pulpits where the Salmi Spezzati were
performed and leaving the spread of sound rays to trace their reflections along
the basilica walls. Some reflections will cover the space of the church tens of
times before reaching the listener located under the central dome. With every
reflection, the geometrical space transfers to the incident wave part of its
geometrical features, modifying the internal composition of its frequencies.
The modified sound wave conveys to the listener the sound characteristics of
the space that contained it during all the reflections. Considering, in the
specific, the route of some acoustic rays, it is apparent how they travel far
and wide through the whole space of the basilica, connecting different and
opposing points of the church. Each of these points transfers to the wave its
geometrical features which the sound moves elsewhere, reflection after
reflection. The sound, acting as a sort of dynamic spatial memory, manages to
connect images otherwise scattered at the time of their perception.
Preliminary
studies of the propagation of acoustic rays in volumes with circular vaults.
The drawing introduces the idea of a surface (top centre) that is moved away
and distorted by the sound reflections.
An acoustic image is,
therefore, characterized as the completely absorbing experience of a space,
because it is capable of giving back to the observers, the moment they hear it,
the interaction of a sound with the space that contained it, reflection after
reflection. (…) A sound reflected and sent back from wall to wall saturates the
internal volume of the basilica, and prolongs the impulse for many seconds.
Going back to our example, a listener located under the central dome perceives
the sound coming from each direction, reflected by the walls and floor, with
decreasing volume and reverberation period. Cognitive psychology tells us that
our sensory apparatus places a sound source (also invisible ones) farther away,
the smaller it is in terms of sound volume. With the progressive decrease of
the reverberation, the listener himself, although able to see the orchestra
playing beside him, is instinctively lead to imagine it moving away, beyond the
basilica’s walls, beyond those walls which, like mirrors, reflect both the
sound and its source. Extending the example, it is as if the whole space of the
church dilates beyond St. Mark’s, to the extent of reaching St. George island.
Sound has therefore the power of deforming spacial perception, making space
assume geometrical configurations that are complex and not linear,
configurations of “ghost” spaces extending beyond the physiological boundaries
of our sensory perception.
Acoustic geometry studies.
A bundle of sound straight lines emitted by a punctiform source is reflected by
the walls of a cubic environment, projecting the reflected source on a plane
symmetrical to the original source. Below: a study of the projection of a sound
ray, oblique to all the Cartesian axes xyz. Right: Preliminary studies of the
representation of reflected sources. The resulting sonic space takes on the
features of a cloud of points gathering in limited areas in the space
surrounding St. Mark's.
Geometry of Acoustic Perception.
Towards a
geometry of imaginary.
Sound sources emit
standing waves which expand in all directions, and saturate the acoustic volume
of the basilica. At the outset, this paper will take into consideration two
sources, placed on the pulpits inside St. Mark's, where the choir singers used
to sit. The geometrical procedure used to trace the sound rays consists of a
straight line - incident on a surface - having the same angle as the reflected
one, both on the plane and in space. As displayed in these diagrams, some
reflections travel the church's length hundreds of times before finally
reaching the listener, positioned under the central dome. A few rays seem to
"get lost" in an endless series of reflections, as if they were
trapped inside the resonance chamber of the north and south transepts. The
procedure only includes the calculation
of 5 rays, placed in each square meter of the basilica, reaching a total of
3,800 reflections covering the whole angle of the source. From physics, we know
that the angle of incidence is equal to the angle of reflection, and the sound
straight lines are arranged on symmetrical axial planes. Consequently, the real
source is mirrored on the symmetrical straight line and moved beyond the
surface at a distance d, which is proportional to the space existing between
the listener and that surface. It is then evident that, as the number of
reflections increases, the imaginary sources - those which are perceived as
real - apparently move away from the listener, reaching a considerable distance
that we can quantify, by means of geometry, as being equal to the sum of the
single segments travelled by each acoustic ray[4]. If we apply this method
to all sound rays and try to represent on a Cartesian plane all of the
reflected sources (the red points in the final render and the letter “S” in the
CAD studies), we are able to observe how they form "cloud"-like
clusters, almost creating a force field within which the golden surface is
passively distorted. It is as if the sound produced by a source and the
reflection coming from the walls had "fluidized" the church's
surface, progressively expanding it in a hazy and rarefied space.
Each geometrical
projection establishes, through the sound rays, a biunique correspondence
between the Cartesian space and the acoustic space. As already mentioned, a few
rays get lost in the basilica's gaps, only reaching the surface after thousands
of reflections and with a sound intensity close to null. Since the physiology
of our aural apparatus allows us to pick up only the sounds above a certain
threshold [13], many projections - theoretically possible - actually
become pointless in terms of phenomenology, since they are impossible to
decipher in images. To prevent transforming our imagination into an a-priori
geometrical product [5], it is necessary to set
a limit beyond which the task of the reflexive projections can be considered
concluded. At this point, an extremely fascinating horizon opens before us,
because the Cartesian unit that could once describe the basilica's physical
space, if considered in terms of sound, becomes a discontinuous system of
presence and absence. We find ourselves poised between a literal translation of
Euclidean space and the beginning of the indeterminate realm of permanent
transiency. The sonic space, originating from the lucid and crystal Cartesian
geometry, evolves into an existential condition of suspension, forcing the subject
into a state of aesthetic passiveness.
The Realm of Antithesis.
Contradiction in
Perceptive Processes.
A sound’s echo dilates —
during the period of its reflexions — a space already existing in the sight of
the observer. As a consequence, the observers find themselves between, so to
speak, two contradictory realms: an “objective” realm, connected to the sense
of sight and conditioned by perspective; an “imaginary” realm created by echo
and sound reflexions. From the geometric viewpoint, perspective and sound
reflexion behave in ways as opposite as the spaces they generate. Perspective
tends to compress differences in distance on the line of the horizon;[6] on the contrary, sound
reflexion phenomena prolong the geometrical space in many directions, extending
it beyond the horizon of the visible. The situation that comes into being
represent a paradox — from both the Cartesian (two contradictory linear
projections) and a psychological point of view. The doubling of space, in fact,
triggers a process of internal division: it is as if our cognitive apparatus
has to process contradictory data, albeit sensing their common origin [17]. Moreover,
anthropologically speaking, the sense of belonging to a space is based on the
univocal identification of all the sensory data gravitating around that
particular environment.[7] The very principles of logic and
Euclidean geometry are known as principles of identity and non-contradiction;
in the specific of our example, this means that being in a place excludes being
at the same time in another.[8]
.This study, however, demonstrates how some constructions,
due to their geometry, compel the observer to experience the simultaneous
existence of many spaces, causing a feeling of disorientation foreboding the
loss of identity.
Antithesis and Rewriting.
The Sublime.
Like Kant, in his
Critique of Judgement [9], we understand the ‘sublime’ as the
aesthetic value created by the perception of something measureless and
immeasurable that generates within us an ambivalent frame of mind. It is exactly
the perception of a space shown as limited by our sight, but proven to be
immensely vast to our hearing which is ambivalent in this case. On the one
hand, we are disappointed because the visual image cannot embrace the sweep of
our aural image; on the other hand, we are fulfilled because our consciousness
is driven to raise to the idea of an infinity suggested by this boundless
acoustic space. The disappointment our imagination suffers the pleasure
experienced by our reason, because boundless spaces have the power to evoke
inside us — through sound — the idea of a superior infinity. In this sense, the
initial phenomenological dissociation is then recomposed in a dynamic feeling
able to transform the subject’s physical smallness into a final awareness of
spiritual greatness. In other words, becoming aware of the fact that the real
sublime is not in the architecture we are looking at — with its twofold and
ambiguous space [10] — but in
ourselves, we convert the initial regard for the geometrical objects into a
final regard for the subjects, i.e. for the supersensitive and qualified beings
that we are. St. Mark’s space, like the space of any wide, resonant geometry,
is called sublime because it uplifts imagination so that it might represent
those cases in which the mind is able to “feel the sublimeness of its
destination” [11]. Initially
depressive, the feeling of the sublime becomes exaltation, and our anguish
turns into an active enthusiasm, able to project us beyond the immediacy of the
phenomenon, beyond the confines of the geometrical space, and into the
experience of pure space.
First CAD
model for the display of reflected sources (S letters). The light coloured
nurbs represent the way the sources arrange themselves in space, showing the
forces that determine the arrangement and justifying the subsequent distortion
of the golden surface (light brown).
References.
Geometry
as Frozen Music:
·
[1] George, L. Hersey, Architecture
and Geometry in the Age of the Baroque,
The University of Chicago Press, Chicago and London, 2000. See chapter 2:
“Frozen music”, pp. 22-52.
·
[2] George, L. Hersey, The
Monumental Impulse. Architecture’s Biological Roots,
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·
[3] Tipler P.A., Invito alla fisica, Zanichelli, Bologna
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·
[4] Helmut A.Muller, Principles and
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·
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·
[5] I. Fenlon, “Strangers in Paradise: Dutchmen in Venice in 1525,”
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·
[6], “Architectural Spaces for Music: Jacopo Sansovino and
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·
[7] Jeffrey Kurtzman and Linda Maria Koldau,
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of the Sixteenth and Seventeenth Centuries,”
in Journal of Seventeenth-Century Music,
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·
[8] Angelo, Gardano,
Canto, concerti di Andrea et di Giovanni
Gabrieli etc. In Venetia: appresso Angelo Giordano, 1587.
·
[9] Giovanni, Gabrieli,
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7-19. Tam vocibus, quam instrumentis. Editio Nova etc.Venetiae: Aere
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Acoustic
Geometry
·
[10] Marin Mersenne, Harmonie Universelle, Contenant la Théorie et la Pratique
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R.E., Martinus Nijhoff, The Hague,
Netherlands 1957.
·
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·
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Geometry of Acoustic Perception.
·
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·
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·
[15] Abbagnano, Nicola, Giovanni Foriero, Filosofi e Filosofie nella Storia, Edizioni Paravia, Torino, 1992. See Vol. II, pg. 228-33.
·
[16] Cremaschi, S., L'Autonomia
Spirituale. La teoria della Mente e delle Passioni in Spinoza, Vita e Pensiero,
Milano 1979, See the introduction, pg. XV-XXIII, and chapter 3, pg. 89-94.
·
The Realm of Antithesis:
·
[17] Durand, Gilbert, Les structures anthropologiques de l'imaginaire :
introduction à l'archétypologie générale, 11e éd. Paris : Dunod , c1992.
See the introduction
“Convergent Method and Psychologist Methodology”, pp33-41.
·
[18] Casey,
E. S., Getting
Back into Place. Bloomington, Indiana
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·
[19] Rapoport,
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·
[21] Merleau‑Ponty, The Phenomenology of Perception, Humanities
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·
[22] Heidegger,
M., Being
and Time, Harper & Row, New York 1962.
Anthitesis and Rewriting:
·
[23] L.
Pareyson, The
Aesthetic in Kant, London Press, London, 1976.
·
[24] R.Assunto, L’estetica di Emmanuel Kant, Loescher,
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·
[25] B.
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·
[26] Immanuel
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·
[27] Immanuel
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