3_SEEING THE UNSEEN

SEEING THE UNSEEN

NOTES ON SOUND VISUALISATION

Melioli Matteo

THE RELATIONSHIP BETWEEN SIGHT AND SOUND

Why is it important to try to represent sound? Why should we discuss its form or movement when these are attributes of visible bodies? The answer is perhaps that sound is both an acoustic and a visual image. Numerous writings in the past have covered subjects such as the visualisation of sound and the representation of its movement. Transmission of energy via pressure waves as in the case of sound, and via electromagnetic waves (for light and therefore for sight) are very different phenomena. However, once decoded and inserted in our sensorial system, they become elements which our organism can compare and assimilate, and perhaps even sum up and superimpose. It must be this innate connection between various sensations which enables us to move easily from one topic to another, lexically and metaphorically. Therefore, we can jump easily from the description of a bright yellow flash of light to a tune in G major, from the concave shape of a wall to a sonorous wave, from the roughness of a surface to talk of dissonance. If we consider that study of the processes which allow us to assimilate sonorous and electromagnetic waves is relatively recent, whereas the metaphorical language which links light and sound goes back centuries, it is obvious that the linguistic expressions used will not derive exclusively from our knowledge of biophysics, which has increased greatly only in the last few decades, allowing experts to connect many facts and events. However, the fact that these metaphors were formed, and that our language has preserved many of them, must surely mean that a bridge between acoustic perceptions and those related to light has always existed. Moreover this bridge has always been a means of transmission: in one direction sound and silence have passed, in the other light and darkness. In recent times experts have come to understand the significance of the so-called ’intermodal’ condition during the stage of a child’s cognitive development, that is the zone of our perceptive system which seems to move horizontally between different sensorial channels, connecting them sometimes in a rather astonishing way, in spite of their apparent incompatible differences.[1] The fact that we can talk or write without effort about ‘tone colour’ or a ‘bitter word’, rather than surprise us should make us consider that our perceptional system tends to reduce the ‘physical’ aspects of stimuli in favour of images that can act as a mediator between them.

Regarding images which refer to space, for example, the expressions ‘high’ or ‘low’ can be used to express the tone of a sound or the position of an object in a room. The term ‘space’ can be used for a vast number of images, and on account of their ‘spatial’ quality we can talk of sounds in terms of form, position and movement. However we cannot establish a relationship between sounds, space and form if first we do not define the terms of this relationship. Does sound, for example, refer to the object which vibrates, to the person who hears the sound, or to the air which transmits the wave front? In each of these cases the idea of the acoustic space changes because the connection which the sound forms with the listener, or the surrounding space, also changes.

Image 2.2.a. This is an abstract representation of Theodoor Rombouts, The Concert (c. 1620) applying elements of acoustic geometry and projection of reflected sources as described Appendices, Notes on Acoustic Geometry.

2. B. As we go closer towards the source, the wave front overtakes us and passes over our shoulders. If we continue towards the source we enter a zone of silence, where the only sound possible is the one reflected off the walls. As this is a reflection, the sound seems to be coming from a distance and a direction opposite to that of our movement forward. Expressed in these terms the sonorous source and the place in space occupied by the sound are in opposition to one another.

3. C. This state of opposition creates an imaginary axis around which the vanishing point of the perspective cone and that of Sonorous irradiation oscillate. In other words the sound arrives from the background of the picture, whereas the light moves in the opposite direction. The arrows in the picture go from the interior to the exterior and from the exterior to the interior, whereas the two cones, (the perspective one and the one of sonorous irradiation), rotate in the opposite direction, following a pervasive movement, which is tied to the expansion of the sonorous body in space.

The cones of vision and hearing become interwoven and gain volume at each other’s expense, following an erudite tradition which places the two sensorial forms in opposition to one another, a line of thought which can be seen, for example, in the discussions between Descartes and Mersenne.

WHERE IS SOUND?

To see what changes in the relative concept of acoustic space, we can start with a simple situation: of a room which is a cube and where sounds are acoustic waves located in a medium, surrounding an acoustic body which includes the listener. This example is perfectly in line with the classical idea of sound. As Descartes states:

Most philosophers affirm that sound is no other that a certain vibration in the air which manages to reach our ears, thus if our sense of hearing were to represent in our thoughts the real image of the object, instead of a sound, it should enable us to understand the movement of the parts of the air, which in the movement vibrate against our ears (Descartes 323).

This movement can be understood in a physical sense, as the movement of a wave front which reaches and makes contact with the listener. It is implicit that inside the room there is air which, as Descartes noted, acts as a medium to transfer the acoustic wave from the source to the person listening.

Although the classical theory appears to accord with physical principles it conflicts with certain data relating to phenomenology. Consider for example a tuning fork which vibrates in an air-free, airtight bell. Sound begins only when air is introduced into the bell, and stops when there is none. However, does the tuning fork begin to vibrate and then stop vibrating when we introduce or extract the air? On this point ideas diverge: contrary to the classical theory we assume that the tuning fork continues to vibrate, independently of the presence or absence of air, and that from time to time its sound is not audible because the medium is no longer present to transmit the acoustic information. It is obvious that if the sound were the acoustic waves in the surrounding medium we would be obliged to say that the tuning-fork begins and stops reverberating intermittently.

An example taken from visual experience can help us understand the situation. Consider a black circle that slides, from left to right, behind a white screen and then reappears to the right of the screen. We have the impression that there are not two circles (one which disappears on the left and another which appears on the right of the screen) but one circle momentarily placed out of view. We have the impression that only one event is taking place: the uninterrupted movement of the circle which becomes momentarily invisible.

Ordinary phenomenology of what is visible to us includes, therefore, the notion of the existence of something that is not actually perceived, both for objects, as in the case of the circle, and events as in the case to the movement of the circle. The phenomenology related to our sense of hearing is not an exception in this regard. If the tuning fork vibrates, and the conditions related to us being able to hear it change (the momentary absence of air has the same function as the white screen in the example of the circle) this does not mean that the tuning fork does not resound.

The traditional concept of sound, defined as perturbations of the surrounding medium, does not take into account the fact that sounds ‘are also events happening to material objects, as they are located at the sound’s source, and are identical with vibrations processed in the source itself’ (Pasnau 27). According to Robert Pasnau, the crucial point is not to determine if these events are of an undulating nature, but to realize above all that the sounds are related to the spatial region occupied by the sounding object[1]. If we continue to follow Pasnau's line of thought, we can affirm that the acoustic perturbations in the object are limited to the object itself and do not move in the surrounding space any more than the sound does. They do not propagate from the object to our ears, nor does the sound, which remains in the object that vibrated. Moreover, and this is important, the tuning fork and the other acoustic bodies sound independently from the medium in which they are immersed: in other words, we do not create sounds by surrounding a vibrating body with a specific medium, we merely reveal them. As radical as Pasnau's position is, it opens up a fascinating concept: we consider the acoustic field as discontinuous, made up of sound and silence, according to whether or not the vibrating body comes into contact with the surrounding medium (image 2a). Pasnau affirms that sounds are located in the source and not in space. This, however, contradicts the data gathered from experience, if sounds are not also present in space, then why does their intensity decrease as the distance between listener and source increases? We can also consider the phenomenon of echolocation, the way in which sound travels through space, is reflected off walls, and returns to the person listening: this can only be explained by sound having intrinsic spatial characteristics. For example, when an acoustic wave, coming from a source on a person's right is reflected off a wall on the person's left (which produces the effect of an echo), the person hears a sound that is coming from his left. Every reflection creates the effect of a split, as in the case of an echo, between the acoustic source on one side and the acoustic sensation on the other. One of Hobbes' sophisms here comes to mind: colours are not in objects because we can see them reflected in the mirror:

For if those colours were in the bodies or objects that cause them, they could not be separated from them, as we see they are in the reflection of light in mirrors and in the repeated sound of echoes, where we know that the thing we see is in one place and the appearance is in another (Hobbes 165).

The idea is the following: when we see something in a mirror this does not mean that there is a second immaterial object, located in a presumed immaterial space behind the mirror. This immaterial object does not exist: we see only one real object and we locate it in an inexact way, based upon what we see. In the same way, when we experience the sound of an echo, we hear only one sound, and we locate it in a different place from where it was actually produced. We could simply say that an echo does not exist as an independent entity separate from the vibrating body but only the sounds which produce the echo, which is a result of the reflections which take place in the space in which the source is located.

The examples of the echo and the mirror also explain the fact that the way in which a sound is perceived depends upon the material properties of the vibrating body and also on the undulatory nature (and reflectional quality) of the medium. In the first case we can say that the sound is an event located in the source; in the second, that the source, as it vibrates, is responsible for a perturbation in the acoustic field and that this perturbation travels through space. Thus we have a third definition of sound, which takes into account all the fundamental aspects of acoustic transmission. Casey O’Callaghan has developed such a view at some length. He argues that:

Sounds are best conceived not as pressure waves that travel through a medium, nor as physical properties of the objects ordinarily thought to be the source of sounds, but rather as events of a certain kind. Sounds are particular events in which a surrounding medium is disturbed or set into wavelike motion by the activities of a body or interacting bodies. This Event View of sounds phenomena provides a unified perceptual account of several pervasive sound phenomena, including transmission through barriers [...] and echoes (Caillois 26).

GEOMETRICAL ACOUSTICS

Once we have established that sound is energy, and that the acoustic field is the space which contains its movement, the easiest way to monitor its changing position is with simple geometric constructions. The wave front is schematically represented as a radial sheaf of straight lines, each of which represents part of the acoustic flux. This method, although approximate, has historic and scientific foundations (see Appendices: Notes on Acoustic Geometry).

The scientist and musical theorist Mersenne maintained that ‘sonic rays’ (‘radios sonorous’) are projected in conical form. The beginning of his treatise Harmonicorum Libri (1636), shows how rays can bounce off inclined planes and be mapped onto screens using reflectors shaped like half-ellipses or parabolas (Marsennes 144). The reflectors focus and project sounds by locating the speaker or player at one of the ellipse's two foci.

There is also Athanasius Kircher who, when writing about caves and classical buildings where strange echoes can be heard in Musurgia Universalis (1650), reinforces the analogies, common in the late Renaissance, between music and light (Gorman 47). He proceeds to diagram the geometries of the lines of phonic action: for Kircher acoustics, like optics, is a matter of spherical and conic geometrical sections.

Image 5. Diagram 1 and 2: first-order and second-order virtual image sources and corresponding paths inside a room. Diagrams 3-5: the trajectory of the sound ray is obtained by repeated reversals of source S and perceiver P. The reflected sources are imaginary points of space obtained by joining perceiver P to the point corresponding to the last reflection. The resulting straight line represents the direction from which P actually hears the sound coming. The distance of the location of Sr is the sum of all the lengths travelled by each reflection. The greater the number of reflections the longer the distance.

The language of geometry enables us to approximate the behaviour of a sound phenomenon. Although not limited to this, geometrical acoustics is a starting point we cannot avoid. We can, for example, consider a cubic environment within which are placed a sound source and a listener, the latter located in the geometrical centre of the space (image 5, diagrams 3-5). Sound propagates along straight trajectories; when these rays strike the cube's sides they are reflected at an angle that equals the angle of incidence. These reflections are ‘axial homologies’, transformations in which the points of a figure revolve around a straight line (axis), so that they maintain the geometrical characteristics of the original figure (Cremona 20). In this case, in both 2D and 3D, the room’s perimeter represents, in each of its 12 edges, the axis of the homology; the subsequent reversal of source and perceiver determines the images of a virtual source and perceiver (P*, S*).

Image 5 (diagrams 3–5) shows that the source's rotation around axis AB determines point S*. From an acoustic perspective the wall ‘mirrors’ the source outside the figure, while the source-perceiver system (S-P) inside the environment becomes equal to a virtual one (S*-P) deprived of its sound chamber [1]. As the number of reflections increases, the geometry of the acoustic ray becomes even more complex, resulting in the successive repetition of homologies and in the displacement of the sound sources outside the cube to locations even farther away as the number of reflections increases (images 7, 8).

This acoustic phenomenon renders the perception of the space of the cube as a progressively expanding volume. Anyone who has experienced a reflected sound inside a large room can testify to the capacity of sound to expand the perceived space. Imagine walking in a cave and listening to the sounds of your steps propagating and fading away in the distance underneath its vaults: as you walk forward, you feel you are moving in an endlessly extensive space.[2]

In a closed environment sound ‘distorts’ the perception of space because we perceive sounds as if coming from imaginary sources outside the environment. Each reflected source (Sr) represents the point in space from where the listener P perceives the sound coming from [1]. In acoustic perception a sound source represents what a focal point is in visual perspective. In graphic representation a sheaf of parallel straight lines converges at a vanishing point (the focal point); in acoustics the same point (the reflected source) attracts space towards itself, triggering a distortion of the perceived geometry.

Image 6. Left page: this set of diagrams describes the behaviour of a sound reflected inside a room assumed to be cubic. The sound is an 'invisible' event since we cannot see the acoustic front moving in space. However, sound travels from one end of the room to the other, transferring energy from the source to the listener. This course can be represented graphically with segments of straight lines joining points in space, or straight lines at the point of incidence on the surface. In the latter case the angle at which the sound is reflected is identical to the angle of incidence. In this diagram geometrical studies show the reflection of straight line incidence on orthogonal Cartesian planes , similar to a cube where the sides are perpendicular to one another. The geometric technique used here is that of homology: in descriptive geometry a transformation of the plane obtained by the composition of two central projections, one for the ray of incidence and one for the reflected one. The course of the acoustic ray is marked in red. The right page shows its projection on three walls of the room. Image by the author.

Image 7. By increasing the number of reflections the complexity of the geometric patterns increases. Faced with this difficulty the method which Luigi Cremona calls 'the method of concatenate rotations' has been applied. (Cremona 25) This consists in the ‘automatization’ of the reflections which allows the final point of the chain to be calculated and, therefore, the position of the reflected source. Another problem taken into account here is that of projecting the reflected sources three-dimensionally. In space sound expands by means of spherical waves. The examples so far show just one acoustic ray, when in reality a concentric bundle of straight lines should be considered. Only some of these reach the listener after two or three reflections, the others become lost in what was previously called the ‘reverb cluster’ (Orlowski 46, Bonsi 223). To understand which ones reach the ear of the listener I have resolved the problem by proceeding in the reverse order, singling out the only ray possible among the infinite number generated by the acoustic source. Image by the author.

Image 8. The physical behaviour of an acoustic ray can be approximated to an example of axial homology. In this diagram the technique of ray tracing has been used, which consists in rotating a bundle of straight lines around an axis. In the drawings the straight line has a point of incidence on the side of the square at an angle equal to the angle of reflection. With the same geometric procedure the course of the so-called second-order and third-order acoustic rays have been calculated. Image by the author.

Image 9. Preliminary studies of the representation of reflected sources. The resulting acoustic space takes on the features of a cloud of points gathering in limited areas in the space surrounding the listener. Image by the author.

REPRESENTING SOUND

Image 10 is a graphic representation of this idea. Within the room are reflected rays, outside it the virtual sources. Sound transforms the cube’s surface into a volatile substance, phenomenally speaking, like a dust cloud which the wave front expands to the outside of the space [1]. This idea is studied in a series of sketches (image 9) where the acoustic dust condenses around a central point where the listener is imagined to be placed. The cloud represents the acoustic space perceived by the listener, and each point of which it is made up represents an imaginary source from which the sound originates. The cube’s walls are no longer represented, because in reality it is as if the sound has liquefied them, progressively expanding and projecting walls in a hazy and rarefied space.

If we consider every point, no matter how small, to be a sound source, then the cloud represents the form taken on by the acoustic swarm in space. By saying this we are also affirming that sound has a physical extension: the acoustic dimension and the architectural one have become fused in a new kind of language. This is a crucial step because to represent an acoustic space is like momentarily taking sound away from music in order to turn it into an architectural element. This position brings to mind the installation of Bernhard Leitner who wanted ‘to work with the medium of sound architectonically and sculpturally, to design space’ (Leitner 1 94). In Serpentinata (Image 11), for example, a series of loudspeakers are positioned along a metallic structure: the sound emitted from each loudspeaker transforms the whole sculpture into a sonorous object, an object that is at the same time space and sound.[2]

Image 10. Sound produced within a cubic space is here depicted as a force expanding to the limits of the physical space. Image by the author.

In a perceptively accurate comment Cathrin Pilchler defines the act of listening to space as an ‘experience of a spatiality encompassing the listener who thus becomes part of an immaterial architecture’ (Leitner 1 78). As if all architecture, even an acoustic one, talks through the shape and geometry of its space, Leitner writes that:

A line is an infinite series of points. Space can be defined by lines. A line of sound is produced when sound moves along a series of loudspeakers. Space can be defined by lines of sound: the lines delineate the configuration of space and simultaneously make it a specific expressive experience. Non-linear movements of sound between two or a larger number of loudspeakers accentuate points in space: they mark out space physically and simultaneously give it an expressive shape (Leitner [2] 77).

He produces an acoustic shape by distributing speakers in the actual space, as for example the floor or the walls of a room, (Sound Field, 1972 and Ton-Raum, 1984) whose preparatory diagrams show that the sound produced by the speakers is represented by points, whereas the acoustic flux joins the points together.

The idea of materializing sound in a point is not, however, new in the history of music. Annie Belis in her book on Aristoxenus of Tarentum, for example, dedicates an essay to the experience of sound space and its ancient representation in points and lines. The glossary of the Elementa harmonica contains many references to ‘acoustic place’, ‘resonant point’ and the movement of sound in space (Belis 137). It is clear that this kind of terminology presupposes a ‘spatial’ concept of acoustic movement, the same to which my diagrams refer even if in a different form, as do Leitner’s experiments. On the union of visual language with that of musical language Walter Burkert comments:

There are two systems by which [...] the total continuum of the acoustic space may be described and represented […] one can think of the interval in a spatial metaphor, and equal intervals as representing equal distances between visual points or lines [...] The image of a line and its division is especially natural for us, because of our familiarity with the piano keyboard, and our system of musical notation; but the Greeks used this image, too, as is shown even by the word they use for interval (punctuate) (Burkert 369).

In fact Aristoxenus’ antecedents conceived sounds as points without dimension, placed along a spatial continuum represented by ascendant or descendant lines and by points of different dimensions and positions. As now, the difficulty of talking about sound, something which cannot be seen or touched, led the ancients to visualize musical reality in order to be able to express a series of abstract concepts. The ‘sounding’ line or point, therefore, alludes to an acoustic reality, not in a physical sense but in a figurative one. [1]

Image 12. These sketches explore different ways of representing acoustic space visually. The first (left) is based on Bernhard Leitner’s drawing ‘Ton-Raum’ (1984). The lines indicate the several journeys of the sound inside the room. The sketch on the right, based on the idea that a point in space is a sound, associates the shape of the acoustic space to the configuration of the reflected sources. Image by the author.

Image 11. Bernhard Leitner Sound Field, 1972 (left) and Serpentinata, 1984 (right).

Following Aristoxenus, I would like to describe another experiment regarding the representation of sound. Consider once again a cubic environment within which are placed a sound source and listener, the latter in the geometric centre of the space. Sound propagates in rays along straight trajectories. When these rays strike the sides of the cube they are reflected at an angle equal to the angle of incidence . The outcome of this reflection is that the real sound source is projected beyond the walls of the room as virtual sources in locations that appear farther and farther away as the number of reflections increases. The sum of the infinite reflected sources defines the shape of the acoustic space, both in geometric and perceptual terms. In fact, when perceiving sounds coming from somewhere far away or close by, the listener is led to imagine the existence of a space the boundaries of which follow the acoustic event he is experiencing. Whether we consider the experiment from the point of view of physiology, geometry or phenomenology, the fact remains that in a closed environment sound distorts spatial perception, because we perceive sounds coming from sources that are not real.

Figure 13 a, 13 b. In a lapse of one second, a 1000 cubic metre space is covered by an acoustic ray almost one million times, generating thousands of reflections. The intensity of these reflections diminishes exponentially as time passes, quickly falling below the threshold of audibility. The first reflections are, therefore, those that really determine the perception of an acoustic space and are represented in succession in this diagram. In reality, acoustic space also undergoes, beside deformation, an expansion that has not been represented here. If we compare the original solid and the final solid, it is evident that the figure's vertexes revolved clockwise, shrouding the space around the core, reminding us of the movement of a vortex.

As time and reflections increase little by little the ‘cubic’ shape of the sound chamber is transformed, in our perception, into an expanding sphere. The sides of the cube, during the process of deforming, extend like thin films wrapped around the main body of acoustic space. The final configuration is like a curved space, wrapped in six layers originating from the six sides of the cube. In a time lapse of one second a space is traversed by an acoustic ray almost one million times, generating many thousands of reflections. The intensity of these reflections diminishes exponentially as time passes, quickly falling below the threshold of audibility. The perception of an acoustic space is primarily determined, therefore, by the first few reflections, which are represented in sequence in the diagram. In reality, in addition to deformation, acoustic space also undergoes an expansion that has not been represented here. If we compare the original solid and the final solid it is evident that the figure's vertices have revolved clockwise, shrouding the space around the core, reminding us of the movement of a vortex.

Even if the shape of the acoustic space varies, some of its properties are constant. Each curve has a radius whose centre gradually moves away from the previous one at a distance connected to the size of the room. The centres themselves gather in confined areas of space, corresponding to the cube's centre of gravity. These and other properties show that, even if consistently changing its shape, the acoustic space maintains a connection to the initial cubic space.

With every reflection the geometric space transfers to the incident wave part of its geometric features, modifying the internal composition of its frequencies. The modified sound wave will transfer to the listener the specific sound of that space. In a cube the rays are free to travel through its volume without any obstacles, generating an acoustic space whose profile is continuous and uniform.

As I have just explained the language of geometry enables us to give an approximation of the behaviour of a sound phenomenon. But what happens when the geometry of a particular space is complex? The Basilica of San Marco in Venice is such a space with a broad central body surrounded by an interrupted system of overhead vaulted galleries, alternated with recesses and niches.

Image 14 + 15. Sound sources emit standing waves which expand in all direction, and saturate the acoustic volume of the Basilica. This study starts by considering two sources positioned on the pulpits inside San Marco where the choir 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 length of the church hundreds of times before finally reaching the listener positioned under the central dome. A few rays appear to ‘get lost’ in an endless series of reflections as if trapped inside the resonance chamber of the north and south transepts. The procedure includes only the calculation of five rays placed in each square metre 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 that the sound straight lines are arranged on symmetrical axial planes. Consequently, the real source is mirrored on the symmetrical straight line and moves beyond the surface at a distance that is proportional to the space existing between the listener and that surface. So, 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 equal to the sum of the single segments travelled by each acoustic ray. If we apply this method to all sound rays and try to represent on a Cartesian plane all the reflected sources (the red points in the final rendering 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 Basilica’s walls are passively distorted. It is as if the sound produced by a source and the reflection coming from the walls liquefy the Basilica's surface, progressively expanding it in a hazy and rarefied space.

Inside the Basilica’s the sound sources are positioned on the two pulpits where the singers used to sit, allowing the expanding sound rays to trace their reflections along the Basilica walls. A listener under the central dome perceives the sound as coming from various directions as it is reflected by the walls and floor, decreasing in volume and reverberation period [1]. The outcome of these reflections is that the real sound source is projected beyond the walls of the acoustic chamber as virtual sources in locations that appear farther and farther away as the number of reflections increases. Each point on the drawing represents one reflected source, the point in space from which the listener perceives the sound to be coming from.

It is as if the acoustic field within the Basilica gradually reveals the existence of an imaginary surface shrouding the listener. Using another metaphor, it is as if sound, coming from countless points, materialises its infinite sources on a fluid and porous surface. The reflected sources represent an imaginary space which, as if it were a field of forces, distorts the perception of actual space. I have represented the action of these forces by the image of a surface free to expand beyond the Basilica's central dome, modifying itself as the geometrical configurations change. This distortion is at first connected to a linear language, suggesting a causal relationship between the acoustic visual images. However, another language gradually appears in which the fluid lines represent a condition of increasing indeterminacy because, little by little, the acoustic space starts to acquire probabilistic characteristics.In conclusion, the sonic field that surrounds, envelopes and flows within architecture implicitly endows the architectural space with a new acoustic dimension.

Image 16. By means of geometry it is possible to locate the position of the reflected sources that are arranged around the perimeter of the Basilica, generating concentric surfaces that extend in the distance as the reflections continue their onward movement. The reflected sources represent the experience of an imaginary space which, as if it were a field of forces, distorts the perception of the actual space, represented in the drawing by the light blue area.

Images 17 and 18. The layout of the Basilica of San Marco overlaps the acoustic space generated by the Basilica itself. An observer inside the Basilica perceives an area confined by the architecture of the building. The listener experiences a space the extension and geometry of which is in contrast to the visual information. The drawing represents simultaneously both situations, highlighting the differences between acoustic and visual space.

NOTES

[1] Synesthetic description is when we talk of a typical perceptive experience related to one organ of sense in particular but use terms of reference which are usually associated with a different sensorial system, (for example saying that a colour is warm, a sound is high, a painful vision of life, and so forth). Synesthetic language exemplifies a general characteristic of sensorial experience, that is to say that it depends in a transversal way on various modalities. In fact, perceptive experience is based upon a neural ‘architecture’ which is extremely interconnected and which functions both on a uni-modal and cross-modal level simultaneously.

[2] This position does not exclude the possibility of the existence of a ‘means’ the presence of which is necessary for the transmission of Sonorous information, but not for the existence of sound itself.

[3]The transition from configuration S-P to a virtual equivalent S*-P finds confirmation in acoustics and perception. The reflected sound coming from the wall equals, in frequency and location, the sound coming from a source S* located outside the environment.

[4]

[5] Regarding the connection between source and acoustic event: ‘our experience of listening to sounds is connected to the sources that produce them’ and ‘to hear a sound is often to hear the cause of the sound’ (Gaver, quoted in Forrester 35). Following this idea we can assume a perceptual connection between the acoustic object and the event generated by it. In the example of a listener in a cubic room, there are two distinct acoustic events, the direct one, dominated by the real source S and an indirect one connected to the sound reflected off the walls, reverberation. The latter does not depend upon the source but on the shape of the room, its architectural features and materials; so, following Gaver’s reasoning, the listener will be inclined to identify the reflected sound (acoustic event) with the walls of the room (acoustic object) and therefore with the imaginary sources placed outside the cube.

[6] This kind of representation recalls studies carried out by Preston Scott Cohen and his idea that space is a three-dimensional image of geometrical operations (permutations) such as rotation and intersections of Cartesian planes. For example, in a series of diagrams he subjects a cubic space to a deformation which recalls the sketch of perspectives with two focuses: parallel lines, converging at the extremes suggest an extension of the space along the horizontal line. These diagrams represent the deformation of the space when it undergoes the action of an external force: by shortening the perspective we can understand how the shape of the cube changes as the position of the observer changes. This method clearly belongs to a visual language that has no parallel in the acoustic one: from the geometric viewpoint, perspective and sound reflection behave in ways as opposite as the spaces they generate. Perspective tends to compress differences in distance on the line of the horizon; by contrast, sound reflection phenomena prolong the geometric space in many directions, extending it beyond the horizon of what is visible (diagram F). With this difference in mind I have reinterpreted Cohen’s example, imagining a cube no longer in perspective, but deformed like a solid projected with a central focal point. In this case the focus is represented by the listener from whom a sheaf of straight lines originates, each joining reflected sources.

[7] References to the installation are in P.U.L.S.E. For a picture and a video refer to:

http://www.youtube.com/watch?v=sxyVQb-VywA&feature=related

[8] The need for visual evidence in ancient Greek culture is also common to other sciences, above all mathematics (the word ‘demonstration’ recalls a purely visual context). Musical theory has employed the same methodology using the visualisation of the object studied in order to describe it exactly, a need felt by all musical-theory currents, even if resolved differently (as, for example, when Aristotelians compare sounds to colours).

[9]Once we locate source and perceiver it is possible to trace, by means of geometry, the location of the reflected sources. The complexity of the space here makes it necessary to use fluid dynamics calculus software. With this it is possible to trace the location of the reflected sources quite accurately, extending the calculation to a high number of reflections.

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