2 + 2 = A math primer for the hard of hearing.

Such was the concussive topic, which concluded a day of specialised presentations at the Sound in Space forum; this was the talkfest accompanying the first national survey of acoustic arts at The Museum of Contemporary Art, Sydney (May-July 1995).
That a debate amongst discipline specialists could mire itself in such a prosaic manner caused me to speculate that perhaps certain people in the hall were, as yet, unaware of the operations of the telephone!

More productively this incident, marks the habitual dualistic manner in which ‘sound’ is conceptualised - as real or as virtual, as signal or as noise, as low-fi or as hi-fi et al - establishing the conditions of dilemma - when it may be more useful to consider sound as effectively filling and flowing between the poles of such binary categories, rendering them as marginal definitions rather than central characteristics.

Our (in)ability to recognise and describe sonic experiences is in part due to a dearth of appropriate acoustic metaphors. The metaphoric structure of English is visually overdriven and typically surrenders experience of the aural dimension to the nearest codified category; Music. As a surrogate conceptualisation of all sound, Music and to some extent the Voice, absorb our acoustic experiences and suppress the invention of alternative categories of expression.

Morphology, and now another true story.
The young man spent those difficult pubescent years in purgatory, obsessively working every spare hour of the day in the kitchen of a restaurant, even during the hours of sleep, plagued by nightmares of crockery contaminated with tenacious melted cheese. Finally his torments came to a close, cash in the bank he approached the Music Master only to be devastated - he possessed the wrong shaped mouth (embouchure) to play the Trumpet! He is now a fine Saxophonist (and a sound theorist!).
This is a tale of the fit, look or feel of a literal morphology (the mouth) with an instrument - it points to the inextricable relationship between sound, as a dynamic index or sign, and its (dynamic) source, or referent in the sensible world. But even here at the ground zero of sonic production sound is simultaneously phenomenon and representation always both real and virtual. The polymorphous existence of sound; its ability to simultaneously inhabit the corporeal and the imaginary has long been acknowledged. In the Tempest, Shakespeare conjures a sonorous Island elaborating a view of the natural world under metamorphosis, between noise and music, plying between the evil and benign expressions of a unified life force. Within this context the island itself is an artificial (or rather magical) construct that operates as the ‘architecture’ for the events of the drama. Sound is the principal vehicle for the differentiation of ‘actual’ from ‘magical’ moving between natural soundscape, music and dream imagery.

Be not afeared; this isle is full of noises,
Sounds and sweet airs that give delight and hurt not.
Sometimes a thousand twangling instruments
Will hum about mine ears; and sometimes voices
that, if I then had waked, after long sleep,
Will make me sleep again; and then, in dreaming,
The clouds methought would open and show riches
Ready to drop upon me,
that when I waked, I cried to dream again.

William Shakespeare, The Tempest.

Take this page and fold it in half (2) fold it in half again (4) then again (8) then again (16) and again (32) and yet again (64) should we continue (128) on to (256) the page is now (512) rather small (1024) and becoming (2048) somewhat difficult (4096) to read (8192). Logos + arithmos provide the fundamental structures for biological growth and until the introduction of the metric system (a system designed for and by shopkeepers) provided the basis for virtually all systems of measurement.
Absolute Certainty.

Music is a hidden arithmetic exercise of the soul, which does not know that it is dealing with numbers, because it does many things by ways of unnoticed conceptions, which with clear conceptions it could not do.
Gottfried Wilhelm Leibniz.

During the 6th Century B.C. the Pythagoreans established harmonic correspondences linking microcosmic with macrocosmic structures. Employing the Monochord (an instrument equipped with a single string and a movable bridge) to experiment with musical ratios, principally the integers 1, 2, 3, and 4, the Pythagoreans sought to relate the length of a string (or pipe) to pitch enabling them to formulate the oldest Mathematical expression of the Natural world.

This prototypical arithmetic modelling of the world assembled abstract mathematical principals and geometric forms as a structural underpinning for the subsequent analysis of natural morphologies and cosmic movements. The numerical ratios, which form the musical scale, were developed into a Universal theory and projected by the Pythagoreans into the heavens, where by analogy, as all moving bodies produce sound so too must the planets form the Music of the Spheres. Such an assumption relies upon the propriety of exact correspondence between the quantitative (the numerically calculated) and the qualitative (the actuality of the sensible world). This certainty is expressed in the parable of Plato’s cave, which is premised upon both the existence of absolute truth and man’s ability to seek and recognise it.

The movements of the heavens are nothing except a certain everlasting polyphony.

Within a theological context Absolute truth translates as both the omnipotent position of the Godhead and dogma required to maintain this state (of grace?). From the initial pre-christian harmonisation of the cosmos structured around an absolute schema, scientific development was to witness a gradual slippage toward a dynamic form of chaos as a principle of cosmic organisation; resisted at every turn by theological forces.

In processing the mass of data on the motion of the planet Mars, collected by the Danish astronomer, Tycho Brahe, Kepler was to realise a fundamental discrepancy between the calculations for circular planetary motion and the observational data. This finally led to Kepler’s proposition of elliptical orbit patterns, a proposition radical enough to demand some form of redemption! In Harmonia Mundi Kepler strove to develop his astronomical system and succeeded by redefining the Music of the Spheres in establishing a ratio for each planet - derived from its maximum speed (when nearest to the sun) and its minimum speed (when most distant from the sun) and integrating these ratios within the musical scale. The remarkable feature of Kepler’s planetary ratios is their close correspondence with the integers prevalent in earthly harmonics.

Whilst theoretically pure and appropriate for earlier melodic sequences, mathematical models for polyphonic harmonic structures rapidly turn nasty. The strict arithmetic lay out of pitch produces dissonance in the form of harmonic beating - the bad fifth, for example, was so dissonant it was labelled The Wolf. Bach¹s The Well -Tempered Clavier was one methodology for eliminating, or rather dispersing such dissonant chaos across the keyboard, as is the contemporary method of equal tempered tuning which progresses each note by the ratio of the twelfth root of 2:1 distributing dissonance and consonance throughout the range.

Consonance is the blending of a higher with a lower tone. Dissonance is the incapacity to mix, when two tones cannot blend, but appear rough to the ear.

Such dissonance is a small reminder that natural harmony is a fluid rather than absolute state. That many professional piano tuners work by ear in order to build texture into the range of an instrument speaks of dynamic listening systems which are much more complex than originally proposed by arithmetic formulation.
Euclid demonstrated that between the geometric construction of the Golden Section (the paradigm of harmonic beauty) and its precise harmonic proportion there exists a minute deviation of 0.007. Slippage in the mathematical precision of harmonic systems is also compounded with the distortions and discrepancies which arise from incremental inertial loss in the transmission and reception of sound - the energy required to set objects in motion being in effect drawn from the sound event - even the human ear has an energy demand when it is set in sympathetic resonance to initiate hearing.

The French mathematician Poincare closed the door on the concept of unequivocal mathematical models of nature by demonstrating the shortfalls of Newtonian physics for planetary motion (he proved it was mathematically impossible to predict the exact future behaviour for even a three body orbiting system; whereas Newton has stopped at two and assumed the remainder!). In so doing Poincare illuminated the incommensurability that exist for a precise fit at the interface of scientific analysis and ‘actuality’.
The certainty of uncertainty was finally enshrined by Werner Heisenburg who formulated the collapse between the scientific subject and the object of study in 1927 in the form of the Uncertainty Principal, which states that in choosing the area of study; one, in effect, creates the object of inquiry, echoing Flaubert.

The more developed the telescope, the more stars there will be.

Chaos Theory, with its iterative events, successively looping to congeal about strange attractors is one of the heirs of this retreat from certainty which perhaps puts Plato’s fettered slaves back in the flickering cave with an eternity to figure it all out again!!!
Sounding Bodies.

A phenomenon by definition is inextricably linked to the possession of a sensory body. Naturally it is our habitual (and inevitable) use of the body’s perceptual horizons as indexical mechanisms which have created topologies of embodied and disembodied events or thresholds of the tangible and the intangible. As any foray, beyond a world bounded by Newtonian physics will demonstrate, our perceptually framed understanding of spatial and temporal reality fails to recognise objects and events which refuse to conform to the scale and velocity of the Procrastes bed which the frame of our body has become…....
Nigel Helyer 1992, An Unrequited Space, in Working in Public.

Confusion abounds when we attempt to imagine beyond the limits of our own horizons to encounter the Weltanschauung afforded by instrumentation or as possessed by other species. Even the simple scaling of the fleshy vehicle has a dramatic effect upon perception and the morphology of perceptual structures.

Acknowledging that frequency tends to vary as the inverse square of linear dimension (cf the Pythagorean experiments which demonstrated that as scale diminishes pitch increases) - we find that in a biological context this will produce an effect in which a creature of some 50 times smaller mass than another will be pitched, in both its capacity to voice sound and to perceive sound, at some 2,500 Hertz (ten or eleven octaves) above the larger being. Naturally this scalar effect has not only implications for the perception of tone but relates to the capacity to perceive and experience other magnitudes of depth in time. All this of course would have had serious implications for both Alice in her curiouser and curiouser expanding and contracting universe phase and for Gulliver in his various conversations with the Emperor of Lilliput, whose voice was shrill, but very clear and articulate “.....his Imperial Majesty often spoke to me and I returned answers, but neither of us could understand a syllable…..”
A corollary to this dimension/frequency relationship is the evolution of morphologically divergent structures for communication and environmental perception. Ironically this phenomenon is more clearly illustrated by the size of the eye as compared between animals of varying mass.

By juxtaposing the dimensions of the eye to body size of a mouse with the (proverbial) elephant it becomes clear that the ratio of eye: body is comparatively much larger for the mouse, than the eye: body ratio for the elephant. It would seem that all eyes are developed from an original biological pattern, which is only operational within a certain dimensional range.

Moreover the limiting cause here rests with the size of the rod and cone receptor cells, which remains constant, irrespective of the size of eye they form (the receptor cell being in turn constrained by the frequency of light they react with).  It is significant that smaller creatures, such as insects, have evolved optical sensors, which avoid the diffraction problems, which would inevitably occur in shrinking the mammalian style eye - by developing compound eyes (which coupled with antennae systems) open sensory windows beyond our conception of visual.

We should acknowledge that the Procrastes bed, which the frame of our body has become, is largely responsible for the anthropomorphism by which we stumble past the inhabitants of plural worlds and plural spectra. Although the mammalian ear is the most developed in the biosphere, the human ear only amplifies ambient sound by a factor of x18 - low gain when compared to the Kangaroo mouse, which operates at x100 amplification. To return to the proverbial elephant, we find ourselves disenfranchised, and perhaps surprised, to find that elephants generate a very low frequency growl from their stomachs, giving them the ability to communicate over vast distances of savannah. As physical body size diminishes the morphology of sensory devices must adapt to higher frequencies (i.e. shorter wavelength).

Most insects mirror the networked structures of their optical sensors (ommatidia) with arrays of vibration sensing hairs (usually found on their legs) individually linked to nerve cells and routed directly to the brain - the length of hair determining the frequency response - a compound hearing! Hearing at the micro-scale is often highly adapted to particular a function - the sensory hairs which form mosquito antennae are arrayed like tuning forks which sympathetically resonate at the exact frequency of its species wing beat - a resonant circuit adapted for a single’s bar routine!

What can be sung can also be written down.  Moreover, there are many other new things latent in Music, which will appear altogether plausible to posterity.
Jean de Muris.

As the voice may be considered analogous with thought, so text becomes its mnemonic technology, as do conventional, harmonically structured instruments and musical notation propose grammars and vocabularies to store partial areas of our sonic experience. The development of mnemonic forms capable of encoding sensory experience is un-even. Systematised forms of visual Mnemotechnics predate those of text and sound, with the areas of haptic and olfactory experience totally lacking any substantial, communicable mnemonic form (although a good cookery book goes a long way with taste!!!).

In The New Soundscape, R.Murray Schafer coins the term Schizophonia (split + sound) to refer to the cleavage of sound events from their source. Stripped away by recording technologies from their origin, dislocated sounds circulate in a vast proliferation of de-centred reproduction. As sound by nature androgynously embraces the real and the virtual, it is able to masquerade convincingly in this double role. Conversely, being a relatively opaque technical media, the photograph or video image must constantly announce their mediation in the mnemonic process.

Audio Recording (Analogue or Digital) is a mnemonic technology in which sound is made to flow back and forth as an electro-mechanical analogue, of an event distant in temporal and spatial terms, to debouche into architectural space and/or the space of the ear, to re-create an equivalent aural experience. This transaction goes beyond the representation s of Visual culture, or the open framework for imagination, provided by literature, representation in sound approaches a condition of re-incarnation.
Although perhaps this was not always the case with early attempts to capture the essence of the sound environment.

....to my indescribable astonishment and horror, the devilish metal funnel spat out, without more ado, its mixture of bronchial slime and chewed rubber; that noise that possessors of gramophone and radio sets are prevailed upon to call music. And behind the slime and the croaking there was, sure enough, like an old master beneath a layer of dirt, the noble outline of that divine music. I could distinguish the majestic structure and the deep wide breath and the full broad bowing of the strings…
Hermann Hesse. Der Steppenwolf 1927.

In any event, all forms of representation trade in loss; certain aspects of the environment are excluded, as they are loaded into the narrow bandwidth of the technical vehicle. This is most obvious for the photograph, which excludes almost everything of the world beyond a fraction of a second and a particular angular point of view. Sound is a more complex phenomenon, being dependant upon the type of recording and transmission medium involved. The massive compression we experience in telephone sound constantly announces the voice as simulacra, co-substantial with itself. But this ghosting is increasingly difficult to locate within high-fidelity systems in which sound is transparently mapped back into experience - sound here becomes simultaneously a unique event and a representation: although at a fundamental level this characteristic (of being simultaneously an index and a referent) applies equally to naturally occurring sounds as it does for recorded sounds.

The poor cousin in any discussion of sound concerns another Morphology - Architecture - even in a conventional Musical performance the (ideal) concert Hall is a transmission and moulding mechanism, dynamically fused with the orchestra and the listener. An entire architectural sub-history forms a web of metaphoric correspondence between the physical structures of the body with those of architecture, music and biological structures.

Architecture is frozen Music.

or was it.

Stone is frozen Music.

Architecture lends its morphology to not simply to contain or propagate sound but to modulate and designate sound within a spatial identity. In this respect sound memorises the spatial and textural character of architectonic space, sound being the primary key in our perception of space. Italo Calvino describes a king, transfixed upon his throne - trapped immobile, listening at the centre of his kingdom.

Vestibules, stairways, loggias, corridors of the palace have high, vaulted ceilings; every footstep, every click of a lock, ever sneeze echoes, rebounds, is propagated horizontally along a suite of communicating rooms, halls, colonnades, service entries, and also vertically, through stairwells, cavities, skylights, conduits, flues, the shafts of dumbwaiters; and all the acoustical routes converge on the throne room. Into the great lake of silence where you are floating rivers of empty air, stirred by intermittent vibrations. Alert, intent, you intercept them and decipher them. The palace is all whorls, lobes; it is a great ear, whose anatomy and architecture trade names and functions; pavilions, ducts, shells, labyrinths. You are crouched at the bottom, in the innermost zone of the palace-ear, of your own ear; the palace is the ear of the king.
Italo Calvino. The King Listens - (Under the Jaguar Sun).

Writing in The Grain of the Voice, Barthes develops a morphological site for the voice, operating as a dual production at the juncture between music and language.
The grain of a Russian tenor is….directly the cantors body, bought to your ears in one and the same movement from deep down in the cavities, the muscles, the membranes, the cartilages, and from deep down in the Slavonic language, as though a single skin lined the inner flesh of the performer and the music he sings.

All this detached from individual expressivity to act symbolically - it is a body without personality, one entirely co-substantial with its cultural and environmental context.


“Well! I’ve often seen a cat without a grin”, thought Alice; “but a grin without a cat! It’s the most curious thing I ever saw in all my life!
Lewis Carroll, Alice in Wonderland.

Recording pure abstraction.
Well, I hate to say this but…digital sound does not exist - but digital storage, transmission and manipulation of sound analogues do. The sporadic Analogue versus Digital debate principally hinges upon which boxes contain sounds, once out of the box it’s all analogue anyway; until, perhaps it hits the nervous system! (and we could have various conversations about Synaesthesia here!!!).

A (dis)connection between experience and information is a central characteristic of all mnemonic technologies. In music terms such a cleavage between performed sound and an informatic system, which contains sound data, arrived with the player piano. As a descendant of the Jacquard loom (as are computers) the player piano provided a mechanical recording, not of sound (as did the Gramophone) but of the information required to re-constitute the musical event. Although dependant upon the condition of the re-play instrument, player pianos were theoretically perfect transcription devices, leading Percy Grainger, the prominent Australian composer, to remark that the piano roll represented him as he would like to play.

Early electro-acoustic experiments relied upon analogue synthesis to invent new instruments, soon abandoning clumsy (and expensive) attempts to numerically simulate natural sounds. Such analogue synthesis, which could be considered less radical than the player piano, has acquiesced to the contemporary coupling of digital sampling possibilities with MIDI. Interfaces, which have effectively transformed our conceptualisations of sound as a mutable substance, rendering (recordings of) natural sound as raw material in a new musicalisation of the world. The deciding factor in the ascendancy of either numerically derived sound, or sampled material seems to be the technical relationship between processing speed on one hand and storage on the other (naturally the new Video/film studios in Moscow use all digital control systems to operate analogue storage equipment!!!).

The complex forces, which have motivated the development of digitisation, echo Pythagorean concepts of abstraction and purity. Digitisation is an absolute hygiene of sound divorced from the (now acknowledged) chaos of physicality to be corralled in the realm of the Digisphere. Claude Shannon’s pioneer work in Information Science established the concept of Information as a primary substance, equivalent to matter or energy, permitting Sound, in a laboratory/studio context to becomes a pure substance available for re-formation and re-constitution upon demand. Sound in digital storage is rendered without a referent and ipso facto without morphology, thus doubling Schaefer’s anxious Schizophonia.

An ideal substance capable of being transformed to flow into the mould of new referents, new morphologies, new sonic architectures - a sympathetic magic, in which the world is captured by a transparent recording medium and then asked to lead a life of indenture - assigned to the MIDI keyboard.  Like Kepler, analogue adherents continually fold back into the palpability and inherent complexity, of actuality. This return should not simply be interpreted as nostalgia for obsolete technologies but rather seen as an acknowledgment of the operational relationship, which such technologies share with natural dynamic processes.

Perhaps we should recall the (possibly apocryphal) anecdote of a North Vietnamese defector who landed his Mig. 21 at an American Military base. Delighted with their first intact specimen, the Federales crawled all over the machine - proclaiming in sheer delight when they discovered that all of the Mig’s instrumentation was valve powered. The euphoria at discovering this technical anachronism was instantly cooled when one of the technical team pointed out that valves are not affected by atomic blasts whereas transistorised circuits instantly fuse

Noise + Ambience.
There is a special place - a low mountain range in the Western desert. Rocky slopes on which to do nothing - I have spent a good deal of time there doing just that. It takes two whole days for the tyre rumble to subside from the ears - for the nerves to re-set to zero. Then at night listening becomes possible - It becomes possible to hear absolutely nothing. As for the tape-recorder, it simply inscribes its own irrelevant hiss. Here is an immense quiet; a quiet resting under the luminescence of the Milky Way; a full quietness. The rocks are singing away the day’s heat at some inaudible pitch, the heartbeats of reptiles are slowly rolling down thermal gradients - it is a quiet of solid repose.

But then there is another form of silence. An un-stable silence that peels away behind the stereo voice, drawn into a vacuum of inky and dimensionless space. Arrayed across the horizon, and appearing both proximate and distant are the voices - voices that address us, which converse without falter. Somehow they simply appear, hovering at coordinates plotted into radio-phonic position - whilst all around them the architecture has been demolished. All surfaces, even the very ground, has slipped over the edge of a cataract of silence. That which remains is the space of the promised after-life; a life in which quiet does not exist.
Nigel Helyer, Bell Transfer - Ars Electronica Installation Linz 1989, The ABC and ORF Radio

I experienced my first conscious encounter with a black hole whilst listening to a series of Horspiele radio productions presented by Klaus Schoning of WDR. Köln. This null effect (not dissimilar to an anechoic chamber). was created by the hi-fidelity silences generated in studio processing.

In an attempt to capture content - digital media has the tendency to gate out the insignificant, the marginal and the accidental - moreover it is destined to deny its own presence under the assumption that a disappearance of technical means is proportionally equated to an increase in audio fidelity. We arrive at the myth of a total technical transparency, which mimics the perceptual masking in human hearing; our own perceptual horizons being limited to prevent us from recognising the frequencies of our own nervous system. The ambition of digital recording is to shadow itself in a pretence of naturalism - the black box claims to be a mirror - but a mirror which will not reflect environmental deviation, wear, tear and age very Snow White! In this place, that which is not intended is not simply empty, it does not exist - it is the abyss.

What I sketchily propose here goes just a little further than the kindergarten information theory duality’s of sender/receiver, noise/signal by positing an ecological model, a kind of sonic Gaia - able to generate a morphic field, which through the phenomenon of resonance organises the elements of the (sonic) cosmos. A mnemonic summoning of all the elements of a sounding circuit to resonate across a matrix of (what we could call time and space).

In the sensate world space and time are to a degree palpable; speed being taken as a measure of motility through both domains. In sonic terms speed (of an event) is interpreted as frequency and reveals itself as pitch; whereas dimension and mass are generally associated with resonance, which, of course, also reveals itself as pitch!
Much attention has been paid to Virillio’s collapse of the domains of Space and Time into a vector, Speedspace. The major problem with the Virillian logic is that it is quite literally (to use one of his own titles) War and Cinema, dominated by conceptualisations drawn from the military/industrial mind-set with an idee fixe determined by Vision, more explicitly expressed as trajectory or vector.

Just such a Virillian collapse of all senses into the visual is echoed within the electronic reincarnation of light in fibre optic as informatique. Within telematics the spatiality so vital for the fundamental operational categories of sound experience, surroundedness, immersion, directionality and depth are denied - the principal focus remaining with a narrow definition of signal as content and context as noise. This denial of the architecture of spatio-temporality is not dissimilar to the digital processing of sound, which promises to return the collapsed ambient space as Virtual Space, where time and space are naturalistically re-deployed as metaphors literally standing-in for themselves. Why should we be interested in such Newtonian reconstructions? Why should visual grammars cuckold the metaphoric richness of aural experience only to finally loose perspective in speedspace - a domain in which sound simply disappears!

Henri Bergson once posed the problem; how would it be possible to perceive the actions of a hypothetical agent, who had, overnight, achieved a doubling of the speed of all the events in the Universe? His solution was quite simple, we would discern a great loss in the richness of experience (as phenomenon disappear through the top of our perceptual range).

Every disease is a musical problem.

Perhaps it is appropriate to loop back to our entry point and re-examine our dearth of appropriate sonic metaphors - now placed under even greater duress by the Virillian Houdini act. The cue-point is Entrainment or phase locking is a well-recognised physical phenomenon in which elements of natural, dynamic systems correspond to establish harmonic patterns with one another. This tendency to synchronise frequencies, or to share rhythms is observable across the entire gamut of both the natural and constructed world. Entrainment occurs at the level of cell growth and in the complex biosocial organisation of animal groups it inhabits the tuning circuits of radio receivers and synchronises the habits of twin children.

By establishing Resonance as a new organising metaphor for sound experience we can conceptually assemble both the morphological and the mnemonic domains of sonic events. Such a web-work would function to connect historical actuality, technical mechanisms, architectural acoustics and the listening subject(ivity) into a harmonically coupled organism. An organism capable of operating as an active network, constituted in terms of multiple resonances, feeding at first, upon the redundant metaphors of time, space and speed.

© Nigel Helyer 15/03/96.

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