Woodland Heights is a study of forest canopy ecology. More specifically, the work is an illustration of the premise that “species composition and tree size distributions become more diverse with increasing stand age” and that “with increasing age stochastic processes play increasingly important roles in creating structural complexity” ¹.
The form of the piece maps the growth of a model forest stand over a projected 720-year period, where a crotchet in the score is equal to a year in ecological time. The structure is divided into three successionary periods demarcated by radical change in accordance with the principle that “local disturbances not only maintain the character of the system by maintaining the species that are early colonists but poor competitors; they also maintain the resiliency of the system, preserving the opportunistic species that thrive under the conditions accompanying the unpredictable but inevitable environmental changes that occur at broader spatial scales, such as windthrows or fire.” ²
The imagined forest is composed of seven tree species common to the garden of my original family home in Chorleywood, from which the piece also takes its title. The first two sections map the projected interactions of six species: Silver Birch (Betula pendula), Laurel (Prunus laurocerasus), Holly (Ilex aquifolium), Rowan (Sorbus rosaceae), Beech (Fagus sylvatica) and Oak (Quercus robur) which take their roots from E, A, D, C#, G and C respectively. In the third section, the viola solo introduces the seventh species: Wild Apple (Malus sylvatica) on Bb.
Particular qualities of each species type are translated into musical elements in the score: maximum height, average lifespan and reproductive cycles are expressed through the statistical distribution of the overtone series from the open strings fundamentals of the orchestra, the adaptational qualities of a species by its role in the formal development of the piece and its phyllotaxis by motivical structure.
Writing this piece necessitated an exploration of the fascinating terrain that is contemporary ecology and provided a reassurance that humanity’s deep love of the biosphere still finds expression in our societal priorities. Today’s ecologists have embedded conservational and educational elements deep into their discipline and together form a large and extremely open network of individuals working across the world to better understand and preserve the immense diversity found on planet Earth. In the words of two of canopy ecology’s pioneers: “Perhaps that is the ultimate goal of canopy research – all scientific research for that matter – to produce a sense of the vast and the infinite and to promote our sense of wonder, a curiosity that needs to be fed by experience to be long-lived.” ³
It requires very little rephrasing of this idea to appreciate that the beauty of this statement could be applied equally to the objective of the artist. In composing this work I have come to appreciate the enormous translatative power of music and the many vantage points that it offers us for immersion and enquiry into its sources of inspiration and have also come to understand that the web-like creational processes of investigation, experimentation, epiphany and revision share many commonalities across the Sciences and the Arts. Numerous great minds throughout human history have proved a constant reminder that in reality there is no separation between these two great fields of discipline, and that just as two hands work together in playing an instrument, so these two aspects of human nature form part of a single integrated response to the questions of our environment.
In creating both new work and new theories, we must exercise great freedom in our relationship to a subject matter in order to allow scope for intuitive processes to develop. Similarly we must give free reign to the imagination in order to find connections between ideas and to build structures that can later become material for further development. Perhaps in the future we will understand more about how the imagination works and its evolutionary development, but for now we must be content with understanding that without freedom and diversity there can be no development. The same lesson taught in fact, by forest canopy ecologists with regard to species biodiversity. It is no coincidence that every great work of both art and science contains some unanswered and perhaps unanswerable question buried within itself, and it is this that I believe inspires that ‘sense of wonder’ and imbues it with a complexity that is a microcosm of the depth found in life itself. A work that is the result of a logical or mechanical process alone risks becoming lifeless and predictable – in art, as in life, rules are made to be broken. Our greatest priority at this moment in the history of our planet should be to conserve and protect the spectral magnificence of life in all of its many forms, preserving and protecting the unknown as well as the known will provide a future for our planet and its wealth of expression in form.
I am greatly indebted to numerous individuals who assisted in the creation of this work. In particular I would like to thank Dr. Thomas E. Lovejoy, Dr. Margaret D. Lowman, Dr. Simon Levin, Dr. Henry S. Horn, Dr. Michael Jones, Sven P. Batke and Noel O’Shea for their scientific and technical expertise; Katherine Hunka, Robin Panter, Malachy Robinson, Cora Venus Lunny, Adrian Hart, Olesya Zdorovetska, Francesco Turrisi, Linda Bsiri, Sachiko Kuriowa, Ellen Fallowfield†, Kate Ellis and Russell Rolen for their musical counsel; Sheila Pratschke and Nora Hickey M’Sichili together with all of the staff at the Centre Culturel Irlandais, Paris for the amazing opportunity to work on this piece in such creatively fertile surroundings and finally a special thanks to artist Ruth O’Donnell for providing the beautiful illustrations for the score.
This piece is dedicated to the trees of ‘Woodland Heights’, Greenhills Close, Chorleywood – to the laurel, oak, birch, rowan, beech, holly…and the wild apple.
¹ Hiroaki T. Ishii, Robert Van Pelt, Geoffrey G. Parker, Nalini M. Nadkarni (2004). Age-Related Development of Canopy Structure and Its Ecological Functions. Forest Canopies, Second Edition.
² Simon Levin (1999). Ecological Assembly. Fragile Dominion.
³ Margaret D. Lowman and H. Bruce Rinker (2004). Introduction. Forest Canopies, Second Edition.
† String harmonics image on glossary p.1 taken from http://www.cellomap.com, reprinted with permission of author.
Flocking III explores the mechanisms of the emergent system, in which individual components can be perceived to express themselves as a group. Nature offers many spectacular examples of this type of behaviour, of which perhaps the most beautiful is the flocking of birds in flight.
Of all the birds found in this world, the starling flock is considered to be the most impressive in terms of number and reaction time, and so perhaps for this reason it is given the most beautiful of names – a murmuration. Starling murmurations are also the subject of the most scientific research for these very same reasons; flocks can number greater than 100,000 individual birds and their reaction time whilst in flight as little as 0.026 seconds.
My work on the Flocking Series was informed by the research of computer scientist Dr. Pavlos Antoniou of the University of Cyprus and mathematical biologists Luke Coburn and Dr. Iain Couzin of CouzinLabs in Princeton University. As source material for Flocking I-II, data derived from bird flocking simulators (or boids) and their x,y and z co-ordinates in space was translated in musical values of pitch, attack frequency and dynamic. The streams of numbers yielded behavioural types that emulated the movements of birds in the air and in places the score itself bore resemblance to flock patterns and the motion of the wing.
Flocking III is a new type of score, based on the realisation that humans also display behavioural patterns and can express themselves as a group. In fact we do this every day of our lives, whether walking in a crowd or listening and responding in the language of music.
The grammatical structure of music is formed of basic variables, just as a spoken language is self-organised, and these emergent properties can be translated into action through improvisation. This process is actually how we learn to play music in a large group, as was traditionally found in human societies throughout history and continues simultaneously today in many parts of the world.
Performance of the piece requires each member of the ensemble to listen and reach to three variables in the music. These areas are defined as ZoR, ZoO and ZoA and correspond to the zones of Repulsion, Orientation and Attraction, which are used to translate the motions of flock mechanics into simulations. These areas govern the behaviour of the individual bird; when another bird moves into the zone of Repulsion the instinctual response is to move away, and similarly to align or move towards in the zones of Orientation and Attraction.
The zone of Attraction (ZoA) takes pitch as its variable. The performer should graduate the pitch or pitches that they are playing according to the sounds that they hear around them, always moving towards the notes that they perceive.
The transition to move from ZoA into the next zone occurs when all of the performers play a single unison pitch (or its octaves).
The zone of Orientation (ZoO) takes attack as its variable. The performer should adjust the frequency of attack of the gestures that they are playing according to the frequencies of the rhythmic attacks that they hear around them, always trying to align with these frequencies.
The transition to move from ZoO into the next zone occurs when all of the performers play in rhythmic unison (or in metered polyrhythm).
The zone of Repulsion (ZoR) takes dynamic as its variable. The performer should emulate the dynamic of the performers around them, but also is encouraged to break the rules of this zone and to improvise freely if they feel so inclined.
The transition to move from ZoR into the next zone occurs when all of the performers are playing at a minimum dynamic using breath sounds.
The final structural element of the composition is the introduction of the predator to the group flock dynamic. In a large ensemble, one of the performers should be assigned this soloistic role and either do not participate in the performance with the rest of the group, or leave the flock after a certain number of completed cycles. This performer is then freed to periodically interject with varying dynamic gestures using multiphonics solely. Upon hearing the interjections of the predator, the other performers making up the flock should continue to obey the rules of the particular zone in which they find themselves, but also employ solely multiphonic gestures.
The spatial positions of the performers and the speed of their responses will govern the behavioural characteristics of the sonic flocking effect. Experimentation is invited with this element of the performance, with relation to both the positioning or mobility of the flock and the predator. The default position of the ensemble is a semi-circle with instruments ordered according to pitch range from stage left to right.
Flocking III may begin in any one of the three zones, and the transitional points can lead to either of the two remaining zones. These structural decisions may however be predetermined, in which case the default movement should be ZoA – ZoO – ZoR and continue in a cyclical form. Other predetermined variations may also be developed once the ensemble has performed this initial formal structure. The structure of the work may also, and preferably, by determined in real-time by the improvised responses by the members of the ensemble to the rules for each zone and their transitional movements.
It is worth noting that whilst in a particular zone it will prove beneficial to focus primarily on the musical variable that governs this temporal area, even to the extent of limiting the degree of variance in the other two variables employed at other times during the piece.
 Pavlos Antoniou, Andreas Pitsillides, Tim Blackwell, Andries Engelbrecht, and Loizos Michael, “Congestion control in wireless sensor networks based on bird flocking behavior,” Elsevier Computer Networks Journal, vol. 57, no. 5, pp. 1167-1191, April 2013. [pdf]
“Architecture is frozen music.”
There have been several examples of a perfect fusion between music and architecture, the most striking in recent memory being the work of the composer Iannis Xenakis (1922-2001).
Injured whilst fighting against the Nazis during the Second World War, Xenakis was smuggled out of Athens by his father and sent to Paris, where he eventually found work in the office of the French architect Le Corbusier. Over the years in which he worked in his firm, learning composition through the night, Xenakis grew in stature from a structural engineer to a partner architect and was responsible for many of the company’s great architectural successes, such as the Philips Pavilion, commissioned by the electronics giant for the World Exposition in Brussels, 1958.
The designs of the Pavilion incorporate fundamental ideas from an area of mathematics that fascinated Xenakis and proved to be a rich seam of inspiration for his structural forms, both musical and architectural – the Stochastic principle, or his Theory of Probability.
Xenakis used the word ‘stochastic’ to express the idea of masses tending towards a mean or a goal, such as a stable stage. He speaks of the use of these ideas in terms of composition in his book Formalized Music, although this passage is used earlier in an essay entitled Musique Architecture (Casterman, Paris 1971):
“We can control continuous transformations of large sets of granular and/or continuous sounds. In fact densities, durations, registers, speeds, etc… can all be subjected to the law of large numbers with the necessary approximations. We can therefore with the aid of means and deviations shape these sets and make them evolve in different directions.”
The Philips Pavilion was based on a geometric design that expresses this principle: the hyperbolic paraboloid.
In her definitive biography ‘Xenakis’ Nouritza Matossian makes the point that:
“Lafaille had done pioneering work in hypar shells in 1935 but they had been little used and now Xenakis was putting to great effect the knowledge Lafaille had passed on during their time together. The engineers insisted that stanchions should be added for further support while Xenakis argued that the shells were self-supporting, that they would be supported further by the straight ribs holding the intersections of the curved planes together, so there was no need to block the clean uninterrupted performing space. He was not to be proved right until later…Owing to the novelty of hypar shells as a structural form, preliminary scientific analysis was provided by experts from technical colleges in Holland whose studies verified the structure in theory. The scientists were enthusiastic about the strength of the hypars and the project was passed on to a contracting firm whose engineer, specialising in concrete reinforcement, wrote, ‘We were aware of the outstanding qualities of strength and stability possessed by shells formed as hypar shells’ and these were to be strengthened further by pre-stressing the concrete.”
H.C. Duyster, in his article ‘Construction of the Philips Pavilion in Prestessed Concrete’, published in the Philips Technical Review Vol. 20, 1958/59 states:
“In fact the shape of the walls of the Philips Pavilion lent itself exceptionally well to this treatment owing to the fact that the hyperbolic paraboloids may be generated by straight lines, a property possessed in common with ruled surfaces in general; this made it possible to apply all or most of the pre-stessing wires so that they would run straight.”
Xenakis’ own compositional notes for his first work for orchestra, ‘Metastasis’ show that he was also working with these precepts in his musical work:
‘Metastasis’ was a revolutionary work. Herman Scherchen, the conductor who gave its première, said of it that “In fact it does not come out of music at all, but from somewhere completely different.” Perhaps here he eludes to its mathematical foundations as source material, but this is not new in composition (ref. Bach or Pythagoras) simply that the mathematics in question were born in modernity.
Xenakis’ work teaches us the cohesive power of strong governing precepts in artistic form, within and across disciplines. For an insight into those strong governing precepts as they exist in the world, we turn to the work of the Swiss scientist – Hans Jenny.
Hans Jenny may be described, as Xenakis was, as a Renaissance man. This refers to an era when education (for the minority) was considered in inter-weaving layers of knowledge, and emphasised, as Jenny constantly did, the importance of always trying to understand the whole, rather than its component parts in isolation; Jenny was a scientist, medical physician, linguist, musician, painter, ornithologist, philosopher and founder of a branch of physics that he named ‘Cymatics’.
The name ‘cymatics’ comes from the Greek ta kymatika, meaning “pertaining to the waves,” and it is in essence the study of the physical effects of sound on matter. Although Jenny named the field himself, his work did not appear from nowhere, and can be seen as part of the wider field of acoustics as laid out by the German physicist E.F.P. Chladni (1756-1827).
Chladni discovered the images that are now named after him whilst investigating Lichtenberg figures, themselves named after their discoverer, the German scientist Georg Christoph Lichtenberg (1742 –1799). By stroking metal plates sprinkled with powder with a violin bow, Chladni made the vibration processes visible, and was the first to witness the sonorous figures to which he gave his name.
Jenny himself would have been the first to point out that Chladni was in many ways continuing a line of thought that stretched back to the Greek philosopher Pythagoras and the Flux Theory of Heraclitus.
(A pair of craters located in the
Southern Highlands region of the Moon.)
Meade 8″ LX90 @ f/25. DMK 21AF04
monochrome firewire camera. 09/13/2006.
I include this rather oblique reference to Heraclitus simply because the image strikes me as so similar to the images that I have found in Jenny’s research, particularly the experiments with lycopodium powder.
These images are taken from Jenny’s seminal text, called ‘Cymatics’. Figure 84 shows what happens to a surface layer of lycopodium powder on a paper diaphragm excited by a single tone at a frequency of 50 cps. Figure 85 shows the same experiment, but with a frequency of 300 cps. As Jenny points out, with a higher frequency, the pattern is of a more delicate character.
With the use of modern technology that was able to refine this process and accurately document it, Jenny picked up the trail from where Chladni had left off, and discovered that the recurring patterns that could be made visible were dependant on strict controllable factors, such as frequency and amplitude of the exciting tone, materials (of the excited substance and the diaphragm or plate on which it is placed) and the shape of the plate itself. Under strictly controlled laboratory conditions, Jenny manipulated each of these parameters in turn, producing experiments with quite amazing results. He discovered that changing single parameters whilst the others remain constant yielded visible subsets, or groups of images that show clear relationships to one another.
Jenny used a wide variety of different materials in his research, including glass, copper, wood, steel, cardboard and ceramics for the plates, on which he measured the movements of lycopodium powder and quartz sand. He also performed a series of experiments with liquid glycerin in water and light refracted in a single drop of water containing fine particles that reflect the light source, in a series of experiments that yielded his most famous images.
A layer of glycerin has been made to
vibrate by a tone acting upon a diaphragm.
The result is a continuous formal pattern.
Light refracting through a small sample of water (about 1.5 cm in diameter)
under the influence of vibration. Although there appear to be
12 elements comprising this figure, closer examination reveals that it
actually consists of 2 opposed hexagonal elements.
With reference to this last image, Jenny makes the point that “Still images empashise the structure or form of the figure, which, in actuality, is in constant dynamic motion, oscillating from one phase to the next. This image clearly portrays a harmonic quality in terms of number, proportion, form, centering and symmetry. This quality is also apparent in its dynamics, pulsations, transformations and polarities.” This could be an excerpt from an essay by a painter, a composer, or a choreographer… there is an essential understanding of form in his conception of science that speaks immediately to the artist, as a vehicle for understanding the expression of nature.
Jenny writes in ‘Cymatics’ that “Sharply defined patterns emerge, but they flow away into nothing. Flowing patterns and patterned flux appear before us. Thus, the problem of cymatics exists not only in observing in the experimental field but also in formulating concepts with which to press towards comprehension of the actual realities. In attempting to leave the cymatic phenomenon intact and unharmed in our intuitive vision, we can derive from it the following spectrum with form at one end and movement at the other: figurate, patterned and textural on the one hand, turbulent, circulating, kinetic and dynamic on the other, and in the centre, acting in either direction, creating and forming everything, the wave field, and thus as ‘causa prima’, creating and sustaining the whole, the ‘causa prima creans’ of all – vibration.”
Jenny explains these three aspects of cymatic phenomenon in terms of their ‘triadic’ relationship to one another. The Triadic concept is his unifying philosophical precept. The essence of it lies in the three component parts to the manifestation of the forms that he witnessed: figure, movement and period.
He goes on to explain “The three fields – the periodic as the fundamental field with the two poles of figure and dynamics – invariably appear as one. They are inconceivable without each another. We cannot therefore number them one, two, three, but can only say they are threefold in appearance and yet unitary; that they appear as one and yet are threefold.” What he means by this is that in each pattern created in the various permutations of his experiments with vibrations, these aspects are simultaneously expressed.
All of the patterns display a periodic nature. The waves themselves, which are acting on the materials, can be measured in terms of their periodicity; therefore it stands to reason that this is expressed in their action on matter. Jenny constantly makes the point that in order to develop a comprehensive understanding of cymatics, one must build up ‘experiential knowledge of the field’, and we believe that this pertains to the necessity to witness the moving images in real time. In video footage of his experiments, both from his original films and subsequent research, the flux patterns can be clearly seen, some of the experiments use coloured grains in order to witness this aspect of the phenomenon more clearly. Within this ‘fundamental field’ of periodicity, the patterns also contain figurative elements, expressed in clearly discernible formal elements and symbolic imagery, and a dynamic element, expressed by the constant movements of the materials whilst under the influence of vibration.
This last aspect is expressed well in the following image, a still from one of Jenny’s lycopodium experiments:
This is a close-up of the centre of a large circular pattern, which would look something like this:
The motion in the video shows a clear axial rotation, like the blade of a helicopter, which rotates clockwise at certain frequencies and anti-clockwise at others. This is a good illustration of the dynamic principle at work within the phenomenal triad.
The triadic concept very clearly delineates a working structure for the creation of new work; indeed we, as artists, believe that the necessity of “formulating concepts with which to press towards comprehension of the actual realities” demands expression of this concept in new artistic form.
Jenny himself states: “Again and again, and in ever new forms, the cymatic method reveals the basic triadic phenomenon which man can feel and conceive himself to be. If this method can fertilize the relationship between those who create and observe, between artists and scientists, and thus between everyone and the world in which they live, and inspire them to undertake their own cymatic research and creation, it will have fulfilled its purpose.”