ELEMENTARIDADES

A Compositional Approach via Functorial Correspondence to
External Structures
Joana Lopes , Raul do Valle ,3, Jonatas Manzolli2, and Adolfo Maia Jr3,4.
GITD/ NICS/ IMECC
State University of Campinas (UNICAMP) - Brasil


ABSTRACT
We describe the creation of an interdisciplinary piece named ELEMENTARIDADES based on Algorithmic Composition, the Rudolf Laban’s Theory of Expressive Motion and the physical model of elementary particles of matter. The sound envinronment of ELEMENTARIDADES was constructed via concepts of Sound Functosr and Categories. The choreography was developed by the Interdisciplinary Group for Theatre and Dance (GITD - UNICAMP) and the music was composed using algorithmic composition software developed at the Interdisciplinary Nucleus for Sound Communications (NICS - UNICAMP).


1. Introduction and resume of the Physical Model

It is well known that crossing of different areas of human knowledge leads to fertilisation and creativity. In this way new structures and methods can be developed, enlarging frontiers. A interesting example of creative crossing is that one between art and science through applications of the technology and abstract mathematics as well. Computer Music is a very good example of this kind of crossing. So, it is not difficult to guess that this crossed fertilisation is now invading the world of dance and theatre empowering new ways to create and express artistic manifestations. In order to connect the different fields we need to construct an abstract representation of each one of them, which should be suitable to a theoretical analysis. In our case, the piece ELEMENTARIDADES, this was provided by three systems: the Standard Model of the fundamental structures of the matter in the universe, a choreographic system based on Rudolf von Laban model of the analysis of motion, and a sound environment developed by using tools of Computer Music developed at NICS (UNICAMP). All the three systems listed above share the aspect that they are reducionist in the sense that they try to get the minimal parts of information and construct complex structures out of them. Once obtained these atoms of information of each field, a mapping between their fundamental blocks is defined. ELEMENTARIDADES is the result of this correspondence. The piece is divided in 5 sections, namely: Baryons, Leptons, Gyros, Chaos and Cosmogenesis. The sections Baryons and Leptons describe some of the modern view of the fundamental particles which form most part of visible matter in the universe. Baryons( heavy in Greek) names a family of particles in which are included the most common ones, such as protons and neutrons. Inside baryons there are three particles named Quarks. So along Baryons section repetitive short three-parts structures are presented in blocks meaning these particles are permanently confined inside baryons.
The electron is part of a family of particles named Leptons (meaning light particles in Greek). There exist six leptons: the very known electron, the muon and the tau and their respective neutrinos namely, electron neutrino, muon neutrino and tau neutrino.
The section Gyros describe one the fundamental aspects of quantum systems, namely, the concept of spin, which means that elementary particles have an intrinsic angular momentum, a kind of elementary rotation, named simply spin (Gyros in Greek).
Another important fact about matter is that there is no rest at all in the universe. At microscopic level, Quantum Mechanics shows that there exist always a residual motion of matter due to so called vacuum fluctuations. At macroscopic level the universe is in constant expansion and also there exists an apparent random distribution of galaxies and clusters of galaxies at very large scales of distance in the universe. Instead using white noise to describe these aspects of matter in sounds, ELEMENTARIDADES present them as short percussive blocks of sound but randomly distributed in the section Chaos.
Modern view of cosmology is described by the Big-Bang model in which the universe came to existence as a by-product of a very huge explosion from which all matter in the universe was created. So we ended the piece with sound representation of the creation of the universe in the section Cosmogenesis. Sound elements of the other sections are presented in Cosmogenesis in order to show the coherence and correlation between all parts of the model as well other ones suggesting the psychological awe we, humans, have to this mysterious Universe, our home.

2. The Labanian Model of Expressive Motion

The idea here is to transport some properties describing the elementary particles to motion of dancers. In ELEMENTARIDADES all dancers motion are elementary, in accordance with Rudolf von Laban’s Theory of Expressive Motion, but put together the several possibilities of articulation and combinations it can be generated body motions of great physical complexity, using all corporal vectors, which represent elementary particle motions such as we suppose there exist, for example, inside protons and neutrons. Therefore it is possible to analyse and create a Labanian notation for this piece and then it could be used as a case study for classes in choreography.
Besides the scientific point of view on the concept of motion we have in this interdisciplinary piece an artistic dimension when a human body creates transient images with strong symbolic interpretation.
Our method has been basically observation of a multitude of motions and a subsequent analysis of this set of motions and to extract from it those ones which seems more interesting for our purposes. Another interesting aspect of ELEMENTARIDADES is that dancers dialogue with sounds, so they do not follow the music, but music and motion are complementary for the description of the physical model.


3. The Sound Environment

The music of ELEMENTARIDADES embodies, in its conception, reducionist aspects, not in strictu sensu as minimalist music, but as sound representation. In its gross structure it is kind of a programmatic music since it contains musical gestures derived from the Standard Model of particles as well as from the Labanian decomposition of complex motions. In order to compose the music, we have made use of some computer music software developed at Núcleo Interdisciplinar de Comunicação Sonora (NICS- UNICAMP) such as KIKLOS, Vox Populis, Curvasom, etc.
The main idea here is to assign (and this is an arbitrary act of the composer) some sounds to each particle we are considering as well a sound representation of its properties, such as light, heavy, strongly or weakly interacting with other particles, etc. These are fundamental blocks to construct the sound environment. Most part of them was generated by software developed at NICS as mentioned above. So we have sounds representing electrons, quarks, muons, etc. This material is then worked out in a “polyphonic” way resulting in a dynamical and complex sound mass evolving in time.
Here we had in mind an application of the concept of “transference of structures” from physics and the art of motion to domain of sound. In a recent work [1] we present the notion of “sound functor” which has just this property of transfer structures from a category of objects to another one, preserving relations and operations between objects in both categories. Below we show a small diagram of the process.
Of course many adjustments were necessary which were made by the composers.

4. Conclusion

In this paper we described the construction process of the piece ELEMENTARIDADES. As stressed above, ELEMENTARIDADES is an interdisciplinary piece in its essence. In addition it could be used for educational purposes in choreography. So it is suitable to be performed as case study, mainly for Labanian notation approach to the study of motion.
From the point of view of computer music composition it has a reducionist structure, since its composition was suggested by an analogy to the Particle Physics Model. In this way fundamental sound blocks are introduced and worked along the piece using the concept of Sound Functor (Manzolli, J & Maia, A. (1998)), which is an application that tranfers struuctures and operations from a category of objetcs to another one which in our case is a set of synthesized sounds.

5. References
Laban, R. (1999) L’arte del movimento. Ephemeria Editrice, Bolonha, ISBN 88-87952-00-6.
Moroni, A., J. Manzolli, F. von Zuben & R. Gudwin (1999). Evolutionary Computation applied to Algorithmic Composition. Procedingos of the IEEE, Artificial Inteligence Section, Washginton, USA.

Manzolli, J. & A. Maia Jr. (1998). “Sound Functors Applications”. Proceedings of the V Simpósio Brasileiro de Computação e Música, XVI Congresso Nacional da Sociedade Brasileira de Computação.