For the concept of the simple and the complex we depart from the model of dynamic complexity of the Complex Adaptive Systems (CAS) proposed by Murray Gell-mann (3) and John Holland (4). A CAS is a system made from a finite number of simple elements, which gather driven by some modality of the principle of recursion. That principle explains the capacity of simple entities for recombining into a potentially infinite number of complex systems. A CAS is a dynamic complex system whose individual entities interact simultaneously with each other, in parallel mode, and evolve in time as an adaptive reaction to the actions of other individual entities in the system. The interaction of the individual agents gives rise to emergent properties not possessed by the individual parts (5).
What is the force that compels the individuals to evolve? The force that allegedly activates the evolution in time of CAS are paradoxes. The individual agents are puzzled by the entities or events that live in the edge of chaos (5), contradicting the familiar order. The CAS, after detecting the regularities of the unknown events makes a conjecture, modeled as an “schema” of interpretative and action rules. The CAS unfolds the schema into the world and checks its predictive force. The CAS may make an infinite number of modifications to the schema to adapt it to new events (3). Some examples of CAS that have been studied are the diversity and complexity of forms of living entities, the dynamic of civilizations, the evolution of culture, the acquisition of language, the evolution of language. Given the great variety of systems that have properties of a CAS, they have been object of multidisciplinary research.
The world of Music has the structure of a net of dynamic relations that show the properties of CAS. The agents are the composer, the work of music, the performer, the hearer, the sound itself and the location and time when it is produced. The behavior of those agents also have properties of CAS. We propose researchers to consider two of those CAS: the sound itself and the hearer.
What is the ontological nature of sound? Recent research resulting from the important cooperation of composers, performers and scientists has shown that a sound entity has a complex dynamic morphology. A sound is not an invariable entity, frozen in time, which may be repeated without variations. A sound entity is a CAS that evolves as the result of the interaction of its parts. The individual agents of a sound entity (frequency, timber, dynamics, duration) interact among each other and evolve in their relation with the environment.
The use of sound objects by contemporary composers differs from that found in standard compositions, whose composers depart from the assumption that a sound object is an indivisible atom. For contemporary composers, the particles in a sound entity are not hierarchically ordered, but they interact in time according to the principles of CAS. The possibility of using and manipulating the particles of a sound entity has enable composers to create relations that were until then inaccessible. Some instances of those relations are the harmonic use of timber, the continuum time-frequency, fractal structures, embedded rhythmic structures (2), the simultaneous combination of no-synchronized rhythmic voices. Such a dynamic conception of sound posses an important problem for musical notation. What is the simpler and more efficient way of transcribing the dynamic sound events into discrete units and symbols, which would be compatible with the notation used by performers?
What is the nature of the human faculty for music? How does the hearer acquire this faculty? How does the hearer perceive the simple and the complex? Does he or she do it by instinct, by computing or by both of them? What is the limit of the instinctive perception of complexity? What is the limit in computing complexity? Is there a genetic base for the perception of complexity in music? What kind of experiments can be performed to measure the human perception of music complexity?
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