Projection of Time in Space – The Musical Form

1. Prolegomena. The concept of cyclic phenomenon is a universally perceptible reality. The very idea of cycle and cyclicity needs a clearer and more profound definition. The science that can give it an accurate, apodictic, definition is mathematics. Particularly, in the field of music, due to the oriented existence of the Time vector, the correct representation should always be not the cycle but cycloid and the related family of curves. 2. Subiectio - Cycle, Cyclic and Cyclicity in the Musical Discourse. Different hypostases of the phenomenon are examined and the sources, as well as the specific principles of construction identified. Such an issue obviously integrates itself within the essential distinction between the fundamental opposition between Identity and Alterity. How much identity should there exist at the level of a discourse deemed cyclic? How much alterity should there exist for the recurrence or reiteration to be different and significant? 3. Adjectio – Musical forms and mathematical isomorphism. We find a significative congruence between Hamiltonian graphs on polyhedra and important formal solutions in the field of musical forms such as: tripartite form with reprise, rondo, bitematic sonata. This reality is supported by strong arguments and the complete isomorphism of the three cases presented is not only exciting or disturbing, but also generator of new and important significations. 4. Postegomena – Like polyhedra or the Hanoi tower, the musical forms, elaborated in a long process of discursive evolution and studied by historic and systematic musicology, obviously evoke the same superior models of order and symmetry. The construction of musical forms could be described in the light of Chaos theory as a chaotic phenomenon. The creation of hundreds of composers tends to be regulated in this case by a strange attractor: the regular polyhedra.

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