FRACTAL

Fractals are geometric figures that show the same structure to whatever level they are examined, so that a fragment of theirs is, in a sense, equal to the whole one. For example, the trunk of a tree is divided into various branches, these in twigs, and so on. If you proceed to infinity a branch would be, apart from the proportions, identical to the whole tree. And it is what we really perceive, despite the process of bifurcation end, on condition that we look from a distance, skiping details. Equally the stars form galaxies, the galaxies clusters of galaxies, in them turns linked in superclusters. The structure of the universe appears similar if examined on different scales.
In this musical piece the last two movements are nothing else that the first two “in the mirror” (from the last note to the first one), in every movement the second half is specular compared to the previous one, and so on until the symmetry of the single series . Dodecaphonic technique has been freely used, since a group of three notes (and not an only one, as would be permitted) is repeated twice; the game of symmetries sees to it that this license becomes a rule.
Some modern physical theories (for example, the one on the unification of the fundamental forces), foresee, under certain conditions, a symmetry breaking: effect gotten in the composition through the chiaroscuros, that, differently from pitchs and durations of the notes, are extraneous to the structure of the fractal and don’t follow particular rules, except those of the violin (or, for specularity, of the flute) in third and fourth movement. This last are assigned to every note through a predetermined, but casual, succession (pppp-ppp-mf-ppp-pp-mf-ppp-pppp-mp-ppp-pp-f-f-ff-ffff-ff-f-pppp-mf-f-ff-ff-ppp-mf-fff-ppp-ff-f-p-mf-f-pppp-mp-ffff-ppp-ffff-f-p-pppp-ppp-pp-ff-mf-p-fff-p-ffff-ppp-f-ppp-ffff-ppp-pppp-p-mf-ppp-mp-ppp-mp-ff-pppp-p-f-pp-mp-fff-pppp-ff-ppp-p-mp-mf-ff-ppp-mp-ppp-pppp-p-fff-ff-p-mf-pp-mp-pp-pp-mp-mp-ff-mp): exactly the opposite of a fractal, that, having to respect a complex game of symmetries, is extremely deterministic and therefore predictable.

DOWNLOAD

(The score is available in .MUS for Finale 2003 or .pdf for Acrobat Reader format)

SCORE - movement I (.MUS - 27 K) SCORE - movement II (.MUS - 32 K) SCORE - movement III (.MUS - 32 K) SCORE - movement IV (.MUS - 28 K)

complete SCORE (.pdf - 156 K)

MIDI - movement I (3 K) MIDI - movement II (3 K) MIDI - movement III (3 K) MIDI - movement IV (3 K)

MP3

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