Denis Lorrain

Construction 042

Due cose, mille cose

Algorithmic composition for MIDI piano

(2013, total duration: *ca.* 21 mins)

Programme Note

   This Construction essentially rests on two materials.

   The Prouhet-Thue-Morse sequence is a fractal structure, composed of two symbols — e.g. A and B—and created by starting from one of the two symbols and recursively applying two very simple production rules:

      1) A generates A B

      2) B generates B A

The result is a remarkable coincidence of utter simplicity and great complexity. I use this sequence by applying it to two pitches, or two durations, two loudnesses, etc.

   The Erdös-Szekeres theorem of monotonous subsequences: Out of a sequence of n²+1 different numbers, one can extract an increasing or decreasing subsequence of length n+1. This theorem proves that some order always resides in everything, even in randomness. I apply this paradox on pitches: within a sequence of n²+1 different random pitches, the n+1 constituting a monotonous subsequence are marked — e.g. by contrasting loudnesses and/or durations.

   A third material episodically appears in the piece: fast melismatic lines inspired by vegetal growth, simulated by a fractal process distorted by randomness.

   The Construction itself is freely elaborated with these materials: concrete musical elements are realised, interrelations are created, layouts are organised, forms are deployed on various levels...

DLO

Karlsruhe

2013