Denis Lorrain

Construction 079

QVASI OPVS ESSET

Algorithmic composition for MIDI piano

(2025, total duration: *ca.* 10')

Programme Note (short version)

   This piece consists of three linked movements, each lasting approximately two to four minutes. Several algorithms and techniques contribute to its composition.

- Harmonic sequences based on a pair of hexachords containing all intervals from one to five semitones (*all-interval hexachords* algorithm by Jan Vandenheede). I have previously used and described this algorithm in earlier *Constructions*.

- Appoggiaturas that launch trills that prolong them. Their composition is based on the same pair of hexachords and the same process as the harmonic sequences.

- On instruments with short sound emission (e.g. plucked or struck strings), trills are traditionally used to artificially prolong their sonority. In addition to this acoustic purpose, trills also serve an ornamental function.

- The *Prouhet-Thue-Morse* sequence is a fractal structure composed of two symbols linked endlessly, starting from one of them, by recursively applying two simple production rules. An algorithm based on this sequence composes the layers of percussive low-pitched minor second dichords that predominate in the first two movements.

- Stochastic distributions affect certain characteristics. For example, the composition of the accents in the low percussive dichord layers follows the first law of Laplace. The intensities of all notes, as well as all time intervals and durations, undergo slight variations governed by the normal law.

- Markov chains are a process used to generate sequences of elements. Second-order Markov chains compose the rhythms of the low-pitched percussive dichords. First-order Markov chains control the number of notes constituting the successive chords of the harmonic sequences.

   The latin title *QVASI OPVS ESSET* means "As If Need Were": what is this compulsion that drives us... *quasi opus esset*?

DLO

Cologne

September 2025