Denis Lorrain

Construction 079

QVASI OPVS ESSET

Algorithmic composition for MIDI piano

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

Programme Note (long version)

   Musical composition is the result of nonverbal mental activity. Music can be commented on, described, analyzed. The emotions it evokes can potentially be verbalized. But music is nevertheless not essentially verbal. Hypothetically, this could even be true of musical ideas that can be likened to rhetorical schemes—stylistic forms such as anaphora, antithesis, etc. Perhaps would these stylistic figures themselves emanate from musical archetypes: they would only be verbal by application, a posteriori.

   A musical idea is clear, immediate, and instantly operational in the mind of who grasps it on the fly. All artistic, mathematical, or scientific intuitions are of this nature. It is the laborious realization of the idea, through the slow progression of human consciousness and hand, which lets intuition slip into the verbal realm.

   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 hexachords containing all intervals from one to five semitones (*all-interval hexachords* algorithm by Jan Vandenheede). A pair of hexachords forms a dodecaphonic series, which is itself varied and multiplied by means of generalized axial symmetry operations in a circular representation of the chromatic space. Beyond their constituent notes, this algorithm attempts to optimize the *position* of the chords—that is, the distribution of their notes in the instrument's register.

- Appoggiaturas of varying lengths which, in the third movement, 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 a short sound emission (e.g. plucked or struck strings), trills are traditionally used, as tremolo, 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 (e.g. A and B) linked endlessly, starting from one of them, by recursively applying two simple production rules:

1) A generates A B

2) B generates B A

An algorithm based on this sequence composes the layers of percussive dichords of low-pitched minor seconds that predominate in the first two movements.

- Stochastic distributions affect certain characteristics. For example, the composition of accents in the low percussive dichord layers mentioned above follows the first law of Laplace. The loudness (MIDI velocities) of all notes, as well as all time intervals and durations, undergo slight variations governed by the normal distribution—also known as Gaussian.

- Markov chains are a process used to compose sequences of elements. The control exercised is statistical, but can be almost deterministic, depending on the number of preceding elements taken into account in the sequencing. Such processes are one of the building blocks of generative artificial intelligence. A chain that takes into account *n* preceding elements is said to be of *order n*. In a rather non-deterministic way, Markov chains of order 2 compose the rhythms of the low percussive dichords. Even less deterministic, Markov chains of order 1 control the number of notes constituting the successive chords of 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