Denis Lorrain

Construction 059

Streams of Khrónos

Algorithmic composition for MIDI piano

(2019, total duration: 14 mins)

Programme Note

   As in some of my preceding constructions, this piece stems from two ideas. Two types of musical material. Two concrete algorithms, which originate in examples demonstrated in the course of my teaching in Lyons and Karlsruhe.

   The first algorithm implements the scaling, compression or expansion, of a melodic motif, with an arbitrary number of fractal sub-levels — including zero, of course. The unique melodic motif used here is a *dodecaphonic series* based on two *all intervals hexachords* (containing all intervals smaller than a *tritone*). The selection of the two hexachords, among the twenty-four possible (algorithm of Jan Vandenheede), follows certain constraints, in particular that the resulting series features a *minor sixth* or *minor seventh* interval between its first and last notes. A minor sixth in the present case. This dodecaphonic motif, source for all the piece, is candidly exposed at the end of the first movement, orchestrated by its harmonics, in the manner of mixtures.

   Such peculiar dodecaphonic series are no novelty, and have formerly been used by composers. However, the scaling algorithm allows to put into light and exploit an innovative potentiality of such series: it happens that, without any additional fractal levels, certain notable expansions, of course rounded to the nearest semi-tones, result in other new dodecaphonic series. In this specific case, the usable factors, not expanding the series over the limits of the piano range, are 1.875, 2.125, 5 and 7. Greater factors possess the same property, but drive out of range: 9.875, 10.125, 11, etc. This remarkable feature of the expanded motif contributes very widely to the piece.

   Also generated by this first algorithm, and from the same dodecaphonic motif, numerous fractal melodies are noticeable, or fragments thereof, most often in counterpoint.

   The second source of material, based on a straightforward numerical interpolation algorithm, implements polyphonic rhythmical interpolations. Many instances of such processes are heard, on chords of which the articulation of constitutive notes evolves either from disorderly towards synchronous (from polyrhythmic towards homorhythmic), or inversely.

   The piece consists of two movements:

      A — 7'52"

      B — 6'05"

DLO

Karlsruhe — Quéven

April — June 2019