Commissioned by: Gerard Bouwhuis & Heleen Hulst, with financial support from the Netherlands Fund for the Creation of Music
First Performance: Gerard Bouwhuis & Heleen Hulst, February 21 2006, De Link, Tilburg
Instrumentation: violin and piano
Duration: 30’

Score samples

Info/Program note:
Written in 2004, for the duo Gerard Bouwhuis and Heleen Hulst, this 30-minute duo for violin and piano is the last in a series of pieces written in 2003/2004 – along with the works 9 through 99, the Formalist Dance and 6 Parts for 7 Players - in which automatic mathematical procedures determine all facets of the composition.

In this way, Chromatic Fundamentals – consisting of three 10-minute movements - deals entirely with square root proportions and other forms of exponential growth. The first Movement is based on a descending 3-note chromatic figure centering on the root of 3 (3, 9, 27, 81 etc) which grows exponentially as the movement itself also proceeds through three different sections. With the exception of the final part of this movement, which expands and then contracts via multiplications of 3 (i.e. + 6, + 18, + 21 etc), the material is entirely chromatic, with each new entry dropping a minor second at a time, parallel to the initial figure, and entering continually in different registers. The second Movement deals with squares of 2 (2², 2³, 2⁴ & 2⁵) and expands in four sections, while maintaining the same principles as the first movement: whatever happens in the initial bars returns exponentially expanded in the next section, and so on. The material is a combination of diatonic and chromatic intervals which are mirrored in both instruments and accompanied by a little perpetuum mobile in the piano. The last Movement finally drops all linear motion in favor of a wedge-figure consisting of 9 repeating eighth notes in a 5/4 bar. The initial figure is itself subjected to 3 minor pattern alterations and basically expands according to multiplications of 9. The proportions however are jostled in their sequence and are also subject to internal change within the sections themselves.

In its clear three-movement form, Chromatic Fundamentals is probably one of my most conventionally ‘classical’ – and excessively difficult to play.