schlick’s approximation (2010)
For clarinet, violin and piano. Dedicated to Les Pratt. Commissioned by Manchester Pride to celebrate the centenary of the birth of Samuel Barber. First performance 27th August 2010 – Manchester.
schlick’s approximation is performed by Chroma (Stuart King, clarinet; Marcus Barcham-Stevens, violin; Martin Cousin, piano) recorded at the Cosmo Rodewald Concert Hall, Manchester on the 27th August 2010.
schlick’s approximation was commissioned by Manchester Pride in 2010 to celebrate the centenary of the birth of American composer Samuel Barber (1910 – 1981).
The title for the work is drawn from the physics of refraction, in this case, refraction and reflection of light from metal surfaces (schlick’s approximation). *Please see technical note below.
I felt that the physics of refraction best reflected some of the compositional processes and considerations that went into creating this music. My inspiration and starting point was the beautiful and lyrical work by Barber called Canzone, for flute and piano. From this piece I took the second phrase notated for flute (see extract below) and refracted (distorted) and harmonised it to the point where it was still recognisable but had become something quite different. The refracted material is reproduced for reference at the start of the score. It is not intended for performance as part of schlick’s approximation but can be performed purely for illustrative purposes. For my purpose, it serves as an unheard quasi introduction that leads into the piece. A falling motif taken from this silent introduction is further refracted. Performed primarily by the violin, it appears obsessively in nearly every other bar throughout the piece. Towards the end of the work, both clarinet and violin are singularly obsessed by it. This refracted motif represents the ‘ghost’ of the Canzone.
There is also reference to a work of mine: shadow and the moon. The refracted material from Canzone permeates the entire work but much of the fragmentary melodic material is extrapolated from shadow and the moon. Together with new material for the piano, the combined elements create a trio that I hope reflects much of the lyricism found in Barber’s Canzone whilst reflecting my own compositional aesthetics and language.
*In 3D computer graphics, Schlick’s approximation is a formula for approximating the BRDF of metallic surfaces. It was proposed by Christophe Schlick to approximate the contributions of Fresnel terms in the specular reflection of light from conducting surfaces. According to Schlick’s model, the specular reflection coefficient R is given by where θ is the incident angle (which equals the reflected angle for specular reflection) and R0 is the reflectance at normal incidence (i.e. the value of the Fresnel term when θ = 0).
The bidirectional reflectance distribution function (BRDF; ) is a four-dimensional function that defines how light is reflected at an opaque surface. The function takes an incoming light direction and outgoing direction both defined with respect to the surface normal and returns the ratio of reflected radiance exiting along to the irradiance incident on the surface from direction . Note that each direction is itself parameterized by azimuth angle φ and zenith angle θ, therefore the BRDF as a whole is 4-dimensional. The BRDF has units sr-1, with steradians (sr) being a unit of solid angle.
Music from Schlick’s Approximation is used in this video: ‘Barbara Hepworth Considers the Visitors at Trewyn’ – Poetry Film, words by Rosie Jackson, video by Gordon McKerrow