Raymond Deane: Quaternion for piano and orchestra.

A 'quaternion' is a set or group of four elements; in mathematics it is an operation transforming one vector into another, associated with the 19th century Irish mathematician William Hamilton. The four movements of my "Quaternion" (1988) explore different modes of encounter between soloist and small orchestra that emphasise the disparity between the two.

In the first movement, they alternate without overlapping. In the second, the piano disappears and is replaced only late in the day by celesta (the interplay of celesta and tuned percussion, and the prevalence of a hexatonic scale, gives this section a faintly 'oriental' aura). In the third, the orchestra disappears and the piano plays a kind of savage canon in which the two voices continually move away from and return to each other. In the last movement, soloist and orchestra play in rhythmic unison; they begin with piano in its lowest range and orchestra in its highest then move towards one another until at point of contact (which doesn't occur in the middle!) they sustain a concerto-like 6/4 chord of F major. Finally they drift apart again and disappear in opposite directions.

'Quaternion' was first performed at the 1993 'Accents' Festival in Dublin's Gallagher Gallery, with soloist Anthony Byrne and the RTÉ Concert Orchestra under Prionnsías O'Duinn.