Work

Programme Note

These pieces utilise Abelian form, a concept I developed whereby the proportions of a large form were reflected in its constituent parts. A large form, for instance, has sections A, B, C, D, and E, with respective durations t1, t2, t3, t4, t5. A, B, C, D, E also have subsections whose proportions are also t1, t2, t3, t4, t5. We can designate the subsections of A as Aa, Ab, Ac, Ad and Ae, and similarly for the others. The whole process can be shown in the following table: Aa Ab Ac Ad Ae Ba Bb Bc Bd Be Ca Cb Cc Cd Ce Da Db Dc Dd De Ea Eb Ec Ed Ee This looks like a mathematical Abelian Group – hence the name. The durations of subsections symmetrically placed about the leading diagonal (Aa, Bb, Cc, Dd and Ee) are also equal because duration of Ab = duration of Ba, duration of Ac = duration of Ca, etc. This fact led me to use the same material in matching subsections, often mirrored. In PIANO POEMS 1, 4, 8 and 9 I use this form; although the proportions are all equal, the Abelian shape determines the order. 1 Abelian form (3 X 3 matrix) with overlaps 2 a mirror piece 3 a chance piece: the contents of the four different chords and their order and the interruptions by the fist rolls were all determined by chance 4 Abelian form (4 X 4 matrix): all sections are four bars long. Subsection Ab is the mirror of subsection Bb, etc 5 Free form 6 Bogen form: A, B, C, C’, B’, A’, where A’ is the augmentation of A, etc 7 Free variations on a short melody 8 Abelian form (3 X 3 matrix): all repetitions are shortened 9 Abelian form (4 X 4 matrix) using fragments from sections 1 to 8

Difficulty:

Advanced

Dedication:

To Douglas Lilburn on his 80th birthday, November 2nd 1994.

• Douglas Lilburn