**Hamiltonian Cycle: Saxophone**

for

alto-saxophone accompanied by wood-block

by

Robert Morris

**Program Notes**

*Hamiltonian Cycle: Saxophone*,
written in 1979 for the composer-saxophonist David Mott, is one of a projected series of works
whose compositional design is based on the properties of one of the five *Platonic
solids*. Platonic solids are those three-dimensional polyhedra that possess equal-sized and
equal-shaped faces. (The cube and pyramid are examples.) The work at hand is determined by the
dodecahedron, a twenty-edged, twelve-faced (each a pentagon) form.

In order to generate a musical form, I labeled the dodecahedron's faces with the basic kinds
of musical materials to be used in the composition. Then I traced a *Hamiltonian cycle*
(named after the 19th century Irish mathematician, William Hamilton) over the vertices
(corners) and edges of the solid. As each vertex and edge occurs once and only once in a
Hamiltonian cycle, the cycle determines a unique and efficient ordering of all the musical materials.
As I moved from vertex to vertex along the solid's edges, the materials assigned to faces
adjoining each vertex determined the character of a musical passage associated with that
vertex.

Thus, the piece proceeds by passing through a series of musical "states" each set-off by a
"crack" from the woodblock (here a Japanese *hyoshigi*, used in *Kabuki* performances) which
corresponds to the arrival at a new vertex.

The details of pitch organization within each section is governed by the mutual relationships among a family of related pitch sequences. The resulting compositional structures are articulated by the use of harmonics, sub-tones, micro-tones, timbre-trills and the like. As in other works I have written for saxophone(s), the lines, rhythms, and articulations are meant to suggest the flavor of jazz improvisation.

In this piece I regard the entire Hamiltonian process to be only partially cyclic; it serves to transform the
opening F natural into the final A-flat. This can be considered as a fading in from then out
to the atemporal space of *anahatanad*, or "unstruck sound" of Indian music philosophy.

David Mott has recorded *Hamilton Cycle: Saxophone* on Music Gallery
Editions, MGE-35.