Symmetrical Structures in Xenakis’s <i>Okho</i> : At the Intersection of Mathematics and Literature

While there are abundant discussions of Xenakis's works through the lens of mathematics, formulated from the composer's own treatise Formalized Music: Thoughts and Mathematics in Composition (1992), scholars have rarely addressed how his interest in Greek literature manifests in his compositions beyond programmatic titles.Xenakis reveals his fascination with classical antiquity in numerous publications, yet critics have not explored how his literary interest intersects with his compositions in structural terms.An examination of classical Greco-Roman literature reveals a frequently used rhetorical structure prevalent among classical authors-chiasmus.This structure emphasizes the centermost clause surrounded by parallel clauses stated in reverse order.This article analyzes Xenakis's Okho (1989) for three djembes through the lens of symmetrical structures, unveiling a cohesive narrative centered on the contrast of stability and chaos achieved through construction and deconstruction of palindromes and chiasmi.These processes evolve over time; smaller chiasmi initially embedded within a single bar expand into larger multi-measure structures constructed through Fibonacci sequences.Such structures are systematically diminished and dismantled as the piece approaches its conclusion.By examining the intersection of intervallic structures with symmetrical structures, the once elusive connection between Xenakis's mathematical processes and Greek literature comes to light.Xenakis bridges mathematics and literature, harmonizing modernity with classical antiquity by integrating intervallic structures into his chiastic structures.