Symmetrical Structures in Xenakis’s <i>Okho</i> : At the Intersection of Mathematics and Literature
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".