From local kernels to global form: modeling the emergence of musical content

Abstract

Markov models are established tools for symbolic music, including non-homogeneous formulations. The narrower contribution examined here is an observation-driven estimation mechanism: overlapping sliding windows derive a trajectory of local transition kernels from one symbolic sequence rather than from an exogenous formal partition. We test this mechanism on 273 logical note events from Debussy's Syrinx (1913), using the often-proposed A-B-A'reading as a reference rather than ground truth. We apply the same validation to absolute-pitch and notated-duration kernels. At $L=6$, both reference boundaries attain the Jensen--Shannon maximum in both dimensions; the duration plateau is substantially narrower (64 of 267 comparisons) than the pitch plateau (210 of 267). Because the theoretical maximum for consecutive sliding-window comparisons is set by window geometry and equals $1/\sqrt{L-1}$ for maximal turnover of the entering/leaving transition, the pitch value at $L=6$ and its broad plateau are not, by themselves, strong evidence. Their cross-dimensional alignment is consistent with boundary sensitivity, while the broad plateaus preclude treating either curve alone as a unique automatic segmenter. Five-hundred-draw re-synthesis experiments quantify departure from the source in both dimensions and expose an exact-copy degeneracy at $L=2$.