Artificial Rosetta Stone: Constrained Maximum A Posteriori (MAP) Reconstruction of Symbolic Raga Sequences via Order-k Markov Models

Abstract:Reconstructing a damaged musical fragment is an inverse problem: the observed sequence contains partial information, while a raga encodes constraints limiting allowable completions. This paper formalizes a mathematical framework for this, proposing the Artificial Rosetta Stone (ARS). We separate three claims often conflated: a symbolic sequence can be reconstructed probabilistically; a sequence can be consistent with an explicit grammar; and a historical performance can be authenticated. We only support the first two. We model a raga via a finite alphabet and constraint system, using an order-k Markov model for melodic probabilities. A symmetric Dirichlet prior yields a tractable posterior. We pose missing-note reconstruction as a constrained MAP problem. For fixed-length sequences and finite-order constraints, optimization admits an exact dynamic-programming solution with worst-case time complexity $O(TN^{k+1})$. We derive the parameter count $N^k(N - 1)$, prove a concentration bound under explicit mixing assumptions, and analyze estimation error propagation. A reproducible synthetic experiment uses six raga-inspired alphabets, orders $k \in \{1, 2, 3\}$, and masking rates up to 50%. This is a proof of concept, not historical reconstruction. A real-audio feasibility pilot evaluates 30 usable sequences from 42 Yaman clips via automated pitch extraction, segmentation, and quantization. Lacking documented provenance and relying on automated transcription, this is not expert-validated archival reconstruction. Claims are tied to stated conditions, not universal properties of Hindustani music. Code: this https URL.

Sound (cs.SD); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2609.01064 [cs.SD]

(or arXiv:2609.01064v1 [cs.SD] for this version)

https://doi.org/10.48550/arXiv.2609.01064 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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