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(TNk+1). We derive the parameter count Nk(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 ∈ {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: https://github.com/mathacker23/ArtificialRosettaStone.
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BibTeX
@misc{raghavendran2026artificial,
title = {{Artificial Rosetta Stone: Constrained Maximum A Posteriori (MAP) Reconstruction of Symbolic Raga Sequences via Order-k Markov Models}},
author = {Saanvi Raghavendran and Abhishek Bhattacharjee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01064},
eprint = {2609.01064},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01064},
}
RIS
TY - UNPB
TI - Artificial Rosetta Stone: Constrained Maximum A Posteriori (MAP) Reconstruction of Symbolic Raga Sequences via Order-k Markov Models
AU - Saanvi Raghavendran
AU - Abhishek Bhattacharjee
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01064
UR - https://arxiv.org/abs/2609.01064
AB - 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 ∈ {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: https://github.com/mathacker23/ArtificialRosettaStone.
ER -