Organizations: Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy
Abstract
Heterogeneous graph built on notes, lyric syllables, and accompaniment events is a natural representation of symbolic music score, providing a substrate for both philological analysis and computational tasks. Music features are therefore well-captured by graph geometry and its properties. This representation has proved effective for analytical tasks as cadence detection, voice separation, and stylistic classification. In the present work, the reduction of harmonic complexity of a music score on graph, by preserving task-relevant information, relation between notes, and graph structure is investigated. A compression scheme for the piano subgraph of vocal-pianistic scores, built on binary wedge partitioning trees, is proposed. The wedges are generated through a fully adaptive greedy algorithm that recursively minimizes the L2-error within a six-dimensional Tonnetz embedding of musical notes. The partitioning process employs a splitting criterion based on harmonic distance, resulting in regions that accurately reflect the intrinsic harmonic relationships among notes. The reconstructed music scores obtained through piecewise-constant functions and the mean values of the notes inside each wedge are used as a new simplified scores human-readable and playable. Some experiments on a corpus of symbolic music scores of three different composers are performed to assess the proposed approach.
High-polyphony symbolic music is increasingly used in generation, analysis, and arrangement, yet many downstream tasks require bounded representations with fixed tracks or slots. Converting richly orchestrated scores into compact forms is therefore necessary, but existing approaches relying on heuristic simplification or generic representation-space reduction often fail to preserve structural roles, orchestration compatibility, and playability under strict budgets. To address the issue, this study reformulates the compression problem as a fixed-budget structured routing problem and proposes Unbalanced Optimal Transport for Information Routing (UOT-IR), a training-free framework based on constrained unbalanced optimal transport. UOT-IR combines an orchestration prior, adaptive marginal relaxation, temporal decoding, and playability-aware projection to produce compact and musically coherent bounded representations. This work further studies two practical settings under the same slot budget: template standardization, which maps each input to a predefined bounded template, and adaptive preservation, which retains representative content without assuming an external template. Experiments on the SymphonyNet corpus show that UOT-IR delivers strong overall performance across both settings, including the best Note-F1 in adaptive preservation (0.9120), together with the lowest structural cost (14.7165) and bad structural confusion rate (0.3406) in template standardization. This work establishes a principled paradigm for fixed-budget symbolic music compression, offering a practical path toward compact, structured, and musically coherent symbolic representations.
We present an audio-to-analysis pipeline that produces composer-level information-theoretic profiles : reflecting compositional vocabulary as it emerges from aggregated performances : from raw recordings, built on a transcription layer whose accuracy we certify on a standard benchmark (F1 = 0.9791 on the MAESTRO v3.0.0 test set). Applied to 1,238 pieces and 15 MAESTRO composers with at least ten attributed pieces, spanning the Baroque through the early twentieth century, the pipeline derives empirical distributions over harmonic scale degrees and analyzes them through Shannon entropy, asymmetric Kullback-Leibler divergence, and Zipfian rank-frequency modeling. The resulting profiles (i) order composers along an interpretable axis of harmonic predictability, with a narrow entropy range (3.33-3.86 bits) that reveals the marginal-level similarity of tonal vocabularies; (ii) recover known stylistic lineages (Haydn-Beethoven, Liszt-Rachmaninoff, Schubert-Schumann) through the smallest KL divergences in the corpus, with Mendelssohn emerging as a stable outlier within this corpus; and (iii) separate contemporary neoclassical artists (Richter, Frahm, Glass, Arnalds, Jóhannsson) from historical composers on the quality of Zipfian fit to the transition distribution, with mean R2=0.78 for neoclassical versus 0.46 for historical (N ≥ 10 pieces each). This gap is larger than the spread within either group and is consistent with a minimalist compositional tendency: a compact transition vocabulary used with sharper frequency-rank regularity than historical composers. All estimates are reported with Laplace-smoothed bootstrap 95% confidence intervals.
We study the assignment of local tonalities to chord sequences, a task useful for harmonic analysis, composition, and jazz-oriented improvisation. Standard dynamic-programming approaches minimize modulations but can introduce unnecessarily many tonal centers. We compare this transition-only objective with pure minimum-vocabulary analysis and with tonal parsimony, which minimizes lexicographically the number of modulations and then the number of distinct tonalities. Although this joint objective is combinatorially hard in general, we give exact algorithms exploiting the fixed 24-tonality major/minor universe. On 31,032 LMD Chords sequences, tonal parsimony preserves the transition optimum while reducing tonal vocabulary in 55.8% of cases. With weighted jazz-substitution closure, it lowers mean tonalities from 3.802 to 3.206 and modulations from 16.728 to 12.141. On 1,555 annotated jazz standards, it improves compatible chord-scale agreement to 95.6%, supporting tractable professional-scale harmonic analysis.