Zeng Ren

Zeng Ren

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Music as Flow: A Formal Representation of Hierarchical Processes in Music

Published in ISMIR 2023, 2023

Modeling the temporal unfolding of musical events and its interpretation in terms of hierarchical relations is a common theme in music theory, cognition, and composition. To faithfully encode such relations, we need an elegant way to represent both the semantics of prolongation, where a single event is elaborated into multiple events, and process, where the connection from one event to another is elaborated into multiple connections. In existing works, trees are used to capture the former and graphs for the latter. Each such model has the potential to either encode relations between events (eg, an event being a repetition of another), or relations between processes (eg, two consecutive steps making up a larger skip), but not both together explicitly. To model meaningful relations between musical events and processes and combine the semantic expressiveness of trees and graphs, we propose a structured representation using algebraic datatype (ADT) with dependent type. We demonstrate its applications towards encoding functional interpretations of harmonic progressions, and large scale organizations of key regions. This paper offers two contributions. First, we provide a novel unifying hierarchical framework for musical processes and events. Second, we provide a structured data type encoding such interpretations, which could facilitate computational approaches in music theory and generation.

Recommended citation: Ren, Z., Gerstner, W., & Rohrmeier, M. (2023). Music as Flow: A Formal Representation of Hierarchical Processes in Music. In ISMIR (pp. 627-633).
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Formal Modeling of Structural Repetition Using Tree Compression

Published in International Society for Music Information Retrieval Conference (ISMIR 2024) , San Francisco, California, USA and Online, November 10-14, 2024, 2024

Repetition is central to musical structure as it gives rise both to piece-wise and stylistic coherence. Identifying repetitions in music is computationally not trivial, especially when they are varied or deeply hidden within tree-like structures. Rather than focusing on repetitions of musical events, we propose to pursue repeated structural relations between events. More specifically, given a context-free grammar that describes a tonal structure, we aim to computationally identify such relational repetitions within the derivation tree of the grammar. To this end, we first introduce the Template, a grammar-generic structure for generating trees that contain structural repetitions. We then approach the discovery of structural repetitions as a search for optimally compressible Templates that describe a corpus of pieces in the form of production-rule-labeled trees. To make it tractable, we develop a heuristic, inspired by tree compression algorithms, to approximate the optimally compressible Templates of the corpus. After implementing the algorithm in Haskell, we apply it to a corpus of jazz harmony trees, where we assess its performance based on the compressibility of the resulting Templates and the music-theoretical relevance of the identified repetitions.

Recommended citation: Zeng Ren, Yannis Rammos, & Martin A. Rohrmeier. (2024). Formal Modeling of Structural Repetition Using Tree Compression. Proceedings of the 25th International Society for Music Information Retrieval Conference, 53–60. https://doi.org/10.5281/zenodo.14877282
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A Computational Cognitive Model for Processing Repetitions of Hierarchical Relations

Published in CogSci 2025, 2025

Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within sequential data, and develop a candidate computational model of how humans detect and understand such structural repeats. Based on a weighted deduction system, our model infers the minimal generative process of a given sequence in the form of a Template program, a formalism that enriches context-free grammar with repetition combinators. Such representation efficiently encodes the repetition of sub-computations in a recursive manner. As a proof of concept, we demonstrate our model’s capability on short sequences from music and action planning. The proposed model offers broader insights into the mental representations and cognitive mechanisms underlying human pattern recognition.

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Semester project with Lorenz Zauter

Supervision, Semester project by Lorenz Zauter in the MSc Applied Mathematics at ETH Zurich written at DCML, EPF Lausanne, Switzerland, 2024

A Music-Theoretically Informed Metric for Evaluating Generated Harmonic Progressions