Hierarchical representations provide powerful and principled approaches for analyzing many musical genres. Such representations have been broadly studied in music theory, for instance via Schenkerian analysis (SchA). Hierarchical music analyses, however, are highly cost-intensive; the analysis of a single piece of music requires a great deal of time and effort from trained experts. The representation of hierarchical analyses in a computer-readable format is also a further challenge. Given recent developments in hierarchical deep learning and increasing quantities of computer-readable data, there is great promise in extending such work for an automatic hierarchical representation framework. This paper thus introduces a novel approach, AutoSchA, which extends recent developments in graph neural networks (GNNs) for hierarchical music analysis. AutoSchA features three key contributions: 1) a new graph learning framework for hierarchical music representation, 2) a new graph pooling mechanism based on node isolation that directly optimizes learned pooling assignments, and 3) a state-of-the-art architecture that integrates such developments for automatic hierarchical music analysis. We show, in a suite of experiments, that AutoSchA performs comparably to human experts when analyzing Baroque fugue subjects.

Music composition and analysis is an inherently creative task, involving a combination of heart and mind. However, the vast majority of algorithmic music models completely ignore the "heart" component of music, resulting in output that often lacks the rich emotional direction found in human-composed music. Models that try to incorporate musical sentiment rely on a "valence-arousal" model, which insufficiently characterizes emotion in two dimensions. Furthermore, existing methods typically adopt a black-box, music agnostic approach, treating music-theoretical and sentimental understanding as a by-product that can be inferred given sufficient data. In this study, we introduce two major novel elements: a nuanced mixture-based representation for musical sentiment, including a web tool to gather data, as well as a sentiment- and theory-driven harmonization model, SentHYMNent. SentHYMNent employs a novel Hidden Markov Model based on both key and chord transitions, as well as sentiment mixtures, to provide a probabilistic framework for learning key modulations and chordal progressions from a given melodic line and sentiment. Furthermore, our approach leverages compositional principles, resulting in a simpler model that significantly reduces computational burden and enhances interpretability compared to current state-of-the-art algorithmic harmonization methods. Importantly, as shown in our experiments, these improvements do not come at the expense of harmonization quality. We also provide a web app where users can upload their own melodies for SentHYMNent to harmonize.

The fast-growing demand for algorithmic music generation is found throughout entertainment, art, education, etc. Unfortunately, most recent models are practically impossible to interpret or musically fine-tune, as they use deep neural networks with thousands of parameters. We introduce an interpretable, flexible, and interactive model, SchenkComposer, for melody generation that empowers users to be creative in all aspects of the music generation pipeline and allows them to learn from the process. We divide the task of melody generation into steps based on the process that a human composer using music-theoretical domain knowledge might use. First, the model determines phrase structure based on form analysis and identifies an appropriate number of measures. Using concepts from Schenkerian analysis, the model then finds a fitting harmonic rhythm, middleground harmonic progression, foreground rhythm, and melody in a hierarchical, scaffolded approach using a probabilistic context-free grammar based on musical contours. By incorporating theories of musical form and harmonic structure, our model produces music with long-term structural coherence. In extensive human experiments, we find that music generated with our approach successfully passes a Turing test in human experiments while current state-of-the-art approaches fail, and we further demonstrate superior performance and preference for our melodies compared to existing melody generation methods. Additionally, we developed and deployed a public website for SchenkComposer, and conducted preliminary user surveys. Through analysis, we show the strong viability and enjoyability of SchenkComposer.