Vol. 10 - 2026

MusMat • Brazilian Journal of Music and Mathematics

Generation of Chord Progressions using Guided Markov Chains

Steven Berger

Abstract: In this paper, we study the generation of tonal chord progressions in the style of J.S. Bach chorales. While much of the previous research on stochastic music generation has employed Hidden Markov Models or Neural Networks, we introduce guided Markov chains (GMC) as a method for generating tonal chord progressions. The GMC model constructs an initial base chord progression by restricting the state space of allowable chords at each time step based on composer-specified information about the harmonic function of the next chord. Unlike standard Markov Chains, GMCs give composers local control over the structure and sound of the progression without requiring explicit specification of individual chords. Although knowledge of harmonic functions is well established in music theory, most existing stochastic models must learn this structure from data. We demonstrate that GMC models increase the likelihood of observing chord sequences consistent with the Baroque style relative to a standard Markov Chain and also provide comparisons of cumulative log-likelihoods between GMC and hidden Markov models. Additionally, we prove the Typical Set Cardinality Reduction Theorem and introduce two confidence intervals: a Monte Carlo confidence interval to quantify the difference in standard Markov chain and guided Markov chain entropy for finite-length chord sequences, and a permutation-based confidence interval to assess the statistical significance of a specific harmonic guide ordering. We also outline an extension for incorporating chord inversions.

Keywords: Markov chains. Entropy. Hidden Markov models. Typical sets.

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