Inverting Neo-Riemannian Theory into a Constructive Framework for Harmonic Planning

Neo-Riemannian theory is traditionally used to describe transformational relations within completed harmonic progressions. We invert this use: the simply transitive action of the PLR group on the twenty-four major and minor triads provides the algebraic setting, and harmonic planning is formulated as constrained path construction on the corresponding \(P\)-\(L\)-\(R\) graph. To construct an optimal path limited by conditions, such as a tonic, section lengths, required section-end triads, and a prescribed profile of sectional mean tonic-relative PLR distances, we propose the NRT-DP planner, a dynamic program that optimises each complete section conditional on its incoming context and plans a section of length \(L\) in \(O(L^{2})\) time. Across \(576\) tonic-labelled instances, the planner satisfies all mandatory constraints, realises the prescribed sectional profiles with low error, and exhibits the same large-scale rise and fall when tonal tension is measured with the task-external Spiral Array model. The framework thereby converts neo-Riemannian analysis into a medium for harmonic design, and the resulting harmonic backbone can directly be used to generate downstream melody, accompaniment, texture, or orchestration, providing a novel insight for music generation.