Evoking Harmony via Convolution

Sample retrieval tools can help composers find harmonically compatible material, but querying from a fixed reference sample becomes less informative as arrangements evolve and the harmonic context shifts with each musical decision. We present Reflector, an interactive audio workstation that tracks harmonic combinations as they accumulate on the composer's timeline and adapts retrieval as the arrangement develops. The system is organized around a fixed interval-class oracle: a hand-designed table of weights that scores how pitch-class content combines between sources. An encoder trained entirely on synthetic audio learns to approximate the oracle in a 128-dimensional embedding space, where dot products stand in for compatibility scores at interactive speed. As the composer arranges material on a multi-track timeline, a sweep-line analysis discovers co-sounding regions, computes oracle-weighted centroids, and retrieves against the composite harmonic identity of the session as it evolves. Session centroids projected into a navigable 3-D space reveal structural harmonic relations across the composer's body of work. This paper is a systems account: we give the design rationale for each architectural decision, characterize Reflector's behavior through intrinsic measurements on a working sample library, and describe the implementation. The characterization yields a central finding: the learned embedding preserves the kernel's pairwise judgments while covering the whole library, something the kernel cannot do when used directly as a retrieval rule, because the embedding's normalized geometry cannot express the degenerate solutions that direct scoring favors. The entire pipeline runs locally with no copyrighted training data. Reflector is free, and the training pipeline is open source.

One algorithmic composition may require a Csound score, engraved notation, real-time control, and a rehearsal click. Authored separately, their timelines drift. Temporal System is a Wolfram Language paclet that instead compiles one immutable store of typed entities on a rational beat timeline through backend-specific contracts. It emits Csound synthesis, beta MusicXML 4.0, OSC control, and click artifacts that remain synchronized because they share that store. Conversion to seconds, samples, or hertz occurs only at render time. Csound notes use stable named instruments in external .orc files; curves become k-rate signals declared against score p-fields. The click backend derives rehearsal audio from the same meter and tempo and reuses the Csound serializer. We describe the temporal, semantic, and rendering-contract layers, their practical trade-offs, and the limits of this proprietary authoring environment within an otherwise open-source ecosystem. The archived supplement exposes the reported outputs pending paclet release.

Stem retrieval, the task of matching missing stems to a given audio submix, is a key challenge currently limited by models that discard temporal information. We introduce PHALAR, a contrastive framework achieving a relative accuracy increase of up to $\approx 70\%$ over the state-of-the-art while requiring $<50\%$ of the parameters and a 7$\times$ training speedup. By utilizing a Learned Spectral Pooling layer and a complex-valued head, PHALAR enforces pitch-equivariant and phase-equivariant biases. PHALAR establishes new retrieval state-of-the-art across MoisesDB, Slakh, and ChocoChorales, correlating significantly higher with human coherence judgment than semantic baselines. Finally, zero-shot beat tracking and linear chord probing confirm that PHALAR captures robust musical structures beyond the retrieval task.