nlm: Real-Time Non-linear Modal Synthesis in Max

Modal synthesis is a widely-used technique for simulation of musical instrument dynamics. In the linear case, a modal decomposition leads to an uncoupled system of damped and forced harmonic oscillators which can be efficiently solved by standard time-stepping methods. However, extensions to nonlinear problems are challenging due to the presence of products of modal expansions in the governing equations. In the case of the Föppl-von Kármán plate, the nonlinear coupling between the modes is described by a fourth-order tensor and is prohibitively expensive to evaluate in the modal domain. In this work, we propose a pseudospectral method in which the products are evaluated on a grid in the spatial domain while spatial derivatives are computed exactly in the modal domain. Discrete sine and cosine transforms between the modal and spatial domains are used to impose simply supported boundary conditions for the plate. Finally, we prove non-negativity of the nonlinear potential energy of the system and employ a scalar auxiliary variable technique for explicit and stable time integration in the modal domain. As a result, we reduce the computational cost of modal synthesis while preserving its advantages like a precise control over the simulated frequency range. Sound examples are presented.

PLAUD (Performative Latents and Unsupervised DDSP) is a neural synthesizer and Max for Live instrument for live electronic music, built on NoiseBandNet and trained on small personal sound corpora. We present its architecture, combining a variational DDSP synthesis model, latent smoothing, multi-scale spectral and adversarial losses, and an optional transformer prior, alongside a set of bending operations that intervene directly in the synthesis chain: component limiting, waveshaping, and prior feedback. The Max for Live interface exposes control generation, trajectory sampling, and modulation as primary modes of interaction. Throughout, we thread an affordance analysis arguing that the system's performative character follows from architectural decisions rather than being designed on top of them. The paper contributes both a technical account of the system and a situated affordance analysis of its role in live electronic music performance.

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.