The Markov-Switching Multifractal as a Generative Model of Musical Intensity: An Instrument, Measurements, and a Research Programme

Musical intensity — the joint trajectory of onset density, dynamics, and harmonic tension — shares a distinctive phenomenology with financial volatility: bursts and lulls, clustered at every time scale, with no single characteristic period. We propose taking this correspondence literally. We adopt the Markov-Switching Multifractal (MSM) of Calvet and Fisher — a stationary, causal Markov construction of multifractal volatility — not as a metaphor or a texture source but as the generative core of a musical instrument: we discard the return process entirely and sonify the volatility state itself, read through a fixed band map into four control lanes (dynamics, density, timbre energy, harmonic tension) that drive an authored musical scaffold. We describe a complete reference implementation (the Fenophone), whose event layer is integer/fixed-point and bit-identical across platforms, whose player controls are exactly the MSM parameters (m_hi, f_slow, S, k), and whose "conducting" gesture is clamping individual latent states. We report measured properties of the emitted note streams: with the authored bar template removed as a seasonal trend, per-scaffold median DFA exponents α(onset) of 0.695–0.770 and α(velocity) of 0.676–0.702, every seed exceeding its shuffled-surrogate null; MFDFA widths h(−2) − h(2) of 0.054–0.126, exceeding matched IAAFT surrogate nulls on every seed for three of the four measured packs (the fourth, the least intermittent by design, is consistent with linear long memory at this length and reported as such); and a monotone dose–response of α on the time-scale-span control, with a median gap ≥ 0.09 between span extremes. All measurements are CI-gated, surrogate-compared, estimator-anchored on known-Hurst ground truth, and reproducible from pinned seeds. We then lay out a six-experiment research programme — surrogate discrimination, a preference surface over the (α, width) plane, tension-lane validation, boundary perception against ground-truth latents, counterfactual intervention pairs, and corpus inversion — each with predictions and explicit falsification conditions. The corpus half of the inversion experiment now has first results (2026-07-12; companion analysis): 1,260 MAESTRO piano performances measure median α(onset) 0.717 and width 0.118 under the same protocol — inside the instrument's published band — with fitted parameters identifying composer above chance, while drum-kit onset counts are near-white with the cascade structure appearing on the velocity channel instead. The five perceptual experiments (E1–E5) remain unrun, and the corpus inversion (E6) is complete only on its statistical half; this paper is a preregistration-grade programme, not a report of finished perceptual results. --- Data provenance and attribution This record uses the MAESTRO v3.0.0 solo-piano corpus (Hawthorne, Stasyuk, Roberts, Simon, Huang, Dieleman, Elsen, Engel and Eck, “Enabling Factorized Piano Music Modeling and Generation with the MAESTRO Dataset”, ICLR 2019; hosted by Google Magenta) and the Groove MIDI Dataset v1.0.0 (Gillick, Roberts, Engel, Eck and Bamman, “Learning to Groove with Inverse Sequence Transformations”, ICML 2019). The raw corpora are not redistributed here. They are fetched at run time from their public sources by pinned download scripts that verify each archive against a recorded sha256 (MAESTRO: maestro-v3.0.0-midi.zip, sha256 70470ee253295c8d2c71e6d9d4a815189e35c89624b76d22fce5a019d5dde12c). Only derived quantities — fitted per-piece parameters, DFA/MFDFA statistics, model-selection verdicts, and the figures built from them — are deposited. MAESTRO is licensed CC BY-NC-SA 4.0 (non-commercial, share-alike), which controls over this record’s CC BY 4.0 grant wherever the two conflict, for any MAESTRO-derived material. The Groove MIDI Dataset is CC BY 4.0, so Groove-derived outputs carry no additional restriction. Part of the Feno program. The source repository is private; the reproduction materials for this record are contained in the record itself. Version 2 (2026-09-01): reference-list publication-status notes corrected (the program's reserved DOIs were published 2026-08-31); content otherwise unchanged. Version 3 (2026-09-15). Carries the audited readings of two external results this paper cites: Levitin, Chordia & Menon (2012) on 1/f rhythm spectra (Feno-program audit card 07, Fenocosm record v59, 10.5281/zenodo.22759705) and Roeske, Kelty-Stephen & Wallot (2018) on multifractal structure in songbird rhythm (audit card 08, Fenocosm record v60, 10.5281/zenodo.22759707). A dated correction note near the head of the paper states what each reconstruction reproduces and what it does not; no result of this paper's own measurements changes. The paper now also carries its concept DOI in its header.