Does the Markov-Switching Multifractal describe real music? A fitting pipeline and a statistical Turing test

The Markov-Switching Multifractal (MSM) is a parsimonious volatility model — a product of k independent two-state switching multipliers — that the Fenophone instrument repurposes as a generative music engine, producing onset streams with measured DFA exponents alpha ~ 0.70-0.78 and multifractal widths ~ 0.05-0.13. We ask whether the MSM also describes real music. We build a likelihood-based fitting pipeline that treats the MSM as a 2^k-state hidden Markov model, recover its parameters from synthetic data within ~10% at 10^4 ticks, and pose the closing question as a statistical Turing test: resynthesise from the fitted parameters and ask whether a classifier can separate real from surrogate on held-out summary statistics. Fitting 1,264 MAESTRO piano performances and 198 Groove drum takes (beat-time grid, bar covariate), we find a clean dissociation: real piano onset streams are strongly persistent and multifractal (median DFA alpha = 0.717, width 0.118 — inside the instrument's own published band), the fitted cascade is genuinely non-flat (m_hi_eff = 1.62), and resynthesis retains most of the persistence (alpha = 0.691) — while drum-kit onset counts are near-white (alpha = 0.475) with the cascade structure appearing instead on the velocity channel (vel_m_hi ~ 1.36-1.52 in both corpora). The fitted model is still not sufficient at classifier resolution (accuracy 0.758 piano / 0.932 drums vs a ~0.50 permutation null), so MSM-Cox describes real musical intensity at second order without yet being a complete generator of it. A competitive arm (§5.1) places both the engine and the resynthesis on Zhang et al.'s (2025) audio-envelope battery against 381 Billboard hits and three neural generators, domain-matched: the asymmetry we predicted inverts — the engine holds spectrum-shape dispersion where the neural systems lose it (alpha_peak 1.25x the human IQR against their 0.70-0.86x — under the IQR ratio only; the comparison reverses under the std and span ratios in the same file, §5.1) while our arms fall outside the human band on the DFA alpha family that all three of them match. A subsequent envelope-domain IAAFT null (§5.1, E8) — the first placed under the width family in that domain — leaves 5 of 12 shipped packs' Delta-alpha indistinguishable from a linear surrogate. 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. Scope of the dispersion result (dated correction, 2026-08-30) The record’s one positive claim — that the engine out-disperses Suno, DiffRhythm and YuE on alpha_peak (1.248× the Billboard IQR) and spectrum_skew (0.858×) — holds under the IQR ratio only. The same committed CSV computes a standard-deviation ratio and a span ratio, and under both of those Suno out-disperses the engine on both descriptors (and YuE does under the std ratio). The IQR is defensible on heavy-tail grounds (Billboard’s alpha_peak has skew +3.14, excess kurtosis +12.5 and std/IQR 2.55), but that rationale was written after the statistic was seen to win, so the dispersion statistic is being pre-registered before the pending full run. The Jensen-Shannon excess ordering carries two further caveats — the floor is drawn under a different sampling design from the statistic, and the statistic is bounded, so additive excesses across floors differing by 3.4× are not commensurable; the scale-free contrast excess/(1−floor) preserves and widens the ordering (engine 0.515 > DiffRhythm 0.311 > YuE 0.206 > Suno 0.090). A null under the width family, in the envelope domain (E8) An envelope-domain IAAFT surrogate null finds 5 of 12 shipped packs’ Δα indistinguishable from a linear surrogate — the first null ever placed under the width claim in the domain the competitive descriptors live in. Two disambiguations are mandatory: it measures Δα on audio envelopes, not the two-point MFDFA width on event-time onset streams that the catalogue-wide IAAFT result is measured on; and IAAFT truncates rather than pads, so every series is scored at 16,384 samples (109.2 s) and no number from it is comparable to the human corpus band. Its per-descriptor table runs 168 dependent rank tests at a p floor of 0.05 with no multiplicity control, so counts near 1–3 of 12 are not separable from chance. The null-floor calibration was re-cut (v2, 2026-08-30) The crosswalk’s null calibration is deposited at v2. The v1 record generated its iid “Fano-matched” null streams at the fitted latent Cox rate where the generators take a marginal mean, so its floor curve was measured at 0.577× the corpus’s own operating point. v2 re-runs the calibration mean-parameterized, adds the paired per-piece decorrelation tests, the unclamped surviving fraction, the off-crosswalk-domain counts and a tempo-grid sensitivity arm. v1 is retained unedited, with a dated pointer, because sealed records in this program are append-only. Part of the Feno program. The source repository is private; the reproduction materials for this record are contained in the record itself.