From Latent Cascade to Note Stream: How Scaling Exponents Survive Musical Quantization

Generative systems built on multifractal processes make a quiet assumption: that the scaling structure of the latent process survives the discrete, nonlinear observation path that turns it into events. In the Fenophone — an instrument whose latent core is a Markov-switching multifractal (MSM) — that path is explicit and deterministic: band products are read into [0,1] lanes, mixed through a routing matrix into per-voice drives, thresholded into onsets, quantized onto a metric grid, and gated by harmony. We measure, across a control grid and seed panel, the detrended-fluctuation (DFA-1) exponents of the four latent lanes alongside those of the emitted onset and velocity streams, and the MFDFA width of both. We characterize the transformation empirically — routing decides which latent scaling the note stream inherits (only the routed mid-band lane's α transports; fixed-effects coefficient ≈ +0.32 against ≈ 0 for the unrouted fast band), while the channel's contrast decides how much of it registers (emitted α climbs ≈ 0.51 → 0.83 across the Intensity axis with every latent lane α constant, including exact low-contrast dead zones where adjacent dial positions emit bit-identical streams) — and explain the contrast axis with a level-crossing transfer model: the channel's quantizer is a monotone integer staircase, hence Hermite rank 1, so the latent exponent is preserved asymptotically at every contrast, and what contrast actually sets is the amplitude of the exponent-carrying component against the quantization-noise floor — the crossover scale a fixed measurement ladder reads as an effective α. A no-free-parameter mixture predictor built on that decomposition reproduces the measured climb cell by cell (median |Δα| = 0.009 on the model's theory rung). Three further maps complete the channel's characterization: the per-cell surrogate comparison shows the mid-Intensity width dip is a collapse into the finite-size floor (the dip cell beats neither its shuffle nor its IAAFT null), the latent-vs-emitted width map refutes the natural hypothesis that thresholding compresses multifractal width (emitted ≈ lane width; median per-run ratios 0.88–1.18), and the degeneracy map locates the usable region (the entire primary control plane is non-degenerate at 32 seeds, with all exact dead zones on one pack). The result is a practical design rule for multifractal instruments: a fitted α(Intensity, Spread) surface (R² 0.89–0.996) to invert for targets, which latent scaling survives musical quantization, and by what mechanism. 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. 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.