The Fenophone: A Musical Instrument Built on the Markov-Switching Multifractal, with CI-Verified Spectral Invariants

Abstract

We present the Fenophone, a browser-based generative music instrument whose intensity core is, by construction, the Markov-switching multifractal (MSM) of Calvet and Fisher: a product of k ∈ [3, 12] two-state switching multipliers whose Hz-defined switch rates are spaced geometrically across a player-controlled span. Every primary control is a genuine parameter of that model — Intensity sets the multiplier magnitude m_hi, Change Rate the slowest switch rate f_slow, Spread the time-scale span S, Layers the multiplier count k — and a fixed band map routes the cascade's slow, mid, and fast bands to harmonic tension, rhythmic density, and dynamics. Pitch comes from per-voice stochastic contour walks with provably bounded register drift, sampled at cascade-determined onsets. The event layer is integer/fixed-point and bit-identical across platforms, which makes the instrument learnable, performances exactly reproducible, and — unusually — statistical properties of the output enforceable in continuous integration: a DFA/MFDFA suite measures every shipped scaffold's emitted note stream (per-scaffold onset-stream DFA α medians 0.695–0.770, every seed beating its shuffled-surrogate null; multifractal widths 0.054–0.126, exceeding matched IAAFT surrogate nulls on every seed for three of the four measured packs, with the fourth reported as consistent with linear long memory at this length — a no-verdict at the width statistic's measured power, not evidence of linearity) and CI rejects any content or engine change whose median α falls below a published floor of 0.60 after bar-template removal. We describe the model, the instrument built around it, the playability theorems and mechanized gates, and the measured spectral landscape, and we reflect on what a strictly mathematical instrument buys and what it costs.