Amanous: Distribution-Switching for Superhuman Piano Density on Disklavier

Abstract

The automated piano enables note densities, polyphony, and register changes far beyond human physical limits, yet the three dominant traditions for composing such textures--Nancarrow's tempo canons, Xenakis's stochastic distributions, and L-system grammars--have developed in isolation. This paper presents Amanous, a hardware-aware composition system for Yamaha Disklavier that unifies these methodologies through distribution-switching: L-system symbols select distinct distributional regimes rather than merely modulating parameters within a fixed family. Four contributions are reported. (1) A four-layer architecture (symbolic, parametric, numeric, physical) produces statistically distinct sections with large effect sizes (d = 3.70-5.34), validated by per-layer degradation and ablation experiments. (2) A hardware abstraction layer formalizes velocity-dependent latency and key reset constraints, keeping superhuman textures within the Disklavier's actuable envelope. (3) A density sweep reveals a computational saturation transition at 24-30 notes/s (bootstrap 95% CI: 23.3-50.0), beyond which single-domain melodic metrics lose discriminative power and cross-domain coupling becomes necessary. (4) A convergence point calculus operationalizes tempo-canon geometry as a control interface, enabling convergence events to trigger distribution switches linking macro-temporal structure to micro-level texture. All results are computational; a psychoacoustic validation protocol is proposed for future work. The pipeline has been deployed on a physical Disklavier, demonstrating algorithmic self-consistency and sub-millisecond software precision. Supplementary materials (Excerpts 1-4): https://www.amanous.xyz. Source code: https://github.com/joonhyungbae/Amanous.

Figures (7)

• Figure 1: Four-layer hierarchical architecture. Layer 1 generates macro-form via L-system expansion. Layer 2 maps symbols to distributional regimes (distribution-switching). Layer 3 renders time-stamped events. Layer 4 compensates for VDL and enforces hardware constraints. The dashed feedback path enables Convergence Point events to trigger distribution switches, linking macro-temporal structure (Layer 3) back to the parametric layer (Layer 2).
• Figure 2: Recurrence plots: L-system (left) vs. random shuffle with same A:B composition (right). Each point $(i,j)$ marks recurrence (same symbol at indices $i$ and $j$). The L-system exhibits diagonal structure (repeated subsequences); the random sequence yields fragmented points. Depth 8, $|\Sigma|=55$; generated from RQA analysis.
• Figure 3: Sensitivity of Layer 4 HAL to latency model mismatch. Actual latency is scaled as $L_{\mathrm{actual}}(v) = (1 + \delta)\,L(v)$ with $\delta$ from $-20\%$ to $+20\%$. Jitter (timing error std, ms) with HAL applied remains strictly lower than uncorrected jitter across all mismatch levels; at $\pm 20\%$, HAL retains more than 70% jitter suppression versus no correction. $N = 526$ notes.
• Figure 4: Single-voice coherence as a function of aggregate note density. Amanous (pre-saturation blue, post-saturation red) is characterised by piecewise linear regression; the random baseline (orange) uses pitch and velocity uniform, IOI $\sim$ Exp($1/\rho$)). The null yields flat MC $\approx 0.53$--0.59 with no breakpoint; Tonal Stability from the same run is Amanous TS $\approx 0.08$--0.13 vs. null $\approx 0.02$--0.03 at all densities ($t$-test $p < 0.05$ at low density). A piecewise linear regression on Amanous data identifies a Computational Sensitivity Limit (CSL) at 28.4 notes/s (95% CI: 23.3--50.0). This limit aligns with the regime where average IOI approaches the physical scanning resolution of the Disklavier (${\sim}$1 ms). Pre-saturation slope is $49.3\times$ steeper than post-saturation ($R^2_{\text{piecewise}} = 0.988$ vs. $R^2_{\text{linear}} = 0.442$; $U = 1.0$, $p = 0.002$). The wide CI indicates a transition zone rather than a sharp threshold.
• Figure 5: Distribution independence: Melodic Coherence as a function of density for four IOI distributions (exponential, uniform, Gaussian, constant). All curves drop sharply in the 25--35 notes/s band (shaded), indicating that the phase transition is independent of the choice of temporal distribution.

Theorems & Definitions (2)

• Definition 1: Dynamic Distribution-Switching Mapping
• Definition 2: Convergence Point