A Comprehensive Corpus of Biomechanically Constrained Piano Chords: Generation, Analysis, and Implications for Voicing and Psychoacoustics

TL;DR

This paper introduces the largest open-source corpus of biomechanically feasible piano chords, enabling analysis of voicing and psychoacoustic properties, and challenges traditional pedagogical emphasis on spread.

Contribution

It provides a comprehensive, biomechanically constrained piano chord dataset and demonstrates its utility in psychoacoustic modeling, highlighting skewness over spread in dissonance prediction.

Findings

Voicing shape adds negligible variance to pitch-class identity.

Skewness significantly predicts dissonance, more than spread.

Lower dissonance is associated with negative skewness in voicing.

Abstract

I present the generation and analysis of the largest known open-source corpus of playable piano chords (approximately 19.3 million entries). This dataset enumerates the two-handed search space subject to biomechanical constraints (two hands, each with 1.5 octave reach) to an unprecedented extent. To demonstrate the corpus's utility, the relationship between voicing shape and psychoacoustic targets was modeled. Harmonicity proved intrinsic to pitch-class identity: voicing statistics added negligible variance ($\Delta R^2 \approx 0.014\%$, $p \approx 0.13$). Conversely, voicing significantly predicted dissonance ($\Delta R^2 \approx 6.75\%$, $p \approx 0.0008$). Crucially, skewness ($\beta \approx +0.145$) was approximately 5.8$\times$ more effective than spread ($\beta \approx -0.025$) at predicting roughness. The analysis challenges the pedagogical emphasis on ``spread'': skewness is a stronger predictor of dissonance than spread. This suggests that clarity in ``open voicings'' is driven less by width than by negative skewness; achieving lower-register clearance by placing wide gaps at the bottom and allowing tighter clustering in the treble. The results demonstrate the corpus's ability to enable future research, especially in areas such as generative modeling, voice-leading topology, and psychoacoustic analysis.