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

Mahesh Ramani

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 ($ΔR^2 \approx 0.014\%$, $p \approx 0.13$). Conversely, voicing significantly predicted dissonance ($ΔR^2 \approx 6.75\%$, $p \approx 0.0008$). Crucially, skewness ($β\approx +0.145$) was approximately 5.8$\times$ more effective than spread ($β\approx -0.025$) 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.

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

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 (, ). Conversely, voicing significantly predicted dissonance (, ). Crucially, skewness () was approximately 5.8 more effective than spread () 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.

Paper Structure

This paper contains 20 sections, 5 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Dataset Generation and Search Space
  4. Sampling Strategy
  5. Feature Extraction
  6. Voicing Statistics (Input Features)
  7. Psychoacoustic Metrics (Target Variables)
  8. 1. Plomp-Levelt Dissonance (Roughness):
  9. 2. Harmonicity:
  10. Limitations
  11. Results
  12. The Intrinsic Nature of Harmonicity
  13. Dissonance
  14. Discussion
  15. Intrinsic vs. Extrinsic Musical Properties
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Residual plot for harmonicity predictions (Model 2). Residuals show no systematic patterns as a function of predicted values, confirming model adequacy. Importantly, the residual distribution remains virtually identical whether voicing moments are included (Model 2) or excluded (Model 1), consistent with the negligible $\Delta R^2 \approx 0.00014$.
  • Figure 2: Permutation test for the contribution of voicing moments to dissonance prediction. The histogram shows the null distribution of $\Delta R^2$ values obtained by randomly permuting the residualized voicing features (1,200 iterations). The observed $\Delta R^2 = 0.0675$ falls far in the right tail ($p \approx 0.0008$), strongly rejecting the null hypothesis that voicing shape does not contribute to dissonance beyond pitch-class content.
  • Figure 3: Actual vs. predicted dissonance values for Model 2 (controls + voicing moments) on the held-out test set. Each point represents one chord (N = 10,000 test chords). The diagonal line represents perfect prediction. The model achieves $R^2 \approx 0.71$, demonstrating that voicing shape, when combined with pitch-class content, provides substantial predictive power for psychoacoustic roughness.