构建1930万条受生理限制的钢琴和弦数据集，揭示音色布局新规律。
A Comprehensive Corpus of Biomechanically Constrained Piano Chords: Generation, Analysis, and Implications for Voicing and Psychoacoustics
- 基于双手1.5个八度生理限制，生成超大规模可演奏和弦库。
- 发现音色偏度比音程跨度更能预测不协和感，提升6.75%解释力。
- 挑战传统教学理念，主张低音留空、高音紧凑更利于听觉清晰。
本文构建并分析了目前已知最大的开源可演奏钢琴和弦语料库（约1930万条），涵盖双人手各1.5个八度范围内的搜索空间。为验证数据集价值，研究建模了音色形态与心理声学目标之间的关系：谐波性与音高类身份内在相关，音色统计仅贡献极小方差（ΔR² ≈ 0.014%，p ≈ 0.13）；而音色显著预测不协和感（ΔR² ≈ 6.75%，p ≈ 0.0008）。关键发现：偏度（β ≈ +0.145）对粗糙感的预测能力约为音程展布（β ≈ -0.025）的5.8倍。该结果挑战传统教学中强调“展布”的观念——清晰的“开放音型”更多依赖负偏度，即在低音区留出宽距，高音区允许密集排列。本研究证明该语料库可推动生成建模、声部进行拓扑及心理声学等领域的未来研究。
原文摘要 · Abstract (English)
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.
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