Researchers have mapped out all 19.3 million chords the human hand can play on a piano to reveal why some sound 'clear' and others 'muddy.'
April 1, 2026
Original Paper
A Comprehensive Corpus of Biomechanically Constrained Piano Chords: Generation, Analysis, and Implications for Voicing and Psychoacoustics
arXiv · 2603.29710
The Takeaway
While music teachers have long taught that spreading notes out across the keyboard makes a chord sound 'open,' this massive data analysis of the physics of sound found that leaving specific gaps at the bottom of the chord is actually six times more important for clarity. The discovery suggests that centuries of musical pedagogy have focused on the wrong variable for sound quality.
From the 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 negligi