SPAR-RT:Evolving Representations of Music Timbre, Pitch, Tuning in Symmetric Projection Attractor Reconstruction

Musical sound analysis often relies on linear methods in the time and frequency domains to characterise features such as pitch, timbre, or tuning. However, linear methods fail to capture the inherent complexity of musical signals. In this study, we provide a foundational analysis of using the non-linear Symmetric Projection Attractor Reconstruction (SPAR) to characterise and visualise such music characteristics.<br/>SPAR integrates phase space reconstruction with the Discrete Fourier Transform (DFT), generating attractors whose shapes reflect the signal’s dynamic structure. We used synthetic sound signals to quantify the differences between attractors regarding the interference of different harmonics, music intervals, chords or tuning systems. The analysis revealed that the aliasing effect significantly affects the shape of the attractor, and the perceptual properties, such as dissonance and commensurability, are linked to the attractor's entropy. In real acoustic audio analysis using the NSynth dataset, we validated the method's ability to distinguish timbre through subtle geometric density patterns over a wide range of pitches. Using cluster analysis, we achieved perfect classification accuracy between flute and brass instruments. Additionally, we developed a real-time SPAR visualisation tool (SPAR-RT) that enables interactive analysis and intuitive observation of evolving acoustic features over time. Our results show that the SPAR method extends the analysis of musical signals, providing new non-linear and dynamic perspectives for audio processing, instrument recognition, and music theory research.