Learning the helix topology of musical pitch
This work addresses the problem of understanding pitch perception for music psychology and audio processing, but it is incremental as it applies existing manifold learning methods to this domain.
The paper tackled the problem of discovering the helical structure of musical pitch from unlabeled audio data, and the result was that the learned manifold resembled a helix making a full turn at every octave, as demonstrated on isolated musical notes.
To explain the consonance of octaves, music psychologists represent pitch as a helix where azimuth and axial coordinate correspond to pitch class and pitch height respectively. This article addresses the problem of discovering this helical structure from unlabeled audio data. We measure Pearson correlations in the constant-Q transform (CQT) domain to build a K-nearest neighbor graph between frequency subbands. Then, we run the Isomap manifold learning algorithm to represent this graph in a three-dimensional space in which straight lines approximate graph geodesics. Experiments on isolated musical notes demonstrate that the resulting manifold resembles a helix which makes a full turn at every octave. A circular shape is also found in English speech, but not in urban noise. We discuss the impact of various design choices on the visualization: instrumentarium, loudness mapping function, and number of neighbors K.