Title: Models of music signals informed by the physics of instruments
While instrumental acoustics and audio signal processing target the modelling of musical tones from different perspectives, this work aims at mixing both approaches by constraining generic signal models with acoustics-based information. Thus, it is intended to design instrument-specific models for applications both to acoustics and signal processing. In particular, I focused on piano music analysis for which the tones have the well-known property of inharmonicity that strongly influences the tuning. I will present two Non-negative Matrix Factorization (NMF) variants accounting for the inharmonic structure of piano tones and their application to 1) the estimation of the inharmonicity coefficient and the F0 in a supervised context both in monophonic/polyphonic conditions, and 2) to a polyphonic transcription task from which we investigate the influence of the inharmonicity inclusion in NMF-based models over a simpler harmonic model. I will then introduce a model of inharmonicity and piano tuning along the whole compass of pianos, based on invariants in design and tuning rules. Beyond analysis applications, I will show the usefulness of this model for providing tuning curves for out-of-tune pianos or physically-based synthesizers, for initializing the parameters of analysis algorithms, and finally for interpolating the inharmonicity and tuning of pianos along the whole compass from the analysis of a polyphonic recording containing only a few notes. Finally, I will give directions for further extensions of this work. In particular, I will discuss an application to the guitar for which the estimation of the inharmonicity may be used to retrieve the position of the fingers along the neck in applications to “audio to tablature” transcription.
François Rigaud is currently a post-doctoral fellow within the Signal and Image Processing (TSI) department at Télécom ParisTech. He received the MSc degree in Acoustics, Signal processing and Computer science Applied to Music (ATIAM) from the University Pierre et Marie Curie (Paris 6) and IRCAM in 2010, and the Ph.D. degree in the field of audio signal processing from Télécom ParisTech in 2013. He also received the Agrégation in applied physics (highest-level competitive French examinations for the recruitment of lecturers) from the Ecole Normale Supérieure (ENS) de Cachan in 2009. His research interests include musical acoustics and signal processing with applications to Music Information Retrieval, and more recently multimodal biomedical signal processing. Website: http://perso.telecom-paristech.fr/~rigaud/
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