Piano sound analysis using Non-negative Matrix Factorization with inharmonicity constraint

This paper presents a method for estimating the tuning and the inharmonicity coefficient of piano tones, from single notes or chord recordings. It is based on the Non-negative Matrix Factorization (NMF) framework, with a parametric model for the dictionary atoms. The key point here is to include as a relaxed constraint the inharmonicity law modelling the frequencies of transverse vibrations for stiff strings. Applications show that this can be used to finely estimate the tuning and the inharmonicity coefficient of several notes, even in the case of high polyphony. The use of NMF makes this method relevant when tasks like music transcription or source/note separation are targeted.

[1]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[2]  Roland Badeau,et al.  Multipitch Estimation of Piano Sounds Using a New Probabilistic Spectral Smoothness Principle , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[3]  Nancy Bertin,et al.  Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis , 2009, Neural Computation.

[4]  Vesa Välimäki,et al.  Fast automatic inharmonicity estimation algorithm. , 2007, The Journal of the Acoustical Society of America.

[5]  Bertrand David,et al.  A Parametric Model of Piano Tuning , 2011 .

[6]  Masataka Goto,et al.  RWC Music Database: Music genre database and musical instrument sound database , 2003, ISMIR.

[7]  Emmanuel Vincent,et al.  Harmonic and inharmonic Nonnegative Matrix Factorization for Polyphonic Pitch transcription , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[8]  Simon Dixon,et al.  Joint Multi-Pitch Detection Using Harmonic Envelope Estimation for Polyphonic Music Transcription , 2011, IEEE Journal of Selected Topics in Signal Processing.

[9]  Roland Badeau,et al.  NMF With Time–Frequency Activations to Model Nonstationary Audio Events , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[10]  P. Morse.  Vibration and Sound , 1949, Nature.

[11]  Anders Askenfelt,et al.  Signal representation and estimation of spectral parameters by inharmonic comb filters with application to the piano , 1999, IEEE Trans. Speech Audio Process..

[12]  Gabriel Weinreich,et al.  Coupled piano strings , 1977 .

[13]  M. Davy,et al.  Bayesian computational models for inharmonicity in musical instruments , 2005, IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2005..

[14]  Emmanuel Vincent,et al.  Enforcing Harmonicity and Smoothness in Bayesian Non-Negative Matrix Factorization Applied to Polyphonic Music Transcription , 2010, IEEE Transactions on Audio, Speech, and Language Processing.