Integrating musicological knowledge into a probabilistic framework for chord and key extraction

In this contribution a formerly developed probabilistic framework for the simultaneous detection of chords and keys in polyphonic audio is further extended and validated. The system behaviour is controlled by a small set of carefully defined free parameters. This has permitted us to conduct an experimental study which sheds a new light on the importance of musicological knowledge in the context of chord extraction. Some of the obtained results are at least surprising and, to our knowledge, never reported as such before

Modeling musicological information as trigrams in a system for simultaneous chord and local key extraction

In this paper, we discuss the introduction of a trigram musicological model in a simultaneous chord and local key extraction system. By enlarging the context of the musicological model, we hoped to achieve a higher accuracy that could justify the associated higher complexity and computational load of the search for the optimal solution. Experiments on multiple data sets have demonstrated that the trigram model has indeed a larger predictive power (a lower perplexity). This raised predictive power resulted in an improvement in the key extraction capabilities, but no improvement in chord extraction when compared to a system with a bigram musicological model

Fundamental Moments

Global trade can give rise to global hubs, centers of activity whose influence on the global economy is large enough that local disturbances have consequences in the aggregate. This paper investigates the nature, existence, and rise of such hubs using the World Input-Output Tables (WIOT) to evaluate the importance of vertical trade in creating global hubs that significantly affect countries volatility and their co-movement. Our results suggest that the world has become more granular since 1995, with significant consequences on GDP volatility and co-movements especially in developed countries. These consequences are well explained by international trade

Sorting out typicality with the inverse moment matrix SOS polynomial

International audienceWe study a surprising phenomenon related to the representation of a cloud of data points using polynomials. We start with the previously unnoticed empirical observation that, given a collection (a cloud) of data points, the sublevel sets of a certain distinguished polynomial capture the shape of the cloud very accurately. This distinguished polynomial is a sum-of-squares (SOS) derived in a simple manner from the inverse of the empirical moment matrix. In fact, this SOS polynomial is directly related to orthogonal polynomials and the Christoffel function. This allows to generalize and interpret extremality properties of orthogonal polynomials and to provide a mathematical rationale for the observed phenomenon. Among diverse potential applications, we illustrate the relevance of our results on a network intrusion detection task for which we obtain performances similar to existing dedicated methods reported in the literature

A novel chroma representation of polyphonic music based on multiple pitch tracking techniques

It is common practice to map the frequency content of music onto a chroma representation, but there exist many different schemes for constructing such a representation. In this paper, a new scheme is proposed. It comprises a detection of salient frequencies, a conversion of salient frequencies to notes, a psychophysically motivated weighting of harmonics in support of a note, a restriction of harmonic relations between different notes and a restriction of the deviations from a predefined pitch scale (e.g. the equally tempered western scale). A large-scale experimental evaluation has confirmed that the novel chroma representation more closely matches manual chord labels than the representations generated by six other tested schemes. Therefore, the new chroma representation is expected to improve applications such as song similarity matching and chord detection and labeling

Improving the key extraction performance of a simultaneous local key and chord estimation system

In this paper, significant improvements of a previously developed key and chord extraction system are proposed. The major improvement is the introduction of a separate acoustic model, designed to verify local key hypotheses. The conducted experimental evaluation shows that the presented system improves the state of the art in local key estimation. Our experimental study further demonstrates that the chord estimation performance is already quite robust, whereas the key estimation performance still happens to be sensitive to a number of factors. In particular, we present figures that illustrate the significant impact of the embedded musicological model and the duration of the processed excerpt on the key estimation accuracy