Logic-based Modelling of Musical Harmony for Automatic Characterisation and Classification

The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the authorMusic like other online media is undergoing an information explosion. Massive online music stores such as the iTunes Store1 or Amazon MP32, and their counterparts, the streaming platforms, such as Spotify3, Rdio4 and Deezer5, offer more than 30 million6 pieces of music to their customers, that is to say anybody with a smart phone. Indeed these ubiquitous devices offer vast storage capacities and cloud-based apps that can cater any music request. As Paul Lamere puts it7: “we can now have a virtually endless supply of music in our pocket. The ‘bottomless iPod’ will have as big an effect on how we listen to music as the original iPod had back in 2001. But with millions of songs to chose from, we will need help finding music that we want to hear [...]. We will need new tools that help us manage our listening experience.” Retrieval, organisation, recommendation, annotation and characterisation of musical data is precisely what the Music Information Retrieval (MIR) community has been working on for at least 15 years (Byrd and Crawford, 2002). It is clear from its historical roots in practical fields such as Information Retrieval, Information Systems, Digital Resources and Digital Libraries but also from the publications presented at the first International Symposium on Music Information Retrieval in 2000 that MIR has been aiming to build tools to help people to navigate, explore and make sense of music collections (Downie et al., 2009). That also includes analytical tools to suppor

Improving music genre classification using automatically induced harmony rules

We present a new genre classification framework using both low-level signal-based features and high-level harmony features. A state-of-the-art statistical genre classifier based on timbral features is extended using a first-order random forest containing for each genre rules derived from harmony or chord sequences. This random forest has been automatically induced, using the first-order logic induction algorithm TILDE, from a dataset, in which for each chord the degree and chord category are identified, and covering classical, jazz and pop genre classes. The audio descriptor-based genre classifier contains 206 features, covering spectral, temporal, energy, and pitch characteristics of the audio signal. The fusion of the harmony-based classifier with the extracted feature vectors is tested on three-genre subsets of the GTZAN and ISMIR04 datasets, which contain 300 and 448 recordings, respectively. Machine learning classifiers were tested using 5 × 5-fold cross-validation and feature selection. Results indicate that the proposed harmony-based rules combined with the timbral descriptor-based genre classification system lead to improved genre classification rates

Improving music genre classification using automatically induced harmony rules

We present a new genre classification framework using both low-level signal-based features and high-level harmony features. A state-of-the-art statistical genre classifier based on timbral features is extended using a first-order random forest containing for each genre rules derived from harmony or chord sequences. This random forest has been automatically induced, using the first-order logic induction algorithm TILDE, from a dataset, in which for each chord the degree and chord category are identified, and covering classical, jazz and pop genre classes. The audio descriptor-based genre classifier contains 206 features, covering spectral, temporal, energy, and pitch characteristics of the audio signal. The fusion of the harmony-based classifier with the extracted feature vectors is tested on three-genre subsets of the GTZAN and ISMIR04 datasets, which contain 300 and 448 recordings, respectively. Machine learning classifiers were tested using 5 × 5-fold cross-validation and feature selection. Results indicate that the proposed harmony-based rules combined with the timbral descriptor-based genre classification system lead to improved genre classification rates

Interaction and observation: categorical semantics of reactive systems trough dialgebras

We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is built-in, and semantic equivalence arises from it, instead of being determined by a (possibly difficult) understanding of the side effects of a component in isolation. Behavioural equivalence in dialgebras is determined by how a given process interacts with the others, and the obtained observations. We develop a technique to inter-define categories of dialgebras of different functors, that in particular permits us to compare a standard coalgebraic semantics and its dialgebraic counterpart. We exemplify the framework using the CCS and the pi-calculus. Remarkably, the dialgebra giving semantics to the pi-calculus does not require the use of presheaf categories

Representing chord sequences in OWL

Chord symbols and progressions are a common way to describe musical harmony. In this paper we present SEQ, a pattern representation using the Web Ontology Language OWL DL and its application to modelling chord sequences. SEQ provides a logical representation of order information, which is not available directly in OWL DL, together with an intuitive notation. It therefore allows the use of OWL reasoners for tasks such as classification of sequences by patterns and determining subsumption relationships between the patterns. The SEQ representation is used to express distinctive pattern obtained using data mining of multiple viewpoints of chord sequences

Model Theory of XPath on Data Trees: Part I: Bisimulation and Characterization

We investigate model theoretic properties of XPath with data (in)equality tests over the class of data trees, i.e., the class of trees where each node contains a label from a finite alphabet and a data value from an infinite domain.We provide notions of (bi)simulations for XPath logics containing the child, descendant, parent and ancestor axes to navigate the tree. We show that these notions precisely characterize the equivalence relation associated with each logic. We study formula complexity measures consisting of the number of nested axes and nested subformulas in a formula; these notions are akin to the notion of quantifier rank in first-order logic. We show char- acterization results for fine grained notions of equivalence and (bi)simulation that take into account these complexity measures. We also prove that positive fragments of these logics correspond to the formulas preserved under (non-symmetric) simulations. We show that the logic including the child axis is equivalent to the fragment of first-order logic invariant under the corresponding notion of bisimulation. If upward navigation is allowed the characterization fails but a weaker result can still be established. These results hold both over the class of possibly infinite data trees and over the class of finite data trees.Besides their intrinsic theoretical value, we argue that bisimulations are useful tools to prove (non)expressivity results for the logics studied here, and we substantiate this claim with examples.Fil: Figueira, Diego. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Characterising strongly normalising intuitionistic terms

This paper gives a characterisation, via intersection types, of the strongly normalising proof-terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary lambdal-calculus. The completeness of the typing system is obtained from subject expansion at root position. Next we use our result to analyze the characterisation of strong normalisability for three classes of intuitionistic terms: ordinary lambda-terms, LambdaJ-terms (lambda-terms with generalised application), and lambdax-terms (lambda-terms with explicit substitution). We explain via our system why the type systems iin the natural deduction format for LambdaJ and lambdax known from the literature contain extra, exceptional rules for typing generalised application or substitution; and we show a new characterisation of the beta-strongly normalising l-terms, as a corollary to a PSN-result, relating the lambda-calculus and the intuitionistic sequent calculus. Finally, we obtain variants of our characterisation by restricting the set of assignable types to sub-classes of intersection types, notably strict types. In addition, the known characterisation of the beta-strongly normalising lambda-terms in terms of assignment of strict types follows as an easy corollary of our results.Fundação para a Ciência e Tecnologi