Analysis and synthesis of musical harmonies based on formal grammars

Music is one of the most fundamental and universal forms of expression of humanity, being part of the human society since its origins. As any artistic manifestation, it is a cultural product and its evolution and use in all kind of scenarios show us how important it is for the humanity. The relation between music and mathematics has been a close one, investigated since the Pythagoreans, and one of the main products of this relation is tonal music, considered one of the greatest contributions of western civilization. So not only is music one of the forms of expression that most directly speak to the emotions, it is also the one whose foundations are more firmly mathematical, making music an ideal testing ground for analyzing the formalization of emotionally charged forms of expression, and to explore the limits of such formalization. Music is not subject to simple deterministic rules, but there is an obvious structure underneath it. Investigating and formalizing such structure is important to better understand music and even to develop new ways of composition using computers as a synergistic partner or as an independent composer. Thus, in this work, we consider the usefulness and the limits of applicability of formal grammars. The use of grammars can give important insights into the harmonic structure of a piece of music, and a lot of researchers have developed grammars and applied them to different styles of music. In musical theory there are harmonic concepts that are not well-defined in a mathematical sense. In this work we considered several of these concepts and see how, and whether, grammars can be modified to accommodate them. However, the ambiguous nature of music limits the possibility of formal analysis of harmonic sequences: using the grammars we could not precisely define (and, consequently, recognize) some musical concepts, such as modulation (the change of key within a musical piece). Trying to formalize modulation leads to unavoidable ambiguities in the grammar. Consequently we tried using other methods to formalize these concepts, and we successfully could determine modulations using a numerical costbased method. Then we used grammars to analyze separately the non-modulating segments in which our algorithm has divided the music. The combination of different methods and technologies developed in this work appears to be a very bright perspective for analyzing musical pieces

Microtiming patterns and interactions with musical properties in Samba music

In this study, we focus on the interaction between microtiming patterns and several musical properties: intensity, meter and spectral characteristics. The data-set of 106 musical audio excerpts is processed by means of an auditory model and then divided into several spectral regions and metric levels. The resulting segments are described in terms of their musical properties, over which patterns of peak positions and their intensities are sought. A clustering algorithm is used to systematize the process of pattern detection. The results confirm previously reported anticipations of the third and fourth semiquavers in a beat. We also argue that these patterns of microtiming deviations interact with different profiles of intensities that change according to the metrical structure and spectral characteristics. In particular, we suggest two new findings: (i) a small delay of microtiming positions at the lower end of the spectrum on the first semiquaver of each beat and (ii) systematic forms of accelerando and ritardando at a microtiming level covering two-beat and four-beat phrases. The results demonstrate the importance of multidimensional interactions with timing aspects of music. However, more research is needed in order to find proper representations for rhythm and microtiming aspects in such contexts

Regular expressions as violin bowing patterns

String players spend a significant amount of practice time creating and learning bowings. These may be indicated in the music using up-bow and down-bow symbols, but those traditional notations do not capture the complex bowing patterns that are latent within the music. Regular expressions, a mathematical notation for a simple class of formal languages, can describe precisely the bowing patterns that commonly arise in string music. A software tool based on regular expressions enables performers to search for passages that can be handled with similar bowings, and to edit them consistently. A computer-based music editor incorporating bowing patterns has been implemented, using Lilypond to typeset the music. Our approach has been evaluated by using the editor to study ten movements from six violin sonatas by W. A. Mozart. Our experience shows that the editor is successful at finding passages and inserting bowings; that relatively complex patterns occur a number of times; and that the bowings can be inserted automatically and consistently

Eigenvector localization as a tool to study small communities in online social networks

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool here is localization of eigenvectors of the matrix, by means of which the relevant network segments become visible. We exemplified our approach by analyzing the data related to product reviewing on Amazon.com. We found several segments, a kind of hybrid communities of densely interlinked reviewers and products, which we were able to meaningfully interpret in terms of the type and thematic categorization of reviewed items. The method provides a complementary approach to other ways of community detection, typically aiming at identification of large network modules

Characterizing the Landscape of Musical Data on the Web: State of the Art and Challenges

Musical data can be analysed, combined, transformed and exploited for diverse purposes. However, despite the proliferation of digital libraries and repositories for music, infrastructures and tools, such uses of musical data remain scarce. As an initial step to help fill this gap, we present a survey of the landscape of musical data on the Web, available as a Linked Open Dataset: the musoW dataset of catalogued musical resources. We present the dataset and the methodology and criteria for its creation and assessment. We map the identified dimensions and parameters to existing Linked Data vocabularies, present insights gained from SPARQL queries, and identify significant relations between resource features. We present a thematic analysis of the original research questions associated with surveyed resources and identify the extent to which the collected resources are Linked Data-ready

Generation of folk song melodies using Bayes transforms

The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models

Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using compression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two dual modes are used in different approaches to information system, particularly the relational model for database introduced by Codd in the 70's. This allows to point out diverse forms of a fundamental duality. These operational modes are also reinterpreted in the context of the comprehension schema of axiomatic set theory ZF. This leads us to develop how Kolmogorov's complexity is linked to intensionality, abstraction, classification and information system.Comment: 43 page

Combinatorics in the Art of the Twentieth Century

This paper is motivated by a question I asked myself: How can combinatorial structures be used in a work of art? Immediately, other questions arose: Whether there are artists that work or think combinatorially? If so, what works have they produced in this way? What are the similarities and differences between art works produced using combinatorics? This paper presents the first results of the attempt to answer these questions, being a survey of a selection of works that use or contain combinatorics in some way, including music, literature and visual arts, focusing on the twentieth century.Postprint (published version

Learning, Arts, and the Brain: The Dana Consortium Report on Arts and Cognition

Reports findings from multiple neuroscientific studies on the impact of arts training on the enhancement of other cognitive capacities, such as reading acquisition, sequence learning, geometrical reasoning, and memory