The Computational Attitude in Music Theory

Music studies’s turn to computation during the twentieth century has engendered particular habits of thought about music, habits that remain in operation long after the music scholar has stepped away from the computer. The computational attitude is a way of thinking about music that is learned at the computer but can be applied away from it. It may be manifest in actual computer use, or in invocations of computationalism, a theory of mind whose influence on twentieth-century music theory is palpable. It may also be manifest in more informal discussions about music, which make liberal use of computational metaphors. In Chapter 1, I describe this attitude, the stakes for considering the computer as one of its instruments, and the kinds of historical sources and methodologies we might draw on to chart its ascendance. The remainder of this dissertation considers distinct and varied cases from the mid-twentieth century in which computers or computationalist musical ideas were used to pursue new musical objects, to quantify and classify musical scores as data, and to instantiate a generally music-structuralist mode of analysis. I present an account of the decades-long effort to prepare an exhaustive and accurate catalog of the all-interval twelve-tone series (Chapter 2). This problem was first posed in the 1920s but was not solved until 1959, when the composer Hanns Jelinek collaborated with the computer engineer Heinz Zemanek to jointly develop and run a computer program. Recognizing the transformation wrought on modern statistics and communications technology by information theory, I revisit Abraham Moles’s book Information Theory and Esthetic Perception (orig. 1958) and use its vocabulary to contextualize contemporary information-theoretic work on music that various evokes the computational mind by John. R. Pierce and Mary Shannon, Wilhelm Fucks, and Henry Quastler (Chapter 3). I conclude with a detailed look into a score-segmentation algorithm of the influential American music theorist Allen Forte (Chapter 4). Forte was a skilled programmer who spent several years at MIT in the 1960s, with cutting-edge computers and the company of first-rank figures in the nascent fields of computer science and artificial intelligence. Each one of the researchers whose work is treated in these case studies—at some stage in their relationship with music—adopted what I call the computational attitude to music, to varying degrees and for diverse ends. Of the many questions this dissertation seeks to answer: what was gained by adopting such an attitude? What was lost? Having understood these past explorations of the computational attitude to music, we are better suited ask of ourselves the same questions today

Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts.Comment: The final version of this paper has been published by the Journal of Mathematics and Musi

Networks of Music and Images

Powerful abstraction of mathematical category theory can be used to describe musical procedures and structures. The same mathematical theory can be applied to visual shapes and their transformations, including computational applications. Since we can connect music and images through mappings, we can also connect their networks step by step, describing progressive shape modifications. We propose a new approach to music composition based on these ideas, composing music from a network of images “sonifying” each step, as well as creating a parallel sequence of visual and musical variations

Proceedings of the 6th International Workshop on Folk Music Analysis, 15-17 June, 2016

The Folk Music Analysis Workshop brings together computational music analysis and ethnomusicology. Both symbolic and audio representations of music are considered, with a broad range of scientific approaches being applied (signal processing, graph theory, deep learning). The workshop features a range of interesting talks from international researchers in areas such as Indian classical music, Iranian singing, Ottoman-Turkish Makam music scores, Flamenco singing, Irish traditional music, Georgian traditional music and Dutch folk songs. Invited guest speakers were Anja Volk, Utrecht University and Peter Browne, Technological University Dublin

An information theoretic characterisation of auditory encoding.

The entropy metric derived from information theory provides a means to quantify the amount of information transmitted in acoustic streams like speech or music. By systematically varying the entropy of pitch sequences, we sought brain areas where neural activity and energetic demands increase as a function of entropy. Such a relationship is predicted to occur in an efficient encoding mechanism that uses less computational resource when less information is present in the signal: we specifically tested the hypothesis that such a relationship is present in the planum temporale (PT). In two convergent functional MRI studies, we demonstrated this relationship in PT for encoding, while furthermore showing that a distributed fronto-parietal network for retrieval of acoustic information is independent of entropy. The results establish PT as an efficient neural engine that demands less computational resource to encode redundant signals than those with high information content

A psychoacoustic model of harmonic cadences: a preliminary report

This report presents a psychoacoustically derived computational model of the perceived distance between any two major or minor triads, the degree of activity created by any given pair of triads, and the cadential effectiveness of three-triad progressions. It also provides statistical analyses of the ratings given by thirty-five participants for the "similarity" and "fit" of triads in a pair, and the "cadential effectiveness" of three-triad progressions. Multiple regressions show that the model provides highly significant predictions of the experimentally obtained ratings. Finally, it is argued that because the model is based upon psychoacoustic axioms, it is likely the regression equations represent true causal models. As such, the computational model and its associated theory question the plausibility of theoretical approaches to tonality that use only long-term memory and statistical features, as well as those approaches based upon symmetrical geometrical structures like the torus. It is hoped that the psychoacoustic approach proposed here may herald not only the return of psychoacoustic approaches to tonal music theory, but also the exploration of the tonal possibilities offered by non-standard tunings and non-harmonic timbres

Unleashing creative synergies: a mixed-method case study in music education classrooms

Algorithmic music composition has been gaining prominence and recognition as an innovative approach to music education, providing students with opportunities to explore creativity, computational thinking, and musical knowledge. This study aims to investigate the impact of integrating algorithmic music composition in the classroom, examining its influence on student engagement, musical knowledge, and creative expression, as well as to enhance computational thinking skills. A mixed-method case study was conducted in three Basic Music Education classrooms in the north of Portugal, involving 71 participants (68 students and 3 music teachers). The results reveal: (i) both successes and challenges in integrating computational thinking concepts and practices; (ii) pedagogical benefits of integrating programming platforms, where programming concepts overlapped with music learning outcomes; and (iii) positive impact on participants’ programming self-confidence and recognition of programming’s importance. Integrating algorithmic music composition in the classroom positively influences student engagement, musical knowledge, and creative expression. The use of algorithmic techniques provides a novel and engaging platform for students to explore music composition, fostering their creativity, critical thinking, and collaboration skills. Educators can leverage algorithmic music composition as an effective pedagogical approach to enhance music education, allowing students to develop a deeper understanding of music theory and fostering their artistic expression. Future research should contribute to the successful integration of digital technologies in the Portuguese curriculum by further exploring the long-term effects and potential applications of algorithmic music composition in different educational contexts.info:eu-repo/semantics/publishedVersio

Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates

We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subsets of equal size, computes an independent kernel ridge regression estimator for each subset, then averages the local solutions into a global predictor. This partitioning leads to a substantial reduction in computation time versus the standard approach of performing kernel ridge regression on all N samples. Our two main theorems establish that despite the computational speed-up, statistical optimality is retained: as long as m is not too large, the partition-based estimator achieves the statistical minimax rate over all estimators using the set of N samples. As concrete examples, our theory guarantees that the number of processors m may grow nearly linearly for finite-rank kernels and Gaussian kernels and polynomially in N for Sobolev spaces, which in turn allows for substantial reductions in computational cost. We conclude with experiments on both simulated data and a music-prediction task that complement our theoretical results, exhibiting the computational and statistical benefits of our approach

Analysing symbolic music with probabilistic grammars

Recent developments in computational linguistics offer ways to approach the analysis of musical structure by inducing probabilistic models (in the form of grammars) over a corpus of music. These can produce idiomatic sentences from a probabilistic model of the musical language and thus offer explanations of the musical structures they model. This chapter surveys historical and current work in musical analysis using grammars, based on computational linguistic approaches. We outline the theory of probabilistic grammars and illustrate their implementation in Prolog using PRISM. Our experiments on learning the probabilities for simple grammars from pitch sequences in two kinds of symbolic musical corpora are summarized. The results support our claim that probabilistic grammars are a promising framework for computational music analysis, but also indicate that further work is required to establish their superiority over Markov models