No Longer ‘Somewhat Arbitrary’:Calculating Salience in GTTM-Style Reduction

Following earlier work on the formalisation of Lerdahl and Jackendoff’s Generative Theory of Tonal Music (GTTM), we present a measure of the salience of events in a reduction tree, based on calculations relating the duration of time-spans to the structure of the tree. This allows for the proper graphical rendition of a tree on the basis of its time-spans and topology alone. It also has the potential to contribute to the development of sophisticated digital library systems able to operate on music in a musically intelligent manner. We present results of an empirical study of branch heights in the figures in GTTM which shows that salience calculated according to our proposals correlates better with branch height than alternatives. We also discuss the possible musical significance of this measure of salience. Finally we compare some results using salience in the calculation of melodic similarity on the basis of reduction trees to earlier results using time-span. While the correlation between these measures and human ratings of the similarity of the melodies is poor, using salience shows a definite improvement. Overall, the results suggest that the proposed definition of salience gives a potentially useful measure of an event’s importance in a musical structure

Perception based approach on pattern discovery and organisation of point-set data

The general topic of the thesis is computer aided music analysis on point-set data utilising theories outlined in Timo Laiho’s Analytic-Generative Methodology (AGM) [19]. The topic is in the field of music information retrieval, and is related to previous work on both pattern discovery and computational models of music. The thesis aims to provide analysis results that can be compared to existing studies. AGM introduces two concepts based on perception, sensation and cognitive processing: interval–time complex (IntiC) and musical vectors (muV). These provide a mathematical framework for the analysis of music. IntiC is a value associated with the velocity, or rate of change, between musical notes. Musical vectors are the vector representations of these rates of change. Laiho explains these attributes as meaningful for both music analysis and as tools for music generation. Both of these attributes can be computed from a point-set representation of music data. The concepts in AGM can be viewed as being related to geometric methods for pattern discovery algorithmsof Meredith, Lemström et al.[24] whointroduce afamily of ‘Structure Induction Algorithms’. These algorithms are used to find repeating patterns in multidimensional point-set data. Algorithmic implementations of intiC and muV were made for this thesis and examined in the use of rating and selecting patterns output by the pattern discovery algorithms. In addition software tools for using these concepts of AGM were created. The concepts of AGM and pattern discovery were further related to existing work in computer aided musicology

Towards a general computational theory of musical structure

The General Computational Theory of Musical Structure (GCTMS) is a theory that may be employed to obtain a structural description (or set of descriptions) of a musical surface. This theory is based on general cognitive and logical principles, is independent of any specific musical style or idiom, and can be applied to any musical surface. The musical work is presented to GCTMS as a sequence of discrete symbolically represented events (e.g. notes) without higher-level structural elements (e.g. articulation marks, timesignature etc.)- although such information may be used to guide the analytic process. The aim of the application of the theory is to reach a structural description of the musical work that may be considered as 'plausible' or 'permissible' by a human music analyst. As styledependent knowledge is not embodied in the general theory, highly sophisticated analyses (similar to those an expert analyst may provide) are not expected. The theory gives, however, higher rating to descriptions that may be considered more reasonable or acceptable by human analysts and lower to descriptions that are less plausible

Tension-driven Automatic Music Generation

The Ancient Greeks are one of the first civilisations we know of to have created algorithms to compose music. Since then, algorithmic techniques have vastly improved with increasingly sophisticated computers. In the last two decades, much research in this area has focused on two goals: designing algorithms which generate music as close as possible to that of human composers and implementing those algorithms to automatically generate music in interactive scenarios, such as video games. To meet these goals, automatically generated music should: - focus on higher-level concepts, such as musical tension, - have long-term structure, and - be able to adapt to changes in real time. Combining these three requirements is, however, a challenging task. This dissertation investigates three steps to overcome this challenge. First, we argue that Lerdahl’s model of musical tension is suited to the automatic generation of tonal music that has long-term structure and that matches a given tension profile. By means of an illustrative example, we review Lerdhal’s model and implement a novel computational system to automate it. Second, we show that an effective generation strategy is to combine statistical methods with both rule-based methods and generative grammars to create a music generation system. Third, we implement the system and evaluate it through a collection of computational tests and empirical studies. Our evaluation shows that: (1) the system works effectively in real time, as long as the input tension profiles do not contain too many steep transitions, (2) the hierarchical structure perceived by listeners matches the patterns intended by the system in the generated music, and (3) tension-changing input profiles are accurately matched by the generated music

The Butterfly Schema as a Product of the Tendency for Congruence and Hierarchical Selection in the Instrumental Musical Grammar of the Classical Period

Diverging explanations of local multiparametric schemata are found in music of the common practice period (c. 1600–c. 1900). Associative statistical theories describe schemata as situated structures in particular times and places, whereas generative theories present these constructions as features formed through stability in universal and general rule systems. Associative-statistical theories of schemata elucidate the culturally conditioned relationships between features (distinctive attributes commonly used in grammars and schemata), but do not show the influence of universal psychological constraints; generative theories reveal the implicit structure of music, but do not formalise particular grammatical features and contexts. A synthesis of generative and associative-statistical approaches is necessary to model the interaction between universal and particular constraints of grammars and schemata. This dissertation focuses on a novel localised schema formed in the Classical instrumental grammar, termed the butterfly schema. It is posited that the butterfly schema is generated by a tendency for congruence that is manifest in and between the particular features of this grammar. Computational musicology and psychology provide interdisciplinary insight on the formal possibilities and limitations of grammatical structure. Computational models of schemata and grammars show how the congruent features of musical structure can be represented and formalised. However, they also highlight the difficulties found in the automatic analyses of multiparametric relationships, and may be limited on account of their inductive frameworks. Psychological approaches are important for establishing universal laws of cognition, but are limited in their potential to account for the diversity of musical structuring in grammars. The synthesis of associative-statistical and generative approaches in the present dissertation permits modelling the combination of the universal and particular attributes of butterfly schemata. Butterfly schemata are dependent on the particular grammars of periods of history, but are constrained by the tendency for congruence, which is proposed to be a cognitive universal. The features of the butterfly schema and the Classical instrumental grammar are examined and compared against the features of the Baroque and Romantic grammars, showing how they are formed from diverse types of congruent structuring. The butterfly schema is a congruent grammatical category of the Classical instrumental grammar that comprises: chords that are close to the tonic in pitch space (with a chiastic tension curve starting and ending on the tonic); a textural and metrical structure that is regular and forms a regular duple hierarchy at the level of regular functional harmonic change and at two immediately higher levels; and simple harmonic-rhythm ratios (1:1 and 3:1). A survey conducted using arbitrary corpora in European instrumental music, c. 1750–c.1850, shows the distribution of butterfly schemata. Butterfly schemata are more common in the Classical-period sample (c. 1750–c. 1800) than in the Romantic-period sample (c. 1800–c.1850), suggesting that the tendency for congruence manifest in and between the features common in the Classical grammar generates butterfly schemata. A second component to the statistical analysis concerns the type of schemata observed, since the tendency for congruence is presumed to also apply to the type of features that form in butterfly schemata. Maximally congruent features are generated more commonly than minimally congruent features, indicating the influence of the tendency for congruence. This dissertation presents a formulation of the Classical instrumental grammar as a multiparametrically congruent system, and a novel explanation and integration of the concepts of grammars and schemata. A final component to the dissertation poses that the features of the Classical instrumental grammar and butterfly schema follow a distinct order of dependency, governed by the mechanism of selection in culture. Although the tendency for congruence governs all features of a grammar, features are also formed by the top-down action of culture which selects those features. Thus, a top-down hierarchical selection model is presented which describes how the butterfly schema is formed through the order of selection of features in the Classical instrumental grammar

Explaining Listener Differences in the Perception of Musical Structure

PhDState-of-the-art models for the perception of grouping structure in music do not attempt to account for disagreements among listeners. But understanding these disagreements, sometimes regarded as noise in psychological studies, may be essential to fully understanding how listeners perceive grouping structure. Over the course of four studies in different disciplines, this thesis develops and presents evidence to support the hypothesis that attention is a key factor in accounting for listeners' perceptions of boundaries and groupings, and hence a key to explaining their disagreements. First, we conduct a case study of the disagreements between two listeners. By studying the justi cations each listener gave for their analyses, we argue that the disagreements arose directly from differences in attention, and indirectly from differences in information, expectation, and ontological commitments made in the opening moments. Second, in a large-scale corpus study, we study the extent to which acoustic novelty can account for the boundary perceptions of listeners. The results indicate that novelty is correlated with boundary salience, but that novelty is a necessary but not su cient condition for being perceived as a boundary. Third, we develop an algorithm that optimally reconstructs a listener's analysis in terms of the patterns of similarity within a piece of music. We demonstrate how the output can identify good justifications for an analysis and account for disagreements between two analyses. Finally, having introduced and developed the hypothesis that disagreements between listeners may be attributable to differences in attention, we test the hypothesis in a sequence of experiments. We find that by manipulating the attention of participants, we are able to influence the groupings and boundaries they find most salient. From the sum of this research, we conclude that a listener's attention is a crucial factor affecting how listeners perceive the grouping structure of music.Social Sciences and Humanities Research Council; a PhD studentship from Queen Mary University of London; a Provost's Ph.D. Fellowship from the University of Southern California. This material is also based in part on work supported by the National Science Foundation under Grant No. 0347988

A Parse-based Framework for Coupled Rhythm Quantization and Score Structuring

International audienceWe present a formal language-based framework for MIDI-to-score transcription, the problem of converting a sequence of symbolic musical events with arbitrary timestamps into a structured music score. The framework aims at solving in one pass the two subproblems of rhythm quantization and score production. It relies, throughout the process, on an apriori hierarchical model of scores given by generative grammars. We show that this coupled approach helps to make relevant and interrelated decisions, and we present an algorithm computing transcription solutions optimal with respect to both the fitness of the quantization to the input, and a measure of complexity of music notation

A Cognitive Information Theory of Music: A Computational Memetics Approach

This thesis offers an account of music cognition based on information theory and memetics. My research strategy is to split the memetic modelling into four layers: Data, Information, Psychology and Application. Multiple cognitive models are proposed for the Information and Psychology layers, and the MDL best-fit models with published human data are selected. Then, for the Psychology layer only, new experiments are conducted to validate the best-fit models. In the information chapter, an information-theoretic model of musical memory is proposed, along with two competing models. The proposed model exhibited a better fit with human data than the competing models. Higher-level psychological theories are then built on top of this information layer. In the similarity chapter, I proposed three competing models of musical similarity, and conducted a new experiment to validate the best-fit model. In the fitness chapter, I again proposed three competing models of musical fitness, and conducted a new experiment to validate the best-fit model. In both cases, the correlations with human data are statistically significant. All in all, my research has shown that the memetic strategy is sound, and the modelling results are encouraging. Implications of this research are discussed