On Linear Algebraic Representation of Time-span and Prolongational Trees

In constructive music theory, such as Schenkerian analysis and the Generative Theory of Tonal Music (GTTM), the hierarchical importance of pitch events is conveniently represented by a tree structure. Although a tree is easy to recognize and has high visibility, such an intuitive representation can hardly be treated in mathematical formalization. Especially in GTTM, the conjunction height of two branches is often arbitrary, contrary to the notion of hierarchy. Since a tree is a kind of graph, and a graph is often represented by a matrix, we show the linear algebraic representation of trees, specifying conjunction heights. Thereafter, we explain the ‘reachability’ between pitch events (corresponding to information about reduction) by the multiplication of matrices. In addition we discuss multiplication with vectors representing a sequence of harmonic functions, and suggest the notion of stability. Finally, we discuss operations between matrices to model compositional processes with simple algebraic operations

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

A Musicological Study of the Japanese Koto using Heuristic Finite Element Models

Vol. 1 A Musicological Study of the Japanese Koto using Heuristic Finite Element Models -- Vol. 2 DatasetsThis musicological study investigates the sound of the Japanese koto, a 13-string zither, using heuristic finite element models. It aims firstly to test a new integrated analytical approach with finite element methods; these methods have become more accessible to scholars across many disciplines including systematic musicology in recent decades. This thesis demonstrates how these methods can provide powerful analytical tools for technical studies of musical instruments as part of organological research. Secondly, it applies this method in a heuristic study of the koto to characterise its sound envelope by using a series of models; these models range from a simple box to a more complex and geometrically accurate lofted model developed as part of this study. These models permitted the continual development of the integrated analytical approach during the period of investigation. COMSOL Multiphysics®, the finite element method software used to develop the models, also enabled specialist analysis of sound from the instrument including its qualitative visual representation. Results of these models in turn were validated by comparison with the limited existing literature on the koto’s acoustics and additional physical experiments. During this process initial tests on a plank of paulownia wood were undertaken in order to understand the paulownia wood from which the koto is made. These results then informed more complex, subsequent models. Findings from the study reveal that the anisotropic nature of paulownia significantly influenced predicted resonances when compared to a simple isotropic model. Key characteristics of the koto body that help to explain the relationship between sound production and geometry of the instrument were also identified, for example, the significant influence of the curvature of the top plate and the arching down the length of the instrument on the sound envelope produced. These findings contribute to the understanding of the acoustical behaviour of the koto in particular and East Asian zithers in general. The methods identified and validated in this study also serve more broadly as a template for future organological and acoustical investigations of geometrically complex wooden musical instruments.Thesis (Ph.D.) -- University of Adelaide, Elder Conservatorium of Music, 202

Cognitive Similarity Grounded by Tree Distance from the Analysis of K.265/300e

Lerdahl and Jackendoff's theory employed a tree in a representation of internal structure of music. In order for us to claim that such a tree is a consistent and stable representation, we argue that the difference of trees should correctly reflect our coginitive similarity of music. We report our experimental result concerning the comparison of similarity among variations on Ah vous dirai-je, maman, K. 265/300e by Mozart. First we measure the theoretical distance between two variations by the sum of the lengths of time-spans, and then we compare the result with the human psychological resemblance. We show the statistical analysis, and discuss the adequacy of the distance as a metric of similarity, which moreover becomes a metrics of theory.10th International Symposium, CMMR 2013, Marseille, France, October 15-18, 2013. Revised Selected Paper

2012-2013 Course Catalog

An annual catalog of courses and course descriptions offered at the University of Montana.https://scholarworks.umt.edu/coursecatalogs_asc/1043/thumbnail.jp

2011-2012 Course Catalog

An annual catalog of courses and course descriptions offered at the University of Montana.https://scholarworks.umt.edu/coursecatalogs_asc/1042/thumbnail.jp

Resource discovery in heterogeneous digital content environments

The concept of 'resource discovery' is central to our understanding of how users explore, navigate, locate and retrieve information resources. This submission for a PhD by Published Works examines a series of 11 related works which explore topics pertaining to resource discovery, each demonstrating heterogeneity in their digital discovery context. The assembled works are prefaced by nine chapters which seek to review and critically analyse the contribution of each work, as well as provide contextualization within the wider body of research literature. A series of conceptual sub-themes is used to organize and structure the works and the accompanying critical commentary. The thesis first begins by examining issues in distributed discovery contexts by studying collection level metadata (CLM), its application in 'information landscaping' techniques, and its relationship to the efficacy of federated item-level search tools. This research narrative continues but expands in the later works and commentary to consider the application of Knowledge Organization Systems (KOS), particularly within Semantic Web and machine interface contexts, with investigations of semantically aware terminology services in distributed discovery. The necessary modelling of data structures to support resource discovery - and its associated functionalities within digital libraries and repositories - is then considered within the novel context of technology-supported curriculum design repositories, where questions of human-computer interaction (HCI) are also examined. The final works studied as part of the thesis are those which investigate and evaluate the efficacy of open repositories in exposing knowledge commons to resource discovery via web search agents. Through the analysis of the collected works it is possible to identify a unifying theory of resource discovery, with the proposed concept of (meta)data alignment described and presented with a visual model. This analysis assists in the identification of a number of research topics worthy of further research; but it also highlights an incremental transition by the present author, from using research to inform the development of technologies designed to support or facilitate resource discovery, particularly at a 'meta' level, to the application of specific technologies to address resource discovery issues in a local context. Despite this variation the research narrative has remained focussed on topics surrounding resource discovery in heterogeneous digital content environments and is noted as having generated a coherent body of work. Separate chapters are used to consider the methodological approaches adopted in each work and the contribution made to research knowledge and professional practice.The concept of 'resource discovery' is central to our understanding of how users explore, navigate, locate and retrieve information resources. This submission for a PhD by Published Works examines a series of 11 related works which explore topics pertaining to resource discovery, each demonstrating heterogeneity in their digital discovery context. The assembled works are prefaced by nine chapters which seek to review and critically analyse the contribution of each work, as well as provide contextualization within the wider body of research literature. A series of conceptual sub-themes is used to organize and structure the works and the accompanying critical commentary. The thesis first begins by examining issues in distributed discovery contexts by studying collection level metadata (CLM), its application in 'information landscaping' techniques, and its relationship to the efficacy of federated item-level search tools. This research narrative continues but expands in the later works and commentary to consider the application of Knowledge Organization Systems (KOS), particularly within Semantic Web and machine interface contexts, with investigations of semantically aware terminology services in distributed discovery. The necessary modelling of data structures to support resource discovery - and its associated functionalities within digital libraries and repositories - is then considered within the novel context of technology-supported curriculum design repositories, where questions of human-computer interaction (HCI) are also examined. The final works studied as part of the thesis are those which investigate and evaluate the efficacy of open repositories in exposing knowledge commons to resource discovery via web search agents. Through the analysis of the collected works it is possible to identify a unifying theory of resource discovery, with the proposed concept of (meta)data alignment described and presented with a visual model. This analysis assists in the identification of a number of research topics worthy of further research; but it also highlights an incremental transition by the present author, from using research to inform the development of technologies designed to support or facilitate resource discovery, particularly at a 'meta' level, to the application of specific technologies to address resource discovery issues in a local context. Despite this variation the research narrative has remained focussed on topics surrounding resource discovery in heterogeneous digital content environments and is noted as having generated a coherent body of work. Separate chapters are used to consider the methodological approaches adopted in each work and the contribution made to research knowledge and professional practice

2010-2011 Course Catalog

An annual catalog of courses and course descriptions offered at the University of Montana.https://scholarworks.umt.edu/coursecatalogs_asc/1041/thumbnail.jp