This thesis contains a collection of results in computational geometry that are inspired from music theory literature. The solutions to the problems discussed are based on a representation of musical rhythms where pulses are viewed as points equally spaced around the circumference of a circle and onsets are a subset of the pulses. All our results for rhythms apply equally well to scales, and many of the problems we explore are interesting in their own right as distance geometry problems on the circle. / In this thesis, we characterize two families of rhythms called deep and Euclidean. We describe three algorithms that generate the unique Euclidean rhythm for a given number of onsets and pulses, and show that Euclidean rhythms are formed of repeating patterns of a Euclidean rhythm with fewer onsets, followed possibly by a different rhythmic pattern. We then study the conditions under which we can transform one Euclidean rhythm to another through five different operations. In the context of measuring rhythmic similarity, we discuss the necklace alignment problem where the goal is to find rotations of two rhythms and a perfect matching between the onsets that minimizes some norm of the circular distance between the matched points. We provide o (n2)-time algorithms to this problem using each of the ℓ1, ℓ2, and ℓinfinity norms as distance measures. Finally, we give a polynomial-time solution to the labeled beltway problem where we are given the ordering of a set of points around the circumference of a circle and a labeling of all distances defined by pairs of points, and we want to construct a rhythm such that two distances with a common onset as endpoint have the same length if and only if they have the same label.

This thesis studies measures of musical rhythm complexity. Informally, rhythm complexity may be thought of as the difficulty humans have performing a rhythm, listening to a rhythm, or recognizing its structure. The problem of understanding rhythm complexity has been studied in musicology and psychology, but there are approaches for its measurement from a variety of domains. This thesis aims to evaluate rhythm complexity measures based on how accurately they reflect human-based measures. Also, it aims to compare their performance using rhythms from Africa, India, and rhythms generated randomly. The results suggest that none of the measures accurately reflect the difficulty humans have performing or listening to rhythm; however, the measures do accurately reflect how humans recognize a rhythm's metrical structure. Additionally, the results suggest a need for normalization of the measures to account for variety among cultural rhythms.

In this paper, the mathematical theory of languages is used to investigate and develop computer systems for music analysis, composition, and performance. Four prominent research projects in the field are critically reviewed. An original grammar-type for the computer representation of music is introduced, and a computer system for music composition and performance based on that grammar is described. A user's manual for the system is provided as an appendix.

No description available.

This study attempted to demonstrate that original composition for film can function as a basis for the examination of the technical and expressive factors of music and their interdependence. The study developed a series of creative projects designed as adjunct learning experiences in lower-division music theory classes. These projects were not developed to serve as a complete music theory curriculum. They were designed as a series of supplementary experiences intended to complement the study of the materials, structure and principles as covered in the main core of the curriculum.One section each of freshman and sophomore theory served as the population for the experiment. Continuity of student membership remained fairly constant throughout the academic year. Each class ranged in size from ten to thirteen members with a representative sampling of singers, pianists and players of string, wind, brass and percussion instruments.Students were assigned various film music projects ranging in length from thirty seconds to six minutes. The early compositions from the beginning of each academic year were intentionally limited in scope in one manner or another one instrument and sixty-five-seconds for two instruments. The scope of the experiences gradually expanded until students were composing four- to six-minute compositions for five to ten performers.Not all projects utilized complete films. In some instances a longer film was divided among several students with each one composing for a particular segment. with few exceptions, these compositions were written specifically for the performers available in each class. Therefore, each composer had to work with and reconcile a wide variety of instrumental combinations and range of performing abilities.The style and expressive content of the various films utilized afforded each student the opportunity to explore a broad range of visual experiences. All films used were available through the Ball State University Film :service . Students were permitted to view films at any time during the regular sixty-seven' hours per week provided by the Film Service schedule.An introduction to the study is presented in Chapter I. Chapter TI is devoted to a review of selected literature concerning composition of music for film, creative musical activities in the schools and lower-division music theory in higher education. Chapter III presents the procedures and technical aspects undertaken to implement the study. Chapters IV and V, respectively, offer a report and analysis of the freshman and sophomore project series.music scores from each project. The more successful compositions from the project series are included in Chapter VI. This chapter is concerned with a report of the public performance of selected compositions from the various projects. Chapter VII includes summary comments, recommendations and discussion.

Thesis (Ph. D.)--University of Rochester, 1941. / Typewritten. "Complete list of Hindemith's works": p. 405-414. Bibliography: p. [415]-420. Digitized version available online via the Sibley Music Library, Eastman School of Music http://hdl.handle.net/1802/11574

Thesis (Ph.D.) -- Florida State University, 2003. / Advisor: Dr. Jane Piper Clendinning, Florida State University, School of Music. Title and description from dissertation home page (viewed Mar. 10, 2004) Document formatted into pages; contains 251 pages. Includes biographical sketch. Includes bibliographical references.

Thesis (M.Ed.)--University of Melbourne, Faculty of Education, 2000. / Typescript (photocopy). Includes bibliographical references (leaves 163-166).

Thesis (Ph. D.)--University of Chicago, Department of Music, August 2002. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph.D.)--Michigan State University, 2001. / Includes bibliographical references (leaves 545-562).