This thesis presents and analyzes tools and experiments that aim at achieving multiple yet related goals in the exploration and manipulation of musical cyclic rhythms. The work presented in this thesis may be viewed as a preliminary study for the ultimate future goal of developing a general computational theory of rhythm. Given a family of rhythms, how does one reconstruct its ancestral rhythms? How should one change a rhythm's cycle length while preserving its musicologically salient properties, and hence be able to confirm or disprove popular or historical beliefs regarding its origins and evolution? How should one compare musical rhythms? How should one automatically generate rhythmic patterns? All these questions are addressed and, to a certain extent, solved in our study, and serve as a basis for the development of novel general tools, implemented in Matlab, for the manipulation of rhythms.

This research constitutes a detailed study of 5 - 6 voice-leading technique that is often found in music - theoretical literature and in the tonal repertoire. The study aims to prove that this technique is an essential theoretical and analytical concept for understanding the evolution of tonal music. / The first part of this study examines concepts and descriptions of 5 - 6 technique as they appear in the theoretical literature of the eigthteenth and nineteenth centuries and in the writings of Heinrich Schenker and the modern Schenkerian school. The descriptions of 5 - 6 technique in earlier conterpoint, figured-bass and harmony treatises led Schenker and his disciples to place the technique in a much broader context, though even they do not always grasp the full implications of their procedures. / In the light of William Caplin's recent theory of formal functions, (Caplin 1985; 1998), the second part of the thesis in a substantial selection of musical excerpts from the eighteenth through the early twentieth centuries, demonstrates that 5 - 6 technique as a contrapuntal analatycal concept, provides an effective model for understanding the development of chromaticism and the extension of the tonal language at multiple structural levels.

Composers have long been interested in authentic materials from their own national heritage. Many composers favored folk-based melodies and rhythms. Bela Bartok, for example, collected volumes of Hungarian folk and gypsy melodies throughout his life. Igor Stravinsky's three ballets ( Firebird, Petrushka , and The Rite of Spring ) are also famous for their employment of folk melodies and primitive rhythms. American composers such as Charles Ives and Aaron Copland represented 'Americana' through the use of American pop music, jazz, and folk songs in their compositions. Much of the music of composers who emigrated to foreign countries represents strong implications of nationalism. These composers' efforts to remember their origins, as well as nostalgia for their native culture, were expressed in their music. These qualities appear most interestingly in Asian composers such as Toru Takemitsu and Isang Yun. Despite the drastic difference between Asian and Western music, the two contrasting idioms are handled similarly by these two composers. They not only use non-Western musical materials such as folk melodies and rhythms, but also employ Asian titles, concepts, and traditional instruments to represent Asian inspiration in their music. The composition Lily Park consists of three movements, entitled Wind Bell, Goblin Lights , and Rock of Ages . The three movements are based on my personal impressions of the cemetery Lily Park, located near Deagu, Korea, where all my grandparents are buried. In this composition, Western musical idioms are integrated with the composer's Asian musical heritage. The concept of Lily Park , which is purely non-Western in origination, is realized by utilizing compositional techniques and concepts that have been developed by Western composers, such as tone color, tonality, pitch-class set theory, and serialism, with an ensemble that consists of Western instruments. These ideas are combined with Asian materials such as exotic scales, extended performance techniques associated with Asian music, and ideas that are associated with Asian philosophical and religious thought (the sacredness of the number three, use of space, and isolation).

This paper expands on the work of David Lewin, whose seminal work Generalized Musical Intervals and Transformations proposes, among other functions, the interval function or IFUNC. The interval function catalogs the type and number of directed pitchclass intervals between two different pitch-class sets. This paper proposes the concept of the IFUNC array, an ordered sequence of twelve digits representing the IFUNC values for an interval i = 0–11, reading either left to right or clockwise around a circle. It explores features of the interval function, including symmetry in the IFUNC array, and includes analysis of several excerpts from Anton Webern’s early atonal works. The paper addresses axes of symmetry, both in pitch-class sets and in interval functions. / School of Music

The purpose of this study was to provide a series of teaching units to assist the high school band director in integrating music theory into the daily rehearsal schedule. These units provide a workable alternative to the teaching of music theory within the large performing ensemble.Teaching Units1. All musical examples in these units were written to reinforce the explanations of the given lesson material, and all musical exercises were written to be sung and to be played on the student's own instrument.2. The organization of the teaching units was designed to be flexible enough to meet the individual needs of teachers and students in the band rehearsal.3. Representative material for this study included intervals, modes, major and minor scales, pitch-class and interval-class, triads, seventh chords, and transposition.4. These lessons provided short, sequential units of instruction which were designed to provide opportunities for creative musical development and understanding of our musical languageConclusions1. The systematic utilization of theoretical material and creative exercises will promote an understanding of the relationships between the visual and aural elements of music; it will provide an aid in the performance of the students' musical duties; it will increase the overall musicianship of the ensemble.2. There is a tremendous need for an integrated music curriculum from grades K-12.

This study engages a network of music, myth, and metaphysics within late-ancient and twelfth-century music theory and cosmology. It traces the development, expansion, and demise of a (natural-)philosophical harmonic speculation that stems largely from an a priori commitment to a harmonic cosmology with its deepest roots in Plato’s Timaeus. It argues that music theory not only allowed twelfth-century thinkers to conceptualize the fabric of the universe, but it also provided a hermeneutic tool for interpreting the ancient and late-ancient texts that offered detailed theories of the world’s construction. The twin goals of this study are thus philosophical and musicological: firstly and philosophically, to analyze and re-assert the importance of musical speculation in the writings of the self-styled physici, who probed the physical world and its metaphysical foundations during the ‘Twelfth-Century Renaissance’; secondly and musicologically, to document the sources and scope of this musical speculation and to situate it within the larger tradition of ‘speculative music theory.’ The first part of the thesis (chapters one and two) disentangles the knotty question of sources for and connections between the late-ancient texts (by Calcidius, Macrobius, and Boethius) that form the background of twelfth-century thought, and it sketches the proper domain of musical thought by tracing the expansion of music’s role in quadrivial and natural-philosophical contexts from late-ancient encyclopedism though various twelfth-century divisiones scientiae. The second part of the thesis (chapters three through five) assembles and analyzes the direct evidence for twelfth-century harmonic theory. These chapters, heuristically organized around the Boethian tripartition of music, present an anagogic ascent per aspera ad astra. Chapter three (musica instrumentalis) highlights the occasional and perhaps surprising employ of practical, technical music theory in cosmological contexts, and focuses on the epistemological foundations of hearing and the ontological status granted to the sonorous ‘objects’ of hearing. Chapter four (musica humana) targets the anthropological, psychological, and ethical implications of musical relations in and between body and soul. Finally, chapter five (musica mundana) outlines the cosmological framework, the anima mundi in particular, that underpins the concordant machinations of the machina mundi in all its manifestations.

This study engages a network of music, myth, and metaphysics within late-ancient and twelfth-century music theory and cosmology. It traces the development, expansion, and demise of a (natural-)philosophical harmonic speculation that stems largely from an a priori commitment to a harmonic cosmology with its deepest roots in Plato’s Timaeus. It argues that music theory not only allowed twelfth-century thinkers to conceptualize the fabric of the universe, but it also provided a hermeneutic tool for interpreting the ancient and late-ancient texts that offered detailed theories of the world’s construction. The twin goals of this study are thus philosophical and musicological: firstly and philosophically, to analyze and re-assert the importance of musical speculation in the writings of the self-styled physici, who probed the physical world and its metaphysical foundations during the ‘Twelfth-Century Renaissance’; secondly and musicologically, to document the sources and scope of this musical speculation and to situate it within the larger tradition of ‘speculative music theory.’ The first part of the thesis (chapters one and two) disentangles the knotty question of sources for and connections between the late-ancient texts (by Calcidius, Macrobius, and Boethius) that form the background of twelfth-century thought, and it sketches the proper domain of musical thought by tracing the expansion of music’s role in quadrivial and natural-philosophical contexts from late-ancient encyclopedism though various twelfth-century divisiones scientiae. The second part of the thesis (chapters three through five) assembles and analyzes the direct evidence for twelfth-century harmonic theory. These chapters, heuristically organized around the Boethian tripartition of music, present an anagogic ascent per aspera ad astra. Chapter three (musica instrumentalis) highlights the occasional and perhaps surprising employ of practical, technical music theory in cosmological contexts, and focuses on the epistemological foundations of hearing and the ontological status granted to the sonorous ‘objects’ of hearing. Chapter four (musica humana) targets the anthropological, psychological, and ethical implications of musical relations in and between body and soul. Finally, chapter five (musica mundana) outlines the cosmological framework, the anima mundi in particular, that underpins the concordant machinations of the machina mundi in all its manifestations.

The Saṅgītanārāyaṇa, attributed to the Gajapati king Nārāyad nadeva of Parlākhimidi but almost certainly composed by his guru Kaviratna Purud sottamamisra, is the most extensive surviving Sanskrit treatise on music to have been composed in the eastern region of India now known as Orissa. The treatise contains four chapters, gītanirnaya (on vocal music), vādyanirṇaya (on instruments), nāṭyanirṇaya (on dance and the mimetic art), and śuddhaprabandhodāharaṇa (sample compositions of the śuddha and sālaga varieties). The thesis contains a critical edition of the first, second and fourth of these chapters with an English translation, commentary and introduction. Though the whole text was issued in a printed edition by the Orissa Sangeet Natak Akademi in 1966, the new edition offers substantial revisions and corrections to the published version. Eleven manuscripts have been examined; these are in Nagari, Bengali and Oriya scripts and are held in collections in Orissa, in other South Asian libraries, and in two British libraries. All of the manuscript evidence has been presented in a critical apparatus and in a section of supplementary textual notes. The commentary examines the technical contents of the work in detail and places the treatise within its Eastern Indian context. Special attention is drawn to certain subjects, for instance the account of compositional forms and metres, which represent a regional tradition, but all topics are placed also against the background of Sanskrit musicological traditions from other parts of India; some topics in the traditional sastra are thereby re-examined. In the introduction, the historical setting of the work is assessed, and the manuscript evidence is summarised. The proposed stemma codicum shows two groups of manuscripts, one from Orissa and one based in North India; manuscripts discovered in the future are expected to fit into one of these two.

The core of this study is a new edition and translation of the Proportionale musices of Iohannes Tinctoris (c.1435-1511). The text is preceded by two introductory sections devoted, first, to reviewing the evidence for Tinctoris's biography and the chronology of his treatises as a whole, and, secondly, to examining the sources employed in the edition. In the section on chronology some new information is presented concerning the printing of the incunabulum De inuentione et usu musice, and on the scope of the original compilation from which the contents of the print were excerpted. In the discussion of sources, the first detailed description of the principal Brussels manuscript is given, in which some evidence is adduced for believing this to be an authorial holograph. Some refinements are also made to current knowledge regarding the dating and provenance of the Valencia and Bologna University Library sources. Following the translation of the Proportionale, some notes on the text are offered. Appendices present (a) the documentary biographical material discussed at the opening; (b) a littie-studied letter from Tinctoris to Joanmarco Ginico; (c) Tinctoris's translation into Italian of the Statutes for the Order of the Golden Fleece; and (d) a transcription of some new fragments of De inuentione et usu musice, rediscovered recently in Cainbrai.

<p>A semiminim is typically defined as a note value worth half a minim, usually drawn as a flagged or colored minim. That definition is one according to which generations of scholars have constructed chronologies and provenances for fourteenth- and fifteenth-century music and the people who created it. `Semiminims' that do not match this definition are often portrayed in modern scholarship as anomalous, or early prototypes, or evidence of poor education, or as peculiarities of individual preference. My intensive survey of the extant theoretical literature from the earliest days of the Ars Nova through c. 1440 reveals how the conceptualization and codification of notation occurred in different places according to different fundamental principles, resulting not in one semiminim but a plethora of related small note values. These phenomena were dynamic and unstable, and a close study of them helps to clarify a range of historical issues. Localized traditions have often been strictly bounded in scholarly literature; references to French, Italian, and English notation are commonplace. I explain notational preferences in Italy, England, central Europe, and the rest of western Europe with regard to these small note values but demonstrate that theorists educated in each of these places routinely incorporated portions of other traditions. This process began long before the `ars subtilior,' dating at least to the time of Franco of Cologne. Rarely were regional traditions truly isolated; the various aspects of semiminim-family note values were debated and adapted for decades across these cultural and geographical boundaries. The central theme of my research is to show how and why the theoretical conceptualization of these myriad small note values is key to understanding the continual merging of these local preferences into a more amalgamated style of notation by the mid-fifteenth century.</p> / Dissertation