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

Thesis (M.M.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on April 4, 2008) Includes bibliographical references.

Thesis (Ph.D.) -- McMaster University, 2002. / Includes bibliographical references (leaves 250-253). Also available via World Wide Web.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Psychology, 2004. / Includes bibliographical references.

Thesis (M.F.A.)--Rochester Institute of Technology, 2006. / Typescript. Includes bibliographical references.

The perception of musical intervals by musicians can be envisaged as being accomplished in one of two ways. Most musicians appear to have only one method for identifying musical intervals: they directly evaluate the musical interval between two notes. Musicians with absolute pitch (AP) appear to have two methods available for identifying intervals: they can either directly evaluate the musical interval, or they can first identify the two pitches, and then infer the musical interval between them. This study investigated the perception of sequential musical intervals by two groups of musicians, one group with AP and the other without AP. In the first of four experiments, most subjects in both groups were able to name accurately standard sequential musical intervals based on the equal-tempered scale. In the second experiment, most subjects in the AP group were able accurately and consistently to name notes of the equal-tempered scale, whereas subjects without AP were not able to name them consistently or accurately. In the third experiment, subjects with AP identified, with varying degrees of accuracy and consistency, single notes spaced in 20-cent increments over a 9.4 semitone range, using the standard musical note names. This experiment also demonstrated that not all subjects had the same internal pitch reference. In the final and major experiment, subjects identified sequential musical intervals ranging in 20-cent steps from 260 to 540 cents, using the standard musical interval names. Subjects, both with and without AP, appeared to identify the intervals by directly evaluating the musical interval between the two notes, rather than first identifying the two pitches and then inferring the musical interval. One subject in the AP group showed a strong tendency to use the latter method, but only in certain contexts, the reason for which remains unexplained. Although more research is needed for stronger conclusions to be drawn, it appears that most musicians with AP do not use this ability in the identification of sequential musical intervals, relying instead on their sense of relative pitch. / Medicine, Faculty of / Audiology and Speech Sciences, School of / Graduate

No description available.

While musical sources and documents from throughout the Middle Ages reveal that mode was an enduring and consciously derived trait of monophonic chant, modality in later polyphony shares neither the historical span nor the theoretical clarity of its monophonic counterpart. Modern theorists are left with little more than circumstantial evidence of the early development of modality in polyphony. This study attempts to shed light on the problem by detailed analysis of a select body of paraphrase masses from the early sixteenth century. First, it correlates the correspondence between the paraphrased voice and the original chant, establishing points of observation that become the basis of melodic analysis. Then, these points are correlated with known rules of counterpoint. Exceptions are identified and examined for their potential to place emphasis on individual mode-defining pitches. A set of tools is derived for quantifying the relative strength of cadential actions. Levels of cadence are defined, ranging from full, structural cadences to surfacelevel accentuations of individual pitches by sixth-to-octave dyadic motions. These cadence levels are traced through the Missae de beata virqine repertoire from c. 1500-1520, a repertoire that includes masses of Josquin, Brumel, La Rue, Isaac, and Rener. While the Credos, based on two chant sources—one early (11th century) and one later (15th century)—showed little modal consistency, the Kyries show some suggestion of purposeful modal expression; and the Glorias show even greater implications. Results of the study have potential application in sixteenth-century music scholarship to such important issues as musica ficta, performance practice, text underlay, and form.

The purpose of this thesis is to provide translation of documents on lu from two primary sources for a study of the theory of ,lu, with the main focus on the interpretation and the signification attached to each of the twelve lu-pitch names. To establish the background information of the lu-10 system, an explanation of its acoustical properties is first presented. Based on the most important and widely used tonal system in ancient China -- the san-fen-sun-i system, the illustration is provided for the process of tone generation. Methods proposed by the main theorists who engaged in the discussion of the system of lu are presented. The introduction of the concept of yin and yang in reference to the twelve lu and the signification of the lu-lu system in relation to the human and natural world will also be discussed. The main body of this study is devoted to the translation of written references on the meaning of the twelve lu. The first part is the translation of the selected passages from The Anthology of the Historical Document of Ancient Chinese Music. edited by Tsai-Ping Liang; the second part is the translation of a modern exegesis from an article written by Deh-I Liu. This translation offers a perspective to understand the concept of l-pitch names from the ancient points of view in relation to philosophy, education, religion, and science.

[by] Adrianus J.M. Houtsma and Julius L. Goldstein. / Based on a Ph.D. thesis in the Dept. of Electrical Engineering, 1971, by A.J.M. Houtsma. / Bibliography: p. 71-75.