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One goal of music theory is to describe the resources of a pitch system. Traditionally, the study of pitch intervals was done using frequency ratios of the powers of small integers. Modern mathematical music theory offers an independent way of understanding the pitch system by considering intervals as transformations. This thesis takes advantage of the historical emergence of algebraic structures in musicology and, in the spirit of transformational theory, treats operations that form mathematical groups. Aspects of Neo-Riemannian theory are explored and developed, in particular the T/I and PLR groups as dual. Pitch class spaces, such as 12, can also be defined as torsors. In addition to surveying the group theoretical tools for music analysis, this thesis provides detailed proofs of many claims that are proposed but seldom supported.

The tonal organization of the first-movement development sections of ten Haydn symphonies (nos. 1, 4, 6, 10, 13, 15, 19, 24, 31 and 72), all in D major composed between 1758 and 1765, is directly linked to eighteenth-century theories of modulation. The recent theoretical or musicological literature, with the exception of H. C. Robbins Landon's Haydn: Chronical and Works (1976--1980), has concentrated on Haydn's later high classical style generally ignoring these earlier works composed during his largely self-didactic, most formative years. After evaluating the analytical procedures established by Webster (1991), Wheelock (1992), Sisman (1993) and Haimo (1995) in chapter one, chapter two reviews tonal theories of some eighteenth-century writers. Chapter three presents analytical observations on the Morzin Symphonies (nos. 1, 15, 4, 10). Chapter four extends the discussion of chapter two and focuses on theoretical concepts that determine rank ordering of scale-steps in relation to the tonic. Chapter five focuses on tonal procedures employed in the developments of early Esterhazy symphonies (nos. 6, 13, 72, 24, 31) all of which feature cadentially-confirmed tonicizations of scale-step vi paired with recapitulatory from the main theme. (Abstract shortened by UMI.)

This study aims to examine the ways in which English composer Edward Elgar (1857–1934) expanded common-practice tonality; it shows how Elgar employed harmonic structures and syntax in an innovative manner through specific extended-tonal techniques such as the use of chromatic-third relations (both harmonically and as a tonal plan), harmonic substitutions, and local ambiguous sonorities that at times lead to tonal ambiguity. The system that Elgar expanded upon has been called “Classical diatonic tonality”, which was extended when late nineteenth-century composers such as Elgar infused their music with chromaticism. Through an investigation of Elgar’s extended tonal techniques one can come to a better appreciation of his late nineteenth-century harmonic vocabulary. It has been well documented that Elgar modeled his music after that of Wagner and his Germanic contemporaries (from Mendelssohn to Brahms), so that the Elgarian tonal language is one possible projection of a post-Wagnerian extended-tonal discourse. The discussion presented here will survey those parts of Elgar’s tonal language that he learned from his Germanic contemporaries, thereby establishing the context for his own unique chromatic compositional style. This study of Elgar’s work therefore further represents a study of the broader impact of post-Wagnerian chromaticism on late nineteenth-century English extended tonality.

Ioannes Fuxius per Aevum quod dicitur Baroccum, quo tempore gustus musici celeriter mutabantur, musicum enchiridion palmare, cui titulus Gradus ad Parnassum, edidit. Quo libro modos musicos componendi ratio aetate artium renatarum exorta cum ratione aevo Barocco usitata coniungitur. Auctor historiam artis musicae, vocabula artis propria, normas hoc opere docet per dialogum Latinum et faberrime scriptum, qui inter Palestrinae personam et eam discipuli personam, quam auctor ipse agit, habetur. At nostris temporibus Fuxius innotuit, quod quasi ante omnium oculos regulas uniuscuiusque Speciei Contrapuncti posuit. Liber eius igitur in multos sermones vernaculos est versus etiam paucis annis post primam divulgationem. Nunc temporis quoque in scholis musicis in omnibus orbis terrarum partibus sitis docetur. Hanc commentatiunculam paravi in usum discipulorum qui capita, ubi Species Contrapuncti duarum vocum enodantur, Latino sermone primigenio atque perlucido legere vellent. During the Baroque Era, a time of quickly-changing musical tastes, Johann Fux wrote a seminal music composition textbook, the Gradus ad Parnassum, that bridges the gap between Renaissance Counterpoint and High Baroque Style. Through the beautifully-written, Latin dialog between a teacher (in the persona of Palestrina) and a student (Fux himself), the author teaches the reader about the history, nomenclature and norms of composition. Today the name Fux is synonymous with Species Counterpoint and his celebrated text, translated into many vernacular languages within years of its first publication, is read in music-theory classrooms around the world. This commentary is prepared for the use of students who wish to read the chapters on two-voice Species Counterpoint in the original, and highly accessible Latin.

Syftet med denna studie är att, med inspiration av etnografiska tillvägagångssätt, ut- forska hur några lärare utformar sin undervisning i ämnet musikteori (och gehör) på gymnasial nivå, med fokus på framförallt balans mellan teoretiska och praktiska mo- ment. Den litteratur som tas upp i uppsatsens bakgrund beskriver hur elever eller lärare kan utföra olika läroböckers övningar, dels med hjälp av praktiska verktyg, dels utifrån teoretiska resonemang. Den tidigare forskning som tas upp handlar om elever och lära- res syn på ämnet gehörs- och musikteori. De forskningsmetoder som har använts i före- liggande studie utgår ifrån ett etnografiskt perspektiv med deltagande observation, där forskaren befinner sig i fält med aktörer som skall observeras i sin naturliga miljö. Re- sultatet är uppdelat i tre teman: Inledning och handlingsförlopp, Praktiskt delaktighet samt Lärarnas arketyper. Temat Inledning och handlingsförlopp belyser hur lärarna på- börjar sin lektion, vilka uppgifter som tilldelas eleverna och hur lärarna avslutar lekt- ionerna. I temat Praktisk delaktighet presenteras de praktiska moment som förekom i undervisningen: dialog, diskussion och aktivt lyssnande. Temat Lärarnas arketyper fo- kuseras på olika roller som lärarna faller in i vid olika situationer: bergsklättraren, mäs- tare och lärjunge, samt bollplank. I diskussionen jämförs resultatet med tidigare forsk- ning samt litteratur. I diskussionen dras även några slutsatser och avslutningsvis besk- rivs arbetets betydelse samt hur det kan användas i fortsatt forskning. / The purpose of this essay is, with inspiration from ethnographic method, to explore how teachers design their lessons in the subject music theory at upper secondary school lev- el, with focus on the balance between theoretical and practical element. The literature that is presented in the background chapter describes how students or teachers can per- form the exercises in the books, by using practical tools, as well as by using theoretical arguments. The earlier research that is presented focuses on student’s and teacher’s view on the subject music theory and ear training. The research methods that have been used are based on an ethnographic perspective with participating observation, where the researcher finds him self in a field with participants whom are to be observed in their natural environment. The result is divided in three parts: Introduction and course of actions, Practical participation, and Archetypes of the teachers. Introduction and course of actions illustrates how the teachers begin their classes, what tasks they give the stu- dents, and also how the teachers finish their classes. Practical participation presents the practical elements that occurred during the classes. These elements were dialogue, dis- cussion, and active listening. Archetypes of the teachers focuses on the different roles the teachers takes during certain situations: the mountain climber, master and apprentice, and the sounding board. In the discussion the result is compared to earlier research and also to the literature. Some conclusions are also made in the discussion, At the end of the study the importance of the essay is described as well as how it can be used in later re- search.

A pitch spelling algorithm predicts the pitch names (e.g., C♯4, B♭5 etc.) of the notes in a passage of tonal music, when given the onset-time, MIDI note number and possibly the duration and voice of each note. A new algorithm, called ps13, was compared with the algorithms of Longuet-Higgins, Cambouropoulos, Temperley and Chew and Chen by running various versions of these algorithms on a ‘clean’, score-derived test corpus, C, containing 195972 notes, equally divided between eight classical and baroque composers. The standard deviation of the accuracies achieved by each algorithm over the eight composers was used to measure style dependence (SD). The best versions of the algorithms were tested for robustness to temporal deviations by running them on a ‘noisy’ version of the test corpus, denoted by C'. A version of ps13 called PS13s1 was the most accurate of the algorithms tested, achieving note accuracies of 99.44% (SD = 0.45) on C and 99.41% (SD = 0.50) on C'. A real-time version of PS13s1 also out-performed the other real-time algorithms tested, achieving note accuracies of 99.19% (SD = 0.51) on C and 99.16% (SD = 0.53) on C'. PS13s1 was also as fast and easy to implement as any of the other algorithms. New, optimised versions of Chew and Chen’s algorithm were the least dependent on style over C. The most accurate of these achieved note accuracies of 99.15% (SD = 0.42) on C and 99.12% (SD = 0.47) on C'. It was proved that replacing the spiral array in Chew and Chen’s algorithm with the line of fifths never changes its output. A new, optimised version of Cambouropoulos’s algorithm made 8% fewer errors over C than the most accurate of the versions described by Cambouropoulos himself. This algorithm achieved note accuracies of 99.15% (SD = 0.47) on C and 99.07% (SD = 0.53) on C'. A new implementation of the most accurate of the versions described by Cambouropoulos achieved note accuracies of 99.07% (SD = 0.46) on C and 99.13% (SD = 0.39) on C', making it the least dependent on style over C'. However, Cambouropoulos’s algorithms were among the slowest of those tested. When Temperley and Sleator’s harmony and meter programs were used for pitch spelling, they were more affected by temporal deviations and tempo changes than any of the other algorithms tested. When enharmonic changes were ignored and the music was at a natural tempo, these programs achieved note accuracies of 99.27% (SD = 1.30) on C and 97.43% (SD = 1.69) on C'. A new implementation, called TPROne, of just the first preference rule in Temperley’s theory achieved note accuracies of 99.06% (SD = 0.63) on C and 99.16% (SD = 0.52) on C'. TPROne’s performance was independent of tempo and less dependent on style than that of the harmony and meter programs. Of the several versions of Longuet-Higgins’s algorithm tested, the best was the original one, implemented in his music.p program. This algorithm achieved note accuracies of 98.21% (SD = 1.79) on C and 98.25% (SD = 1.71) on C', but only when the data was processed a voice at a time. None of the attempts to take voice-leading into account in the algorithms considered in this study resulted in an increase in note accuracy and the most accurate algorithm, PS13s1, ignores voice-leading altogether. The line of fifths is used in most of the algorithms tested, including PS13s1. However, the superior accuracy achieved by PS13s1 suggests that pitch spelling accuracy can be optimised by modelling the local key as a pitch class frequency distribution instead of a point on the line of fifths, and by keeping pitch names close to the local tonic(s) on the line of fifths rather than close on the line of fifths to the pitch names of neighbouring notes.

Thomas Kuhn's essay The Structure of Scientific Revolutions has had an overwhelming impact upon academics from various fields, creating a virtual paradigm industry. Authors have frequently had recourse to Kuhn's book, applying insights into the structure and development of the sciences to nonscientific fields. This essay presents a critical review of Kuhn citation in the music-theoretic literature, first reviewing similar citation analyses in the humanities and the social sciences for comparison. While much of the Kuhn citation is problematic, music scholars are found to sin less broadly than those in other fields. After reviewing some of the salient distinctions between scientific and nonscientific endeavors, some of Kuhn's insights into science are found to clarify an issue in the history of music theory, namely the nature of the succession from figured-bass theory to the formulations of J. P. Rameau.

Thesis (doctoral)--Universität Würzburg, 2004. / Includes bibliographical references.

Thesis (doctoral)--Stockholms universitet, 2002. / Extra t.p. with thesis statement and abstract inserted. Includes bibliographical references (p. [137]-143) and index.