This thesis develops an analytical approach to the instrumental music of Orlando Gibbons (1583-1625) based on close readings of historical theory sources, primarily by Thomas Morley, John Coprario and Thomas Campion. Music of the early seventeenth century can be difficult to analyse, since it falls between the more extensively studied and theorised practices of classic vocal polyphony and common-practice tonality. Although English music theory of this period is recognised as strikingly modern in many respects, innovative aspects of English compositions from the same period receive little attention in standard accounts of the seventeenth century. I argue that concepts taken from this body of historical theory provide the basic terms of a technical vocabulary for analysis, which should be further refined through application to real compositions. Successive chapters deal with common counterpoint models or patterns, imitative invention and disposition, cadential progressions, and overall tonal structure. I argue that these analyses show Gibbons's music to be a contribution to new ways of conceiving of instrumental polyphony and tonal structure, which deserves re-evaluation in the context of broader seventeenth-century trends. In particular, Gibbons's use of extended cadential expectations as an expressive element, fascination with sequential progressions, and sectional structuring by harmonic area have clear parallels with later practices. At the same time, early seventeenth century style allows the composer considerably more freedom of harmonic procedures and implications than the musical styles which immediately followed it. Analysis grounded in historical theory provides the best approach to understanding and appreciating this unique musical language.

Bart6k's own expanded tonal ("supradiatonic") pronouncements reveal that his music, notwithstanding tonally camouflaging surface details, clearly had a tonal foundation which in many respects is a reaction to the emerging atonalism of Schonberg. Analysis of three piano works (1908 - 1916) reveal that Bart6k's tonal language embraced intuitively the expanded tonal idiom. The harmonic resources Bart6k employed to obscure tonicisation embrace double-degree constructions, quartal formations, chords of addition and omission and other irregular constructions. Diatonic tonal pillars are evident in pedal points, tonic triads and dominant to tonic root movement. Through an application of the Riemann function theory expanded by Hartmann's supposition of fully-chromaticised scales tonal syntax (especially secondphase Strauss cadences or closes) becomes apparent within an expanded tonal product. The analyses conclude that Bart6k's inimitable "sound-world" is a twentieth-century manifestation of traditional tonality's primary tenets. / Musicology / M.Mus.

In this thesis, we study the following three types of periodic string patterns and some of their variants. Firstly, we consider maximal d-repetitions. These are substrings that are at least 2+d times as long as their minimum period. Secondly, we consider 3-cadences. These are arithmetic subsequence of three equal characters. Lastly, we consider maximal pairs. These are pairs of identical substrings. Maximal d-repetitions and maximal pairs of uncompressed strings are already well-researched. However, no non-trivial upper bound for distinct occurrences of these patterns that take the compressed size of the underlying strings into account were known prior to this research. We provide upper bounds for several variants of these two patterns that depend on the compressed size of the string, the logarithm of the string's length, the highest allowed power and d. These results also lead to upper bounds and new insights for the compacted directed acyclic word graph and the run-length encoded Burrows-Wheeler transform. We prove that cadences with three elements can be efficiently counted in uncompressed strings and can even be efficiently detected on grammar-compressed binary strings. We also show that even slightly more difficult variants of this problem are already NP-hard on compressed strings. Along the way, we extend the underlying geometry of the convolution from rectangles to arbitrary polygons. We also prove that this non-rectangular convolution can still be efficiently computed.:1 Introduction 2 Preliminaries 3 Non-Rectangular Convolution 4 Alphabet Reduction 39 5 Maximal (Sub-)Repetitions 6 Cadences 7 Maximal Pairs A Propositions

This study is concerned with the vertical combinations resulting from late sixteenth century cadential formulae and in passages immediately preceding these formulae. The investigation is limited to Masses dating from the last half of the sixteenth century and utilizes compositions from the following composers: Handl, Kerle, Lassus, Merulo, Monte, and Palestrina, Victoria. This study concludes that the progressions I-V-I and I-IV-I appear to be the only two root progressions receiving high enough percentages to be regarded as significant. These percentages are tempered by the fact that I-V-I and I-IV-I may be interpreted as repetitions of standardized cadential formulae found in the sixteenth century. The study also concludes that root motion by fifth accounts for no less than 67.35 per cent of the root movements analyzed during the investigation. The percentage differential between root movement by fifth and root movement by second (the interval receiving the next highest percentage) at no time drops below 40.41 per cent. The evidence indicates that root movement by fifth does account for the majority of the root motion analyzed in final cadential passages of Masses dating from the late sixteenth century. The percentage differential between root motion by second and root motion by third decreases as the chord progressions become longer. None of the differential percentages were judged to be high enough as to merit placing any significance of root motion by second over root motion by third.

Pianists often have trouble in determining where a phrase ends, or in other words, cadence identification. This is especially true of certain cadences that can be considered either as half cadences or authentic cadences. This analytically ambiguous cadential point can result in different performance decisions, so pianists should make informed decisions about what kind of cadence it is. This study aims to investigate such cadential ambiguity shown at points of phrase boundaries by focusing on Chopin's Piano Sonata No. 2 in B-flat minor, Op. 35, first movement. I offer both possibilities (a half cadence or an authentic cadence) at the phrase ending, suggesting a performance-related strategy based on each possibility. My objective is not to support only one cadential status, but to bring up the cadential problem from the analytical perspective and to demonstrate how cadence identification affects performance results. The dissertation is divided into two parts: analysis and performance, so it relies on a combined method of analytical terminologies and performance-related musical elements. In the analysis, the terminology of William Caplin is employed. The performance part refers to several method books written by prestigious piano pedagogues. After an introduction in Chapter 1, Chapter 2 reviews some literature on cadences. Chapter 3 specifically analyzes the first movement of Chopin's second sonata by means of Caplin's terminologies. Chapter 4 provides a performance-related method and Chapter 5 deals with a practical performance strategy.