Developing a Mathematically Informed Approach to Musical Narrative through the Analysis of Three Twentieth-Century Monophonic Woodwind Works

This project applies mathematically informed narrative to monophonic music in the twentieth century, with a focus on three works for solo woodwinds: Debussy’s Syrinx (flute), Stravinsky’s Three Pieces for Clarinet, and Britten’s “Bacchus” from Six Metamorphoses after Ovid, Op. 49 (oboe). This music poses difficulties for traditional analytical methods due to a lack of explicit harmonies and unusual pitch language that is neither functionally tonal nor serially atonal. Additionally, these pieces present a variety of challenges due to differences in length, number of movements, and presence or absence of programmatic elements. Therefore, nontraditional methods could be beneficial for understanding these idiosyncratic pieces. Mathematical and transformational approaches have shown that such descriptions can elegantly illustrate pitch language in a wide variety of tonal and atonal styles. Visual transformational and geometric approaches, such as oriented networks and graphic representations, can assist in illustrating important changes that take place during a piece. Narrative theory approaches analysis from another viewpoint. While not all music can be considered narrative, a narrative paradigm is applicable to a wide range of musical styles. Because narrative theories focus on large-scale topical and gestural changes for building interpretations, it complements the locally focused nature of transformational theory. Together, a mathematically informed narrative method can reveal connections that are not immediately obvious in these works, and help a listener or performer create an informed interpretation

Music Expectation by Cognitive Rule-Mapping

Iterative rules appear everywhere in music cognition, creating strong expectations. Consequently, denial of rule projection becomes an important compositional strategy, generating numerous possibilities for musical affect. Other rules enter the musical aesthetic through reflexive game playing. Still other kinds are completely constructivist in nature and may be uncongenial to cognition, requiring much training to be recognized, if at all. Cognitive rules are frequently found in contexts of varied repetition (AA), but they are not necessarily bounded by stylistic similarity. Indeed, rules may be especially relevant in the processing of unfamiliar contexts (AB), where only abstract coding is available. There are many kinds of deduction in music cognition. Typical examples include melodic sequence, partial melodic sequence, and alternating melodic sequence (which produces streaming). These types may coexist in the musical fabric, involving the invocation of both simultaneous and nested rules. Intervallic expansion and reduction in melody also involve higherorder abstractions. Various mirrored forms in music entail rule-mapping as well, although these may be more difficult to perceive than their analogous visual symmetries. Listeners can likewise deduce additivity and subtractivity at work in harmony, tempo, texture, pace, and dynamics. Rhythmic augmentation and diminution, by contrast, rely on multiplication and division. The examples suggest numerous hypotheses for experimental research

Dual-Aspect Meter: A Theory of Metrical Consonance, Dissonance, Weight, and Variety

The core argument of the dissertation emerges as a synthesis of ideas introduced in the first four chapters. Resonances with recent metrical theories are explored in chapter 1. Chapter 2 problematizes modern and historical theories through a phenomenological examination of meter and phenomenal accent in a few baroque sarabandes. Meter in these pieces is shown to involve entrainment to both a beat hierarchy and a recurrent weight profile, clarifying that metrical dissonance is fundamentally an expressive category, not a phenomenal category. Chapters 3 and 4 articulate a theory of weight, reviewing and refining phenomenal-accent theory, developing a notion of musical mass, and offering a simple preference-rule system for the comparison of weight between musical moments. Chapter 5 synthesizes the arguments of chapters 2–4, positing a general theory of metrical experience situated on a spectrum of perceived rhythmic consistency. I argue that a listener’s metrical attitude necessarily involves entrainment to or projection of both beat hierarchy and weight profile. The notion of dual entrainment developed in chapter 2 is thus supplemented by single entrainment and dual projection, all of which are categories of dual-aspect meter. The theory’s analytical and hermeneutic utility is demonstrated through a combined metrical and narrative analysis in appendix 1

Conflicting Lines, Cohesive Structures: Multiple-Directed Linearity in Witold Lutoslawski's Third Symphony

Witold Lutoslawski is widely recognized as having contributed numerous innovations to the twentieth-century canon of "Western" avant-garde music. His contributions include new approaches to notation and aleatoric technique (especially in ad libitum sections), formal structure "chain technique" and unusual four movement forms), and pitch organization (interval pairing and non-serial twelve-tone approaches). While emblematic of many of these qualities, Lutoslawski's Third Symphony also demonstrates an overlooked aspect of his late compositions: multiple-directed linear processes. In my essay, I focus on linear processes within several levels of the musical structure (pitch, rhythm, orchestration, register, texture, and form), applying contour theory, set theory, and statistical analysis where appropriate. In Lutoslawski's Third Symphony many levels of the structure arrive at their goal in distinct places, are simultaneously oriented in different directions, or otherwise subvert each other. In addition, singularly directed linear passages interrupt each other in horizontal succession. These types of multiple-directed linearity are the objects of my study. Although multiple-directed linearity is not exclusive to Lutoslawski's music, it is a facet that has been overlooked or mentioned only in passing within Lutoslawski studies. The composition component of my dissertation is Proximate Spaces for piano and chamber orchestra. The formal continuity of Proximate Spaces was suggested to me by competing ideas of the 1990's surrounding the search for a unified theory to explain the fundamental forces, dimensional composition, and existence of matter in the known universe. Much of the pitch material derives from a two-octave mode (18 pitches in series) and three subset hexachords of that mode. The work develops the tension between mechanistic devotion to this mode and episodes of free chromaticism, between strictly repeating rhythmic patterns and rhythmic variation, between instrumentation according to families and a free exchange of musical ideas regardless of instrumental relation. Initially aligned with the mechanistic paradigms of mode and regular rhythmic patterns, in several places the piano breaks free and attempts to incite revolt against the piece's system by abandoning strict adherence to these structures. Although some other members of the ensemble briefly depart from the system, ultimately the machine prevails

Solo Violin Works Influenced By Romanian Lăutari Music

In Romania, professional Roma (Gypsy) musicians called lăutari developed a colorful and unique musical tradition. This study explores the music of the lăutari and its influence on five works for unaccompanied violin: George Enescu’s recently discovered Airs dans le genre Roumain (1926) and “Le Ménétrier” from his Impressions d’enfance (1940), Eugène Ysaÿe’s Sonata No. 3 “Ballade” (1923), Helen Bowater’s Lautari (2003), and Roxanna Panufnik’s new composition Hora Bessarabia (2016). Drawing from written sources, audio and video recordings, and transcriptions, this study first investigates the history, influences, and unique characteristics of the lăutari tradition and approach to violin playing. After discussing each composer and the background behind the five unaccompanied works, this study analyzes how lăutari music influenced these compositions and provides performance suggestions. These suggestions are based on applicable stylistic and technical principles drawn from traditional lăutari violin playing and from the researcher’s own experience learning and performing each piece

Playing with Time: The Creative Embodiment of Knowledge in the Performance of Baroque Flute Music

Expressive microtiming in music is a highly interpretative and contentious matter that varies not only between musical genres and communities of practice, but also from performance to performance. While some performers regard temporal subtleties as entirely intuitive and subjective, inaccessible to academic scrutiny, research in performance science, by contrast, considers microtiming a matter for objective, empirical study. Adopting a different approach, this thesis argues that all interpretative decisions arise from knowledge of some sort. Exploring different epistemic forms and their interaction, the various strains of knowledge that influence temporal expressivity are examined, and the fundamental question of ‘intuition’ addressed: how do epistemically-rooted interpretative decisions masquerade as ‘intuition’? Focusing on a case study of Fantasia No. 7 for solo flute by Georg Philipp Telemann, this thesis interrogates the processes that underpin expressive timing decisions in the performance of Baroque flute repertoire, addressing specificities of Baroque performance practice, as well as overarching questions more widely relevant to performance studies. As a result of the subjective, experiential and covert qualities that inhere within the phenomena of my investigation, critical reflection on my own practice is an indispensable ingredient of my methodology. This is interwoven with a theoretical framework that draws on aspects of historical musicology, cognitive psychology, psychoanalysis, phenomenology, and embodied cognition. Specifically, through lenses of ‘attentional states’ and ‘embodiment’, I examine the ways in which knowledge becomes internalised, transforms into ‘intuition’, is accessed during performance, and is externalised as an interpretative musical decision. In particular, drawing on the theory of ‘image schemata’ (a fundamental concern of recent research into embodied cognition), embodied shapes are revealed as a crucial form of knowledge that guides temporal expressivity. Overall, my research aims to map a holistic understanding of the experiential processes that underpin interpretative timing decisions in the performance of Baroque flute music

Gesture in Steve Reich\u27s Music and its Signification: A Referential Approach to His Process, Stylistic, and Postminimalist Works

When listening to minimalist music, one will more than likely notice the scarcity of materials. Small motifs and repetition pervade the surface, and one might be inclined to interpret such scarcity as mere redundancy of materials with seemingly few meaningful layers underneath the surface. When analyzing minimalist music, one will notice a similar pattern of scarcity. Music-theoretical scholarship on minimalist music, especially formalist analyses, primarily investigates the rhythmic and melodic connections spanning the entire work. The analytical uncovering of such scarcity through formal means has resulted in few novel analytical approaches and, consequently, an attitude that minimalist music itself is resistant to analysis. This dissertation, both in its methodological basis and applied analyses, reconceptualizes minimalist composer Steve Reich’s music such that it deemphasizes the quantifiable properties in favour of its qualifiable ones. The works themselves serve as representations of Reich’s compositional activity. One way to conceptualize this activity is “energetic shaping,” the definitive quality behind Robert Hatten’s theory of musical gesture (Hatten 2004). This dissertation explores the signification underlying Steve Reich’s music, primarily through a semiotically grounded theory of musical gesture. Three different eras in Reich’s compositional output will be examined. His early works of the 1960s focused on bringing an audible process to the listener’s attention. In the 1970s, Reich focused on the rhythmic pattern as he developed his musical style. In the 1980s, the works began sharing similar compositional attributes. These three decades make up his process music, “stylistic” music, and postminimalist music, respectively. The gestures found in these eras are represented by a definitive feature of the work and inferred by the subject of interest. Concerning the former, Reich’s unique musical processes, the rhythmic pattern, and previous analyses are the representative features of interest. Concerning the latter, the listener, performer, and analyst are the ones to deduce the significance underlying each era. The result of this dissertation is an improved understanding of Reich’s music and a new referential perspective that shows minimalist music being open to analysis rather than resistant to it

Ksüleemimahla kaaliumioonide sisalduse ja valgustingimuste mõju puude hüdraulilistele omadustele

Väitekirja elektrooniline versioon ei sisalda publikatsiooneVee transport juurtest lehtedesse on taime ellujäämiseks oluline, kuna mõjutab taime süsiniku omastamist ja teisi elutähtsaid funktsioone. Vesi liigub juurtest lehtedesse mööda juhtkudet, mida nimetaktakse ksüleemiks. Ksüleemi veetranspordivõimet iseloomustab hüdrauliline juhtivus. Taimes liikuv vesi sisaldab alati selles lahustunud aineid, mistõttu nimetatakse seda ksüleemimahlaks. Vee transpordi käivitab aurumine lehestiku pinnalt, mida lühikeses ajaskaalas mõjutab ka ksüleemimahla ioonide sisaldus. Doktoritöö käsitleb ksüleemimahla kaaliumioonide sisalduse, valgustingimuste mõju ja hüdraulika omavahelisi seoseid kiirekasvulistel lehtpuudel nagu hübriidhaab ja arukask. Töö on läbi viidud Järvselja Õppe- ja Katsemetskonna segametsas ning Rõkal asuval metsaökosüsteemi õhuniiskusega manipuleerimise katsealal (FAHM). Töös käsitlen hüdrauliliste ja ksüleemimahla parameetrite ööpäevast muutumist, puukoore eemaldamise ehk floeemi sälkamise mõju hüdraulilise juhtivusele ja ksüleemimahla omadustele, valguse kvaliteedi ja intensiivsuse mõju lehe ning oksa hüdraulilisele juhtivusele. Doktoritöös tõestasin ksüleemimahla ioonide sisalduse mõju katsealuste liikide hüdraulilisele juhtivusele. Leidsin, et suurenenud ksüleemimahla kaaliumioonide sisaldus suurendab hüdraulilist juhtivust, mis avardab meie teadmisi K+ osalusest taimede veevahetuse regulatsioonis. Samuti kattusid hübriidhaava ksüleemimahla ioonide sisalduse ja hüdraulilise juhtivuse ööpäevased rütmid. Floeemi sälkamine mõjutas hübriidhaava hüdraulilist juhtivust ja gaasivahetust, kuid mitte ksüleemimahla omadusi. Valgus mõjutas mitmel eri viisil ksüleemimahla kaaliumioonide sisaldust ja oksa hüdraulilist juhtivust. Nii valgustingimused kui ksüleemimahla ioonide sisaldus mõjutavad oluliselt lehtpuude veetranspordivõimet. Kaaliumioonide sisalduse muutmise teel saavad taimed muutuvates keskkonnatingimustes optimeerida lehtede veevarustust, saavutamaks tasakaalustatud veebilanssi.Water transfer from roots to leaves is essential for plants to keep up photosynthesis, grow and survive. Water moves from roots to shoots through water-conducting tissue called xylem. The water transport capacity of the xylem is characterized by hydraulic conductance. The water inside plants always contains dissolved substances; therefore, it is called a xylem sap. The main driving force for long-distance water transport in the xylem is transpiration, but hydraulic conductance can also be adjusted via changes in xylem sap ionic content on a short time scale. The objectives of the thesis were to investigate circadian patterns of hydraulic conductance and physico-chemical properties of xylem sap; to evaluate the impact of phloem girdling on branch hydraulic conductance and xylem sap properties; to evaluate the impact of light quality and intensity on leaf and shoot hydraulic properties. The study objects were fast-growing broadleaved trees like hybrid aspen and silver birch. The work was carried out in the mixed forest of Järvselja Training and Experimental Forestry District and the Free Air Humidity Manipulation experimental site (FAHM) located at Rõka. In the thesis, I proved that water transport capacity is modulated by xylem sap ionic content – increased K+ concentration of xylem sap enhances trees hydraulic conductance, indicating the involvement of potassium ions in the regulation of trees hydraulic efficiency. Both hydraulic and physico-chemical properties of xylem sap in trees follow coordinated circadian patterns driven by environmental conditions. Phloem transport disruption by phloem girdling at branch base affects hydraulic properties and gas exchange but not xylem sap properties in hybrid aspen. Both light availability and quality and xylem sap ionic content significantly affect trees hydraulic properties. They enable plants to optimize their water use and ensure positive water balance under changing environmental conditions.http://hdl.handle.net/10062/7681