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  Partner: UNT Libraries
 Department: College of Music
 Decade: 2010-2019
 Collection: UNT Theses and Dissertations
161 Glass: Site Specific Music in an Artistic Context
The composition 161 Glass is a 17-minute musical work with percussion, wind and brass instruments in which the intersection of mid-century architecture, and the art and culture of a dynamic city are inextricably linked. Through this paper, I explore the process of composing a musical work in relationship to the significance of site specific context. The paper begins by defining the concept of site specific art works; then reviews the discourse of the intersection of art, music and architecture. I then delve into the cultural and geographic context surrounding this project from the modern era through the present, and how those perspectives apply to the building and my piece. I reveal how the composition relates the musical ideas to the site. Finally, I describe the collaborative process between myself, the musicians and the Dallas Contemporary staff.
The 1896 Vienna Tonkünstler-verein Competition: the Three Award-winning Works and Seven Anonymous Submissions with Clarinet
The Vienna Tonkünstler-Verein (1885-1929) was established for the sole purpose of providing extensive support to the music and musicians of Vienna. The society became renowned in Vienna for its outstanding performances of chamber music and counted among its members many of the city’s foremost musicians and composers. Johannes Brahms had a significant influence on the society as its honorary president and assisted in establishing its composition competitions, aimed at promoting and reviving under-developed chamber genres. Of particular interest to clarinetists is the Verein’s competition of 1896, which aspired to promote chamber music literature for wind instruments. Brahms’s recently completed chamber works for clarinet were clearly influential in fin-de-siècle Vienna; for of the twelve works chosen as finalists in the competition, ten included the clarinet in the chamber combination.The purpose of this document is to provide an English-language history of the Vienna Tonkünstler-Verein and a thorough account of its1896 competition based on my study of the society’s annual reports. In addition, this document will provide the first published account of the anonymous submissions for the 1896 competition. It is my hope that this paper will serve as a springboard for future endeavors aimed at uncovering the identities of the anonymous finalists for this competition.
The Adagio of Mahler's Ninth Symphony: A Schenkerian Analysis and Examination of the Farewell Story
Mahler's Ninth Symphony, since its premier in 1912, has sparked much debate about its programmatic meaning. This thesis provides an in-depth analysis of the Adagio and an examination of the controversy of the farewell story. In the process of the analysis I have compared my findings to some of the important authors in Mahler's field such as Vera Micznik, Henry-Louis de La Grange, and Christopher Orlo Lewis. Some of the conclusions are that a closer investigation of the music is necessary and that the programmatic reading of the farewell story can be appropriate.
Aesthetic and Technical Analysis on Soar!
Soar! is a musical composition written for wind ensemble and computer music. The total duration of the work is approximately 10 minutes. Flocking behavior of migratory birds serves as the most prominent influence on the imagery and local structure of the composition. The cyclical nature of the birds' journey inspires palindromic designs in the temporal domain. Aesthetically, Soar! portrays the fluid shapes of the flocks with numerous grains in the sounds. This effect is achieved by giving individual parts high degree of independence, especially in regards to rhythm. Technically, Soar! explores various interactions among instrumental lines in a wind ensemble, constructs overarching symmetrical structures, and integrates a large ensemble with computer music. The conductor acts as the leader at several improvisational moments in Soar! The use of conductor-initiated musical events in the piece can be traced back through the historic lineage of aleatoric compositions since the middle of the twentieth century. [Score is on p. 54-92.]
Alberto Ginastera and the Guitar Chord: An Analytical Study
The guitar chord (a sonority based on the open strings of the guitar) is one of Alberto Ginastera's compositional trademarks. The use of the guitar chord expands throughout forty years, creating a common link between different compositional stages and techniques. Chapters I and II provide the historical and technical background on Ginastera's life, oeuvre and scholar research. Chapter IV explores the origins of the guitar chord and compares it to similar specific sonorities used by different composers to express extra-musical ideas. Chapter V discusses Ginastera's initial uses and modifications of the guitar chord. Chapter VI explores the use of the guitar chord as a referential sonority based on Variaciones Concertantes, Op. 23: I-II, examining vertical (subsets) and horizontal (derivation of motives) aspects. Chapter VII explores uses of trichords and hexachords derived from the guitar chord in the Sonata for Guitar Op. 47.
Alfredo Casella's Serenata, op. 46, A Performance Guide for the Ensemble and Trumpet Part
Alfredo Casella's Serenata, op. 46 for clarinet, bassoon, trumpet, violin and cello is a composition that received great acclaim at the time of its conception, it is all but unknown to modern audiences and performers. The Serenata has several historical influences from the French and Italian Baroque and Classical periods. At present, there is limited scholarship regarding the Serenata op. 46. The first section of this study presents a survey of historical information, current literature and methods of examination. The second section compares movements of the Serenata op. 46 to other historical forms of similar design. The third section provides a performance guide for the trumpeter and ensemble. Implications and suggestions for performance of the composition are provided for the trumpeter. This performance guide provides the trumpeter and ensemble with performance information to help facilitate an informed performance.
An Analysis and Comparison of Four Rotations Pour Marimba, A Solo Marimba Suite, by Eric Sammut
Four Rotations Pour Marimba (1996) by Eric Sammut has become one of the most important marimba compositions in serious concert solo marimba literature. Four Rotations Pour Marimba is a suite of four short pieces; each of them demonstrates a different musical character while incorporating similar compositional components and techniques. The goal of this thesis project is to create a stylistic analysis for providing the concert marimbist with insight into the interpretation of these four pieces and also giving composers a more in-depth understanding of Sammut's compositional method. This thesis includes a formal analysis and comparisons of compositional elements used in Four Rotations. A brief biography of Sammut and historical significance of Four Rotations Pour Marimba are also included.
An Analysis of Honegger’s Cello Concerto (1929): a Return to Simplicity?
Literature available on Honegger’s Cello Concerto suggests this concerto is often considered as a composition that resonates with Les Six traditions. While reflecting currents of Les Six, the Cello Concerto also features departures from Erik Satie’s and Jean Cocteau’s ideal for French composers to return to simplicity. Both characteristics of and departures from Les Six examined in this concerto include metric organization, thematic and rhythmic development, melodic wedge shapes, contrapuntal techniques, simplicity in orchestration, diatonicism, the use of humor, jazz influences, and other unique performance techniques.
An Analysis of Pitch Organization in Villa-lobos's Rudepoêma
Heitor Villa-Lobos (1887-1959) stands central to the music history of the Brazilian twentieth century. His music represents a synthesis of the European art influences he absorbed and his quest to find a true Brazilian identity, which was not rooted in the deliberate imitation of Brazilian folk elements, but rather in the natural assimilation of them in his compositional style. His early compositions embody strong post-romantic, impressionistic tendencies, especially in regard to their harmonies and use of tone color, whereas the works from the 1920's and onwards show Villa-Lobos increasingly asserting his unusual and strong voice. Villa-Lobos's large-scale composition for piano, Rudepoêma, was composed between 1921 and 1926, and stands as one of the most significant contributions to the Latin-American piano literature. Despite of its importance in Villa-Lobos's oeuvre, it has largely eluded analytical attention. Discourse on Villa-Lobos is often marked by a somewhat one-dimensional approach that identifies the folk and rhythmic elements as the most important characteristics of his compositional style, and displays a certain reticence with regard to in-depth analysis of other parameters of his works. This study redresses the imbalance in the general approach to analytical assessment of Villa-Lobos's oeuvre by illustrating that pitch organization plays an indispensable role in establishing formal unity between the multiple sections of this complex work.
Analysis of Roger-ducasse’s Pastorale Pour Orgue
Pastorale pour Orgue (1909) is Jean Jules Aimable Roger-Ducasse’s only solo organ composition, which demonstrates skillful use of organ colors and demands a virtuoso technique for performance. Writing Pastorale in 1909, Roger-Ducasse synthesized compositional styles and techniques of two very different compositional approaches – impressionism and classicism. This study examines the stylistic characteristics of Pastorale by Roger-Ducasse as examples of both of these influences. the synthesis in Pastorale is primarily evident in the combination of classical forms and generic references with impressionist harmony and color. Thus, examining these musical elements provides hitherto unexplored insights into Pastorale as a master solo organ work of the early twentieth century. the dissertation is divided into four chapters. the first chapter presents the purpose, the significance, and the state of research of the piece. in the second chapter, I examine the traits of classicism through genre, form, thematic variation and other classicist elements of the composition. the third chapter presents the traits of impressionism including harmonic parallelism, extended chords, pedal points, ostinatos, and whole-tone scales. in the fourth chapter, I summarize the study and make a suggestion for further research of the piece.
An Analysis of the Pedagogical Advantages Relating to Combined Study of Euphonium and Trombone through the Use of Specific Repertoire
Doubling is defined as playing two instruments. It is becoming increasingly necessary for low brass musicians to double in the course of their careers. Euphoniumists often learn trombone, and trombonists learn euphonium. The instruments share several surface similarities but also differ in many significant ways. Interviews with six professional doublers highlight strategies for learning, teaching, and performing on both trombone and euphonium. Slide and valve technique, adjustment of intonation, tone quality, air usage, repertoire, and skill maintenance are all addressed. Trombone literature comprises a large part of the euphonium repertoire, due to the fact that most trombone pieces can be performed on euphonium. Euphoniumists should avoid playing pieces that require glissandi or extremely loud dynamics to be effective. Euphonium solos are generally too technical to be practical for trombonists to perform. Grøndahl's Concert pour trombone et piano ou orchestre is a standard piece for both instruments. When performing the piece on either instrument, it is helpful to practice the piece on both trombone and euphonium in order to tap into each instrument's strengths.
Ancient Musical Ideas Through a Twenty-First Century Lens: An Examination of Tarik O’Regan’s Scattered Rhymes and Its Relationship to Guillaume de Machaut’s Messe de Notre Dame
British composer Tarik Hamilton O’Regan (b. 1978, London) is earning a reputation as an important composer of today. The innovative works of O’Regan are entering the spectrum of professional, educational, and community performing organizations across the United States and Europe. Scattered Rhymes’ intricate melodic, harmonic, and rhythmic relationships with Messe de Notre Dame by Guillaume de Machaut (c.1300-1377) make an examination and comparison of the two works significant. Analyzing Scattered Rhymes by tracing its roots to Guillaume de Machaut’s Messe de Notre Dame, results in a renewed interest in this ancient work and brings prominence to Tarik O’Regan’s modern musical interpretation of ancient ideas. Understanding Scattered Rhymes as a work based on ideas from the fourteenth century in fusion with compositional concepts rooted in the modern era promotes Scattered Rhymes as one that is valuable in the current musical landscape.
An Annotated Bibliography of Selected Music for Saxophone by Charles Ruggiero with an Analysis of Interplay for Soprano Saxophone and Piano
Ruggiero's contributions to contemporary music are noteworthy. They include 27 works written for solo instruments, voice, as well as chamber groups and large ensembles. This study serves as an annotated bibliography of selected works written for saxophone by Charles Ruggiero. They include a piece for large chamber ensemble, Dig: From Tunes My Grandmother Heard (2009), a trio for flute, clarinet, and alto saxophone titled Echoes of "Piano Red" (2006), two saxophone quartets, Dig: JSB 1 (2003), and Three Blues for Saxophone Quartet (1981), two works for alto saxophone and piano, Night Songs and Flights of Fancy (2005), and Strayhorn (1999-2000), one piece for soprano saxophone and piano, Interplay for Soprano Saxophone and Piano (1988), a single movement work for alto saxophone, piano, winds, and percussion, Dance Complusions (2004), one duo for tenor saxophone and percussion, Sizzlesax II (2001), one concerto for soprano saxophone and piano, Concerto for Soprano Saxophone and Orchestra (1995, rev. 1999), and a trio for violin, alto saxophone, and piano, Dances and Other Movements (1983, rev. 1984). In addition, an analysis of Ruggiero's composition Interplay for Soprano Saxophone and Piano offers an insight into the compositional style of the composer.
Antonín Dvořák’s Piano Concerto in G Minor, Opus 33: A Discussion of Musical Intent and Pianistic Effectiveness in Vilém Kurz's Version of the Solo Piano Part
Since its premiere in 1878, Antonín Dvořák’s Piano Concerto in G Minor has been underrated and held in low regard by musicologists, critics, performers and audiences alike. Vilém Kurz (1872-1945), a Czech pianist and pedagogue, revised and reworked the piano solo part to incorporate what he considered to be added brilliance and pianistic effectiveness. However, the revised version has not increased the popularity of the work. In recent decades, this concerto has begun to appear more often in the programs and recordings are currently available, utilizing either the original piano part or Kurz's revision or a combination of both. In order to gain a broader analytical perspective and achieve a more authentic interpretation of the piece, a thorough understanding of the relation between Dvořák’s work and Kurz's revisions is indispensable. This study examines these adaptations and compares them with Dvořák’s scoring in order to gain further insight to Kurz's musical intent and pianistic aims. Examples from all movements are evaluated vis-à-vis the original to determine their purpose and musical validity.
Aphorismen, Capriccio, and Heptameron for Piano Solo By Jürg Baur: a Performer's Guide
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The purpose of this dissertation is to give instruction regarding the performance of three important piano works by Jürg Baur (1918-2010). Aphorismen, Capriccio, and Heptameron stand out as his most significant piano works both because of their length and because of their pianistic complexity. Since Baur had a successful career as both teacher and composer during his lifetime, his acclaimed works received many honors in Germany. His works can be performed by intermediate to advanced students. Intermediate students can easily offer simpler pieces like Aphorismen in competitions, while pieces like Capriccio and Heptameron better are suited to a more advanced level. Although some of his compositions are difficult to perform compared with other modern German works, Baur's music is more accessible. In the article, "Auf der Spuren der alten Zeit" Baur is quoted to state that Paul Hindemith and Bela Bartok's music influenced his own compositional ideas. However, although Baur is a modern composer, he didn't write in a totally atonal style, but rather attempted to broaden tonality. While Heptameron is atonal, Aphorismen and Capriccio give the impression of tonality, thus they are more accessible to the audience. I was fortunate enough to study Aphorismen with Baur as well as receiving advice for performance of Capriccio and some movements of Heptameron. Therefore, I gained a primary source of instruction, particularly in regards to pedal markings, rhythmic indications, voice balancing, finger suggestions, articulation markings, and tone of musical expression. In this dissertation, I include my own instructions (accepted by the composer) along with the composer's intentions.
Arvo Pärt and Three Types of His Tintinnabuli Technique
Arvo Pärt, an Estonian composer, was born in 1935. Most of the works at the beginning of his career were for piano in the neo-classical style. After that, he turned his interest to serial music and continued creating works with serial techniques throughout the 1960s. After his "self-imposed silence" period (during the years 1968-1976), Pärt emerged with a new musical style, which he called tintinnabuli. Although, this technique was influenced by music from the medieval period, the texture and function of its musical style cannot be described easily in terms of any single musical technique of the past. This study explores the evolution of Arvo Pärt's tintinnabuli technique in its first decade 1976-1985, which is divided into three different types. It provides musical examples from the scores of selected works, Für Alina, Cantus in Memory of Benjamin Britten, Cantate Domino canticum novum, Missa Sillabica, Stabat Mater and Es sang vor langen Jahren, and their analyses with supporting interpretative sketches. The goal of this thesis is to provide the reader a basis for understanding and recognizing the different types of Pärt's tintinnabuli technique.
The Avatar by Steve Rouse: A Performance Practice Guide
The Avatar for trumpet and piano by Dr. Steve Rouse is one of the most challenging compositions in the trumpet repertoire. Due to The Avatar's challenges and increasing popularity, a study is necessary to aid its performance. Each movement is performed on a different instrument: Bb piccolo (with an optional A piccolo part) for Nativity, Bb Flugelhorn for Enigma-Release and Bb trumpet for Rebirth. In addition, the performer must convey one of the work's possible programmatic meanings: (1) The Hindu belief of an Avatar and its life cycle, (2) the life of Christ or (3) the human lifecycle. Chapter 1 gives historical information about the work. Chapters 2-4 discuss each movement of The Avatar programmatically and pedagogically. Facets of each movement are analyzed including differences in programmatic choices, rehearsal techniques and sound concepts. Chapter 5 provides recording suggestions, including choosing a recording engineer, preparing and planning for a recording section, choosing a venue and the benefits of hiring a tonmeister.
Babel: a Composition for Rock Band, Soprano Quartet, and Chamber Ensemble—music and Critical Essay
Babel is a work for rock ‘n’ roll band (two electric guitars, electric bass, drum set), four soprano singers, and a twenty-one instrument mixed chamber ensemble. The 50-minute composition is based on the Tower of Babel story in Genesis 11:1-9, and the four-movement structure is derived from the form of this narrative. The first movement, “building rebellion,” establishes man’s intent to build a grand city and tower in a rebellion against God, while the second movement, “seeing/coming down,” describes the all-seeing God’s knowledge of man’s rebellion and God’s descent to the city. Movements three and four, “confusion” and “scatter,” depict the actions of God, confusing humankind’s language and scattering him over the earth. This project fuses rock ‘n’ roll influences with contemporary classical improvisation, creating a work that is sonically and dynamically excessive. One compositional goal was to use small amounts of material as the impetus for directed improvisation, which would be developed to create intricate and evolving textures. Each movement’s score is confined to a single page of music per part, necessitating highly graphic and aleatoric notation. The musical history and musicianship of each player greatly shapes the sonic outcome of Babel. Rigorous structure was mixed with extra-musical associations to create intricate layers of musical and metaphorical meanings. Every decision regarding form, pitch, rhythm, and improvisatory state is linked to a meaningful mathematical, philosophical, or theological idea. Out of the intention to illustrate a multi-layered, Biblical text interpreted in vastly different ways, came a complex work of art that challenges, yet welcomes, performers and listeners of all kinds.
Baroque Elements In The Piano Sonata, Opus 9 By Paul Creston
Paul Creston (1906-1985) was one of the most significant American composers from the middle of the twentieth century. Though Creston maintained elements of the nineteenth-century Romantic tradition and was categorized as a “Neo-Romantic” or “20th-century traditionalist,” many of Creston’s compositions contain elements of Baroque music. His Piano Sonata, Opus 9 provides significant examples of Baroque elements, while already foreshadowing his mature style. The purpose of this study is to explore Baroque elements in the compositional language of Paul Creston’s Piano Sonata, Opus 9. All four movements of the Piano Sonata will be examined in regards to its stylistic features associated with Baroque practices. These features mainly consist of rhythm, texture, imitative writing, and repeated phrase structure. Each category of the study will include comparisons of Domenico Scarlatti’s keyboard sonatas with Creston’s sonata. Through an examination of the Piano Sonata and its Baroque elements, this study hopes to inspire renewed interest in the work among musicians and to help the performer give a more stylistically coherent, and accurate, performance.
“Before I Die…”: Original Composition with a Critical Essay Exploring the Techniques of Six Crossover Composers
Candy Chang developed a public art installation where people are given the opportunity to write their answers to "Before I Die I want to ________." in a public space. I created one of these walls in Denton, TX and set it to music in a 12 minutes and 42 second piece titled Before I Die..., which combines elements of South Indian carnatic music, gospel, R&B, jazz fusion, and minimalism. The composition was influenced by the music of several crossover artists Becca Stevens, Michael League (Snarky Puppy), Nico Muhly, Poovalur Sriji, Tigran Hamasyan, and James Blake. Crossover music, fusion, and third-stream are all synonymous terms used to describe music where multiple genres or styles are authentically combined. The purpose of this thesis is to examine the balance of musical elements in crossover works as well as how specific works composed by the artists mentioned have influenced the creation of the Before I Die... piece.
"Being" a Stickist: A Phenomenological Consideration of "Dwelling" in a Virtual Music Scene
Musical instruments are not static, unchanging objects. They are, instead, things that materially evolve in symmetry with human practices. Alterations to an instrument's design often attend to its ergonomic or expressive capacity, but sometimes an innovator causes an entirely new instrument to arise. One such instrument is the Chapman Stick. This instrument's history is closely intertwined with global currents that have evolved into virtual, online scenes. Virtuality obfuscates embodiment, but the Stick's world, like any instrument's, is optimally related in intercorporeal exchanges. Stickists circumvent real and virtual obstacles to engage the Stick world. Using an organology informed by the work of Heidegger and Merleau-Ponty, this study examines how the Chapman Stick, as a material "thing," speaks in and through a virtual, representational environment.
Blueline Concerto: Critical Essay
The purpose of this critical essay is two-fold. First, the essay presents a detailed critical analysis of my original composition, Blueline Concerto for bass trombone and wind ensemble. Second, using Blueline Concerto, the essay presents preliminary findings of my study to develop an approach to composing that takes into account the musicians' health, specifically regarding noise induced hearing loss (NIHL). Through various hypothesized composition- and orchestral-based approaches, I test effectiveness on changes in NIHL risk while also noting that artistic merit and compositional integrity is preserved.
Brass Band History and Idiomatic Writing in Brass Music
The purpose of this research was to explore historical perspective of brass music. There is a brief history of brass bands in Britain. Furthermore, the paper examines the differences between two brass band pieces in the repertoire, A Western Fanfare by Eric Ewazen and Brass Symphony by Jan Koetsier. Both of these pieces were compared and contrasted against the author's newly composed work for brass, Two Companion Pieces for Brass Ensemble. The paper covers different techniques commonly used in brass writing and points these techniques out in all three pieces.
Britten’s Op 47, Five Flower Songs: Breaking Trends in Analysis
Benjamin Britten’s life and music have been the subject of study from early in his musical career. Current trends in psychological analysis of Britten’s music tend to focus on common themes, such as homosexuality, pacifism, the sense of the outsider, and the loss of innocence. Similarly, theoretical analyses tend either to provide general categorizations of the technical elements in Britten’s music or to apply a singular preconceived concept as a tool for understanding his compositions. These approaches have yielded significant information but leave aspects of Britten’s personality and music unilluminated. Britten’s Op. 47, Five Flower Songs, are a collection of five part songs for a cappella chorus that are often included within the canon of 20th century choral literature. This paper examines a new perspective on Britten’s music by examining the relationship between Britten’s friendships and their influence on his compositions. Through the examination of these relationships information is revealed that allows for a new method of analysis that is particularly relevant to the Five Flower Songs. The opus was dedicated to two botanists for the occasion of their 25th wedding anniversary. Contained within specific movements are extra-musical references to scientific characteristics of the flowers that are the subjects of the texts. By examining this work and important connections between other friendships and his compositional output this paper demonstrates the validity of this perspective in analyzing Britten’s life and music.
A-Bu-GE: A Composition for Organ and Percussion
Keyphrases describe a document in a coherent and simple way, giving the prospective reader a way to quickly determine whether the document satisfies their information needs. The pervasion of huge amount of information on Web, with only a small amount of documents have keyphrases extracted, there is a definite need to discover automatic keyphrase extraction systems. Typically, a document written by human develops around one or more general concepts or sub-concepts. These concepts or sub-concepts should be structured and semantically related with each other, so that they can form the meaningful representation of a document. Considering the fact, the phrases or concepts in a document are related to each other, a new approach for keyphrase extraction is introduced that exploits the semantic relations in the document. For measuring the semantic relations between concepts or sub-concepts in the document, I present a comprehensive study aimed at using collaboratively constructed semantic resources like Wikipedia and its link structure. In particular, I introduce a graph-based keyphrase extraction system that exploits the semantic relations in the document and features such as term frequency. I evaluated the proposed system using novel measures and the results obtained compare favorably with previously published results on established benchmarks.
Carlos Guastavino’s Sonata Para Trombón O Trompa Y Piano: Analysis of Argentine Song and Formal Western Music Tradition Applied to Trombone Repertoire
Very few Latin American pieces for trombone as a solo instrument have entered the canon of trombone repertoire worldwide, despite the large number of compositions in this medium. Therefore, when a major composer writes a full sonata for trombone efforts need to be made to bring these compositions to light. The Argentine composer Carlos Guastavino wrote a sonata for trombone and piano that is virtually unknown outside of Argentina, despite the composer’s importance. He is known for his artistic choice of cultivating a traditional romantic style of composition apart from the new tendencies and influences of the artistic novelties of the twentieth century. Guastavino’s artistic position is very clear in the sonata’s highly strict formal organization and Guastavino’s unique treatment of tonality and modality. He was also loyal to his own style as composer, which is ultimately an Argentine song style. He utilized the lyrical qualities of the trombone to convey the type of melodic approach that he used in his vocal works. This paper investigates the Argentine song and Western sonata conventions featured on Carlos Guastavino’s Sonata para Trombón o Trompa y Piano. The paper argues that these features represent his unique approach to musical composition in the twentieth century, thus making this sonata an important addition to the trombone repertoire.
The Changing Symbolic Images of the Trumpet: Bologna and Venice in the Seventeenth Century
The trumpet is among the most ancient of all musical instruments, and an examination of its history reveals that it has consistently maintained important and specific symbolic roles in society. Although from its origins this symbolic identity was linked to the instrument’s limited ceremonial and signaling function, the seventeenth century represents a period in which a variety of new roles and identities emerged. Bologna and Venice represent the two most important centers for trumpet writing in Italy during the seventeenth century. Because of the differing ideologies at work in these cities, two distinctive symbolic images of the instrument and two different ways of writing for it emerged. The trumpet’s ecclesiastic role in Bologna and its participation in Venetian opera put the instrument at the service of two societies, one centered around the Church, and another around a more permissive state. Against the backdrop of the social and political structures in Venice and Bologna, and through an examination of its newly-emerging musical roles in each city, the trumpet’s changing identities during a most important point in the history of the instrument will be examined.
Characterizing Noise and Harmonicity: The Structural Function of Contrasting Sonic Components in Electronic Composition
This dissertation examines the role of noise in shaping the form of several recent musical compositions. This study demonstrates how the contrast of noisy sounds and harmonic sounds can impact the structure of compositions. Depending on context, however, the specific use and function of noise can vary substantially from one work to the next. The first portion of this paper describes methods for quantifying noise content using FFT analysis procedures. A number of tests on instrumental and synthetic sound sources are described in order to demonstrate how the analysis system may react to certain sounds. The second part of this document consists of several analyses of whole musical works. Works for acoustic instruments are examined first, followed by works for electronic media. During these analyses, it becomes clear that while the use of noise in each work is based largely upon context, some common patterns do exist across different works. The final portion of the paper examines an original work which was written with the function of noise specifically in mind. The original work is put through the same analysis procedures as works seen earlier in the paper, and some conclusions are drawn regarding both the possibilities and limitations of noise analysis as a compositional tool.
The Chopin Etudes: a Study Guide for Teaching and Learning Opus 10 and Opus 25
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The etudes of Chopin are masterworks of the piano literature and are designed to go beyond mere technical exercises; moreover, each etude represents not only a technical study but also has a distinct musical character. Alarmingly, the current trend seems to be to assign the Chopin etudes at an increasingly young age to students who are not yet equipped either technically or musically to handle them. As Chopin’s pupil, Carl Mikuli, commented in the preface to his Chopin edition, the etudes were meant for “more advanced students.” If Chopin had intended his etudes for students at an intermediate level, he would have assigned them to most of his students; however, only a limited number of students had his permission to work on their master’s etudes. As a teacher, I have always felt the need to devise a systematic teaching plan to guide students to handle the challenges of these pieces both physically and musically. This study examines the repertoire which might help prepare a student to learn the etudes without overstraining his/her muscular and mental ability. Rooted in Chopin’s teaching and his recommendation of the pieces to learn before tackling the etudes themselves, this pedagogical study guide intends to help students and teachers to work progressively towards the study of these works. While pinpointing some exercises and simple pieces to assign to a student in preparation for studying the individual etudes, helpful works of later composers are also liberally incorporated, as well as some suggestions for practicing the etudes themselves. Finally, I shall provide my own “re-ordering” of the etudes, with a progressive degree of difficulty, as an additional aid to a young pianist who may eventually want to learn the entire opus 10 and opus 25.
The Choral Music of Ola Gjeilo: a New Vision of the Choral Instrument in the 21St Century
The choral music of Norwegian composer Ola Gjeilo (pronounced “yay-loh”) is gaining international acclaim and is widely performed and commissioned by prominent high school, university, and professional choirs. It represents a philosophical approach and vision of the choral instrument for which the conductor must have a clear understanding in order to prepare a meaningful performance. in particular, his music merges diverse musical influences, which results in a product of unique character among choral compositions in the late 20th and early 21st centuries. Gjeilo draws inspiration from a text but then uses its sonic qualities (the sounds of vowels and consonants) to create an atmosphere of sound instead of following the traditions in choral and vocal music of using musical mechanisms (melody, rhythm, and harmony) to reinforce the text poetically. This study provides an overview of Gjeilo’s background, in Chapter 1, and discusses its influence on his compositional philosophy. Chapter 2 contains musical examples from selected works, which are used to illuminate unique attributes found in Gjeilo’s music. Chapter 3 presents important implications to consider aiding choral conductors in their preparation of future performances of Gjeilo’s music.
The Cimbasso and Tuba in the Operatic Works of Giuseppe Verdi: A Pedagogical and Aesthetic Comparison
In recent years, the use of the cimbasso has gained popularity in Giuseppe Verdi opera performances throughout the world. In the past, the tuba or the bass trombone was used regularly instead of the cimbasso because less regard was given to what Verdi may have intended. Today, one expects more attention to historical precedent, which is evident in many contemporary Verdi opera performances. However, the tuba continues to be used commonly in performances of Verdi opera productions throughout the United States. The use of the tuba in the U.S. is due to a lack of awareness and a limited availability of the cimbasso. This paper demonstrates the pedagogical and aesthetic differences between the use of the tuba and the modern cimbasso when performing the works of Giuseppe Verdi operas.
Claude Bolling’s Toot Suite for Trumpet and Jazz Piano: a Performance Guide
Claude Bolling’s Toot Suite for Trumpet and Jazz Piano that was premiered by French virtuoso trumpeter Maurice Andre in 1980 is an important work in the trumpet repertoire. At present, there is limited research regarding Toot Suite. Almost all of the six movements within Toot Suite are performed on a different instrument: C trumpet for Allegre, Eb trumpet for Mystique, Bb cornet for Rag-Polka, Bb piccolo trumpet for Marche, Bb flugelhorn for Vesperale and Bb piccolo for Spirituelle. Chapter 1 examines the life and musical background of the composer. It also exposes the history surrounding the origin of Toot Suite. Chapter 2 discusses the musical influences of the composer that are found in Toot Suite. Chapter 3 provides an analysis of existing studio recordings. Chapter 4 offers specific suggestions regarding preparation and performance of Toot Suite. Chapters 5 and 6 conclude the guide with interviews with the composer and prominent trumpet performers and pedagogues that have recorded and/or have performed Toot Suite live.
The Collective Pedagogy Utilized By the Trombone Instructors at the Rotterdam Conservatory of the Netherlands
The Collective Pedagogy Utilized by the Trombone Instructors at the Rotterdam Conservatory of the Netherlands offers a comprehensive study of the collaboration between the various instructors of the trombone studio within the Rotterdam Conservatory and their pedagogical approach to curriculum, lesson structure, grading process, student body, and social environment. the Rotterdam Conservatory has produced some of the finest trombonists in the global music community. Alumni from the conservatory consistently win positions in professional ensembles, succeed in national and international competitions, and are often featured artists at international music festivals. the success of their alumni warrants closer scrutiny of the pedagogical approach utilized by the faculty of the conservatory.
The Combination of Eastern and Western Musical Worlds: Korean Performance Techniques Applied to Western Symphony Orchestra in Relation to Isang Yun’s Tänzerische Fantasie Für Großes Orchester, Muak (1987)
Isang Yun employed several contrasting methods to achieve the combination of two different musical worlds, Eastern and Western, in his Tänzerische Fantasie für Großes Orchester, Muak. In presenting Eastern elements, he adopts Taoism as his musical philosophy, describes the Korean traditional dance motion Chun-Aeng-Mu (Dance of the Oriole), and applies Korean traditional performance practice in the use of Western instruments. Showing the influence of aspects of Western music, he employs a musical form similar to that of the Baroque Concerto Grosso, evokes Igor Stravinsky’s rhythmic mood and tension from Le Sacre du Printemps (The Rite of Spring), and even uses his own compositional technique Hauptklangtechnik within the format of Western orchestration. In its analysis of Muak, this research project addresses how Korean performance practice can be applied to the modern Western symphony orchestra. This research project also provides insights regarding the sounds of instruments in the Korean tradition and explains how it is possible to create those sounds with modern instruments in order to make Yun’s dream sounds possible. This study provides several examples and describes various performance techniques that appear in Korean traditional music. It provides indications to orchestras and conductors, assisting them to arrive at effective basic performance ideas for the performance of Muak.
Combining of Korean Traditional Performance and Recent German Techniques in Isang Yun's Kontraste: Zwei Stücke für Violine Solo (1987)
Isang Yun (1917-1995) embraced a masterful combination of two elements derived from his life: his Korean cultural upbringing and Western musical traditions. This dissertation explores Yun's distinctive style through an analysis of his Kontraste: Zwei Stücke für Violine Solo. Following the introduction (Chapter 1), Chapter 2 contains a brief biography of Isang Yun, and explores the compositions of his Korean period (1917-1955) and his European period (1956-1995). It also discusses how Yun's musical styles changed during these two periods as a result of important life events and due to cultural and political influences. Chapter 3 examines Korean instruments such as Kayakem, Hae-Kem, and Pak; discusses Nonghyun (traditional string techniques of ornamentation in Korean music); and introduces Korean performance techniques. This chapter also provides explanations of these concepts, illustrated through various examples. A subsequent discussion illuminates Yin-Yang theory and Jeong-Jung-Dong, both elements of Taoist philosophy that influenced Yun's compositional style. This is followed by explanations of Hauptton and Umspielung, two compositional techniques that Yun developed and employed in Kontraste. Yun created the idea of Hauptton to reflect the Korean traditional concept of a single note. He used the term Umspielung ("playing around" in German) to describe his interpretation of the four traditional techniques of Nonghyun within a Western notational framework. In Chapter 5, analysis of Kontraste reveals how the piece's contrasting elements represent the concepts of Yin-Yang and Jeong-Jung-Dong, and shows how the violin imitates the sounds of Korean traditional instruments and instrumental technique. Yun's adaption of Korean traditional performance techniques to the violin in Kontraste is aimed at combining East and West and producing a new aesthetic.
A Comparative Analysis of the 1915 and 1919 Versions of Symphony No. 5 in E-flat Major, op. 82 by Jean Sibelius
The initial composition of the Fifth Symphony in E-flat Major, Op. 82 was undertaken as a commission to celebrate the composer's fiftieth birthday. Unhappy with the initial efforts, two revisions were then performed; the first was in 1916 and the final revision in 1919. Despite the larger form of the work seeming to have been changed between the 1915 and 1919 versions, the smaller gestures of thematic expression in both versions remained similar. On the surface, it had appeared that the composer had eliminated a movement, changing the 1919 version into a three movement form. This view was not challenged by the composer at the time, and since the earlier versions had either been withdrawn or destroyed, there was no way to compare the original efforts to the final product until recently. In comparing the 1919 version to the original, a definite strong parallel can be seen between the two - despite the changes to form, rearrangement of melodic material, and the seemingly different number of movements. However, the parallel is enough that the 1915 version can be a guide to classifying the 1919 version, an act that has eluded many scholars since the 1920s. Most importantly, comparing the two versions shows that the 1919 version is not a three movement form at all; it is a four movement form that is obscured by the connection of the first and second movements by a thematic bridge that contains elements from both movements, but is not placed within either structure.
A Comparative Examination of Six American Master Trumpet Teachers and the Regional Schools of Playing That They Represent
Jet travel and the widespread availability of recordings are factors that have led to an increasingly homogenous sound concept in American trumpet playing; this is a stark contrast to the unique regional sounds that existed in the United States in the middle of the twentieth century. Despite the growing dissipation of these regional sound concepts from the mid-century, it is important to understand the styles and pedagogy associated with these schools. In this paper, six player/teachers are associated with specific regional playing styles: Vincent Cichowicz in Chicago, Louis Davidson in Cleveland, Armando Ghitalla in Boston, John Haynie in the Southwest, James Stamp on the West Coast, and William Vacchiano in New York City. Each of these players made a notable impact on the trumpet world through their performances, recordings, and unprecedented legacy of students. It would be difficult for many modern American trumpet players to trace their “trumpet lineage” without one of these individuals in the picture. Not only are these players an important part of the modern trumpeter’s heritage, but the vast success of their students warrants that their pedagogical methods are still relevant today. This study is unique due to this comprehensive and categorical comparison of pedagogical techniques, and this paper additionally examines the distinct sounds of each player’s regional style through the use of spectrograms. Ultimately this paper provides a myriad of teaching strategies from some of the most influential American trumpet players, which will aid trumpet teachers in negotiating the diverse needs of their students.
A Comparative Study of Two Single-Subject Keyboard Ricercare by Johann Jacob Froberger: Projections of Sixteenth-Century Practice Combined with Features that Forecast Baroque Practice
This study is focused on an analysis of two single-subject ricercare in the keyboard music of Johann Jacob Froberger and examines possible pathways to the development of the Baroque fugue. This dissertation is divided into three parts. Chapter I contains the purpose, significance of this study and composer, as well as characteristics of the seventeenth-century single-subject ricercar. Chapter II details and examines Froberger's two ricercare. Finally, a conclusion of this study is presented in Chapter III. Two appendixes are included in this dissertation: a list of the single-subject ricercare of Andrea Gabrieli, Giovanni Gabrieli, and Johann Jacob Froberger; and an analysis of the two single-subject ricercare, FbWV 407 and FbWV 409, by Johann Jacob Froberger.
A Comparison of Rhythm, Articulation, and Harmony in Jean-michel Defaye’s À La Manière De Stravinsky Pour Trombone Et Piano to Common Compositional Strategies of Igor Stravinsky
À la Manière de Stravinsky is one piece in a series of works composed by Jean-Michel Defaye that written emulating the compositional styles of significant composers of the past. This dissertation compares Defaye’s work to common compositional practices of Igor Stravinsky (1882 – 1971). There is currently limited study of Defaye’s set of À la Manière pieces and their imitative characteristics. The first section of this dissertation presents the significance of the project, current literature, and methods of examination. The next section provides critical information on Jean-Michel Defaye and Igor Stravinsky. The following three chapters contain a compositional comparison of À la Manière de Stravinsky to Stravinsky’s use of rhythm, articulation, and harmony. The final section draws a conclusion of the piece’s significance in the solo trombone repertoire. This study will add to the published material on Jean-Michel Defaye and this influential series of pieces and is intended to further the interest of research into the works of this important composer.
The Compositional Transformation and Musical Rebirth of Leo Ornstein
This study focuses on the transformation of Leo Ornstein’s (1893-2002) musical language of his early years into the strikingly different approach found in his later years. Ornstein’s initial radical compositions from the mid-1910s were no doubt representative of the direction in which modern music was moving. Despite the intense fame and notoriety of his early works, Ornstein did not feel connected to the trends of modern music development, and by the end of the 1930s he withdrew from the public scene and turned to teaching. By the 1950s Ornstein had been almost forgotten, and in later life he became a very private person. He worked in almost total isolation composing a substantial amount of music well into his nineties, and died at the age of 109. The music of Ornstein’s “second life” is very different from the initial works of his early years, and most of it is unknown to the public and should be brought into scholarly light, especially since Ornstein has been considered by historians as a pivotal figure in twentieth-century music. This study examines selected music from different stages of Ornstein’s career: Wild Men’s Dance (1913), Suicide in an Airplane (1913), Arabesques (1918), A Long Remembered Sorrow (1964), Piano Sonata No. 7 (1988). A discussion of the selected compositions will provide an understanding of Ornstein’s compositional transformation, and will familiarize musicians and scholars with this widely unknown music.
The Concept Of “Unity” In Isang Yun’s Königliches Thema Fr Violine Solo
A Korean-German composer Isang Yun.s life was evenly distributed between two different countries, and his music contains both elements of performance practices of Eastern Asian and Western music. This dissertation presents his ethnic and aesthetic musical roots by an analytic examination of his solo violin piece, K♠nigliches Thema (1976). The dissertation is divided into four chapters. The first chapter contains Isang Yuns biography and his works of the four periods. The second chapter studies his philosophy in music and compositional techniques such as twelve-tone technique, Taoism, Hauptton, Hauptklang and the Korean instrumental technique in Western instruments. The third chapter presents a detailed analysis of Knigliches Thema with his Taoist philosophy. The fourth chapter is solely dedicated to the performance perspectives of Königliches Thema in tempo, dynamic and various violin techniques.
Conductor Awareness of, Knowledge of, and Attitude Toward Sound Intensity Levels Generated During Ensemble-based Instructional Activities in College-level Schools of Music
In 2011, the National Association of Schools of Music (NASM) took an official position to recognize the importance of hearing health and injury prevention as a standard for all member-accredited institutions. This is the largest national acknowledgement promoting hearing health and safety within the music discipline and among students seeking a music degree in the United States. The purpose of the study is to describe what conductors (i.e., instructors) of college-based ensembles know about hearing health and the generation of sound intensity levels. The study aimed to describe the 1) current state of conductors’ awareness and knowledge of sound intensity levels, 2) current attitudes of conductors toward learning and sharing knowledge of sound intensity levels, and 3) current teaching practices of conductors in regard to equipment usage (e.g. sound level meter, noise dosimeter, hearing protection devices) relating to sound measurement and exposure. Findings indicate 80.2% of conductors (N = 162, 66% employed by NASM-accredited institutions) agree that sounds generated during ensemble-based instructional activities (EBIAs) in college-level schools of music are capable of harming human hearing, but 24.1% “do not know” if EBIAs they conduct ever exceed sound intensity levels capable of harming human hearing, 54.9% do not know “what services or resources” their home institutions offer/refer to students, 93% are never using a noise dosimeter, 40% have never had an audiology exam, and 70% have never used hearing protection during an EBIA. Conductors have a strong openness to change current teaching practices and inform themselves about hearing health, but few are personally informing and educating their students during the EBIA. The study serves to assist conductors and foster a new dialogue among their students, colleagues, staff, and administrators to revise current curriculum, explore sound measurement technologies, and evaluate current hearing health and safety issues inherent in the practice, performance, and teaching of sound intensity levels generated during EBIAs in college-level schools of music.
Constructions of Choir Identity in a High School
The purpose of this study was to investigate constructions of choir identity among high school choir students in the United States public school classroom setting. The research questions were (a) what are the processes involved in construction of choir identity and (b) how are the processes related to the group identity of the choir. The data were collected through participant observations in one selected choir classroom and semi-structured interviews with students from the choir class. The results included six processes of identity construction as well as identification of the ways in which each process was related to the choir group’s identity. The processes and their links to the overall choir group identity provided further insight into the ways in which high school choir students construct their identities, and they also supported methods of teaching commonly used in high school choir settings.
Correcting the Record: a Comparison of Vladimir Ashkenazy’s Urtext-based Edition of Pictures at an Exhibition with Orchestration By Ravel and Stokowski
Modest Mussorgsky (1839-1881) never published his piano suite, Pictures at an Exhibition. The first publication of the Pictures was Nikolai Rimsky-Korsakov’s (1844-1908) piano edition in 1886, five years after Mussorgsky’s death. Among several piano editions of Pictures, Manfred Schandert’s urtext piano edition of 1984 has shed new light on the piano suite. The urtext edition is based on a facsimile of Mussorgsky’s autograph, and Schandert’s authoritative urtext contains all of Mussorgsky’s musical indications that previous editions neglected to include. Previous orchestrations based on less comprehensive editions include well-known orchestrations by Maurice Ravel (1875-1937) and Leopold Stokowski (1882-1977). Vladimir Ashkenazy (b. 1937), on the other hand, derived his orchestration directly from the Schandert edition. In this study I argue that Ashkenazy offers “corrections” to his predecessors, Ravel and Stokowski, whose orchestrations differ—at times radically—from Mussorgsky’s autograph. This dissertation thus will explore the significant features of Ashkenazy’s orchestration in relation to the urtext edition by comparing it to the orchestrations of Ravel and Stokowski. In an age of attempts to present “authentic” versions of past music, Ashkenazy’s orchestration provides an authenticity that other orchestrations lack. Ashkenazy’s orchestration of Pictures at an Exhibition provides conductors an alternative performance option that is both effective and more closely related to Mussorgsky’s autograph.
The Creation of a Performance Edition of the Georg Christoph Wagenseil Concerto for Trombone with Attention Given to the Surviving Manuscripts and Primary Sources of Performance Practice from the Middle of the Eighteenth Century
The Concerto for Trombone, written in 1763 by Georg Christoph Wagenseil, is a piece in 2 movements for alto trombone and chamber orchestra. The orchestration consists of 2 parts for violin, 1 part for viola, cello and string bass, 2 French horn parts and 2 parts for flute. It is the first concerto form solo work for the alto trombone and was written during a time when wide use of this instrument had been diminished from centuries past. The Concerto for Trombone helped mark the beginning of a time when the musical expressiveness of the trombone began to be noticed in chamber genres where such attention had been lacking in previous decades. Chapter 2 examines the life and musical background of the composer. Chapter 3 discusses the history surrounding the possible origin of the Concerto and its performance history. Chapter 4 provides analytical insights into the construction and format of the piece. Chapter 5 details the creation of an urtext edition of the Concerto. Chapter 6 concludes this document with a performer's guide to the work based on the urtext edition of the solo trombone part to create the performance edition. This performance edition of the work includes historically informed solutions to the problematic technical elements of ornaments. The final section of the chapter makes suggestions regarding the preparation and performance of a historically informed version of the Concerto for Trombone.
The Creative Process in Cross-Influential Composition
This dissertation describes a compositional model rooted in cross-influential methodology between complementary musical compositions that share generative source material. In their simultaneous construction, two composition pairs presented challenges that influenced and mediated the other's development with respect to timbre, transposition, pitch material, effects processing, and form. A working prototype first provides a model that is later developed. The first work Thema is for piano alone, and the companion piece Am3ht is for piano and live computer processing via the graphical programming environment Max/MSP. Compositional processes used in the prototype solidify the cross-influential model, demanding flexibility and a dialectic approach. Ideas set forth in the prototype are then explored through a second pair of compositions rooted in cross-influential methodology. The first work Lusmore is scored for solo contrabass and Max/MSP. The second composition Knockgrafton is scored for string orchestra. The flexibility of the cross-influential model is revealed more fully through a discussion of each work's musical development. The utility of the cross-influential compositional model is discussed, particularly within higher academia.
Critical Discussion of Pleroma: A Digital Drama and Its Relevance to Tragic Form in Music
Pleroma is a digital drama: a work composed of digital animation combined with electroacoustic music, presenting an original dramatic narrative. Pleroma's dramatic elements evoke both the classical form of tragedy and the concept of perceptual paradox. A structural overview of the drama and its characters and a plot synopsis are given to provide context for the critical discussion. Analytical descriptions of Beethoven's Coriolan Overture Op.62 and Mahler's Symphony No. 9 are provided to give background on tragic form and Platonic allegory in music. An investigation into the elements discussed in the analysis of the instrumental works reveals several layers of possible interpretation in Pleroma. Dramatic elements allow for tragic narratives to be constructed, but they are complemented by character associations formed by pitch relationships, stylistic juxtapositions, and instrumentation. A copy of the dramatic text is included to supplement the multimedia production.
Criticism of Beethoven's Pastoral Symphony in London and Boston, 1819-1874: A Forum for Public Discussion of Musical Topics
Critics who discuss Beethoven’s Pastoral Symphony often write about aspects that run counter to their conception of what a symphony should be, such as this symphony’s static nature and its programmatic elements. In nineteenth-century Boston and London, criticism of the Pastoral Symphony reflects the opinions of a wide range of listeners, as critics variably adopted the views of the intellectual elite and general audience members. As a group, these critics acted as intermediaries between various realms of opinion regarding this piece. Their writing serves as a lens through which we can observe audiences’ acceptance of ideas common in contemporaneous musical thought, including the integrity of the artwork, the glorification of genius, and ideas about meaning in music.
Dario Castello's Music for Sackbut: the Sonate Concertate in Stil Moderno (1629)
Dario Castello's Sonate concertate in stil moderno is a collection of 29 trio sonatas in two volumes, with 10 of them employing the sackbut. These works represent a significant repertoire for the sackbut in an era where specific instrumentation was only starting to become a convention. While these pieces are often studied, performed and recorded in Europe, most American trombonists are not aware of their existence. This study seeks to acquaint the American trombonist with the sonatas of Castello and to provide performance suggestions for those less familiar with this genre. Chapter 1 presents a survey of the current literature on Castello. Chapter 2 provides an historical background for music in Venice in the early 17th century, while Chpater 3 focuses on the composer and his music for sackbut. Chapter 4 investigages the sonata in early 17th century Venice. Chapter 5 provides an insight into early baroque performance practice by discussing principles such as affect, tempo, ornamentation, diminution and articulation. Examples from the ten sonatas are used to illustrate these principles, providing the modern trombonist with a framework in which to study Castello's music. The final chapter discusses the implications of this study on the American trombone curriculum.
Deconstructing Webern's Op 25, Drei Lieder: a Multidimensional Assessment
Webern scholarship has not comprehensively examined op. 25, drei lieder. If the selection of text for op. 25 is viewed as one work in three movements they create a ternary form (A-B-A1). To show how this form is developed in the music the author creates a new analytical system based on Schoenberg's Grundgestalt which is defined by three basic ideas: symmetry, liquidation, and variation. The relationship between the voice and accompaniment and Webern's deliberate manipulation of the text is used to reveal the use of a program which is then tied to the numerical symbolism of 2 and 3.