SELECTED NINETEENTH CENTURY VARIATIONS FOR PIANO

The beauty and artistry of the variation form were fully developed and represented in the nineteenth century. The treasures of nineteenth century piano variations are a significant part of the total piano repertoire. The main goal of this dissertation is to show how various composers of the nineteenth century used the variation form to project their imagination and coloring of a simple melody. They used many different techniques to vary melodies and create their own music. Beethoven's Piano Sonata No. 12 in A-flat Major Op. 26 breaks with the conventional sonata design by using variation form instead of sonata-allegro form for the first movement, and having no movement in sonata-allegro form. Chopin's Variations Brillantes on "Je Vends des scapulaires" Op. 12 and Henri Herz's Variations on 'Non piu mesta" from "La Cenerentola" shows how they applied their art to composing variations on opera themes. Mendelssohn's Variations Serieuses Op. 54 was a reaction against the salon music in the 19" century. Schubert applies the variation form to his Impromptus in B-flat D. 935 No. 3. Schurnann's Symphonic Etudes represents a perfect example of the arts of variation, using counterpoint, and special coloring; and Faure's Theme and Variations Op. 73 represents one of the most outstanding nineteenth-century works in variation form. As a traditionalist in the nineteenth century, Brahms favored the variations over other classic forms. I have performed three of his most important sets of variations: including Variations on a theme by Schumann Op. 9, Variations on a Theme by Handel Op. 24, and Variations for two pianos on a Theme by Haydn Op. 56b. The variations listed above were divided into three recitals. These variations represent a very important part of the piano music of the nineteenth century. By discovering, preparing, and performing these wonderful works, I have grown, both as a pianist and as a musician.

USE OF VARIATION AND FUGUE IN PIANO MUSIC FOLLOWING THE CLASSICAL PERIOD

The variation and fugue originated from the 15th and 16th centuries and blossomed during the Baroque and Classical Periods. In a variation, a theme with a particular structure precedes a series of pieces that usually have the same or very similar structure. A fugue is a work written in imitative counterpoint in which the theme is stated successively in all voices of polyphonic texture. Beethoven’s use of variation and fugue in large scale works greatly influenced his contemporaries. After the Classical Period, variations continued to be popular, and numerous composers employed the technique in various musical genres. Fugues had pedagogical associations, and by the middle of 19th century became a requirement in conservatory instruction, modeled after Bach’s Well-Tempered Clavier. In the 20th century, the fugue was revived in the spirit of neoclassicism; it was incorporated in sonatas, and sets of preludes and fugues were composed. Schubert's Wanderer Fantasy presents his song Der Wanderer through thematic transformations, including a fugue and a set of variations. Liszt was highly influenced by this, as shown in his thematic transformations and the fugue as one of the transformations in his Sonata in b. In Schumann’s Symphonic Études, Rachmaninoff's Rhapsody on a Theme of Paganini and Copland’s Piano Variations, the variation serves as the basis for the entire work. Prokofiev and Schubert take a different approach in Piano Concerto No. 3 and Wanderer Fantasy, employing the variation in a single movement. Unlike Schubert and Liszt's use of the fugue as a part of the piece or movement, Franck’s Prelude Chorale et Fugue and Shchedrin’s Polyphonic Notebook use it in its independent form. Since the Classical Period, the variation and fugue have evolved from stylistic and technical influences of earlier composers. It is interesting and remarkable to observe the unique effects each had on a particular work. As true and dependable classic forms, they remain popular by offering the composer an organizational framework for musical imagination.

VARIATION FORMS: A SURVEY THROUGH FOUR CENTURIES OF VIOLIN REPERTOIRE

Variation, or the re-working of existing musical material, has consistently attracted the attention of composers and performers throughout the history of Western music. In three recorded recitals at the University of Maryland School of Music, this dissertation project explores a diverse range of expressive possibilities for violin in seven types of variation form in Austro-German works for violin from the 17th through the 20th centuries. The first program, consisting of Baroque Period works, performed on period instrument, includes the divisions on “John come kiss me now” from The Division Violin by Thomas Baltzar (1631 – 1663), constant bass variations in Sonate Unarum Fidium by Johann Heinrich von Schmelzer (1623 – 1680), arbitrary variation in Sonata for Violin and Continuo in E Major, Op. 1, No. 12 “Roger” by George Friedrich Händel (1685 – 1759), and French Double style, melodic-outline variation in Partita for Unaccompanied Violin in B Minor by Johan Sebastian Bach (1685 – 1750). Theme and Variations, a popular Classical Period format, is represented by the Sonata for Piano and Violin in G Major K. 379 by Wolfgang Amadeus Mozart (1756 – 1791) and Sonata for Violin and Piano in A Major, Op. 47 No. 9 the “Kreutzer” by Ludwig van Beethoven (1770 – 1827). Fantasy for Piano and Violin in C Major D. 934 by Franz Schubert (1797 – 1828) represents the 19th century fantasia variation. In these pieces, the piano and violin parts are densely interwoven, having equal importance. Many 20th century composers incorporated diverse types of variations in their works and are represented in the third recital program comprising: serial variation in the Phantasy for Violin and Piano Op.47 of Arnold Schoenberg (1874 – 1951); a strict form of melodic-outline variation in Sonate für Violine allein, Op. 31, No. 2 of Paul Hindemith (1895 – 1963); ostinato variation in Johan Halvorsen’s (1864 – 1935) Passacaglia for Violin and Viola, after G. F. Handel’s Passacaglia from the Harpsichord Suite No. 7 in G Minor. Pianist Audrey Andrist, harpsichordist Sooyoung Jung, and violist Dong-Wook Kim assisted in these performances.

Analysis of Self-Organization

The dissertation is devoted to the study of problems in calculus of variation, free boundary problems and gradient flows with respect to the Wasserstein metric. More concretely, we consider the problem of characterizing the regularity of minimizers to a certain interaction energy. Minimizers of the interaction energy have a somewhat surprising relationship with solutions to obstacle problems. Here we prove and exploit this relationship to obtain novel regularity results. Another problem we tackle is describing the asymptotic behavior of the Cahn-Hilliard equation with degenerate mobility. By framing the Cahn-Hilliard equation with degenerate mobility as a gradient flow in Wasserstein metric, in one space dimension, we prove its convergence to a degenerate parabolic equation under the framework recently developed by Sandier-Serfaty.

Selected Piano Works by Schumann, Liszt, and Brahms Incorporating or Based on Pre-existing Music

This dissertation shows how Schumann, Liszt and Brahms composed piano works based in a variety of ways on other music that already existed. My idea to do this project came through my fascination with Brahms’s Variations on a Theme by Paganini, which was the first piece selected. Brahms composed six sets of variations for solo piano, and I also chose Variations and Fugue on a Theme by Handel. Besides the variations, I included Brahms’s Ballade in D minor, Op. 10 No. 1, based on the Scottish ballad “Edward”. This piece demonstrates that Brahms applied pre-existing music not only in the form of variations, but also in other genres. Among Romantic composers, Schumann and Liszt are two others besides Brahms whose music frequently quotes pre-existing materials. In Schumann’s output, the inspiration from Clara Wieck is significant. The best examples may be the Impromptus Op. 5 and the third movement of the Grand Sonata No. 3, Op. 14, in which Schumann quotes the music by Clara Wieck as the theme of the variations and in the other movements as well to unify the entire piece. In addition, Schumann quotes the old German folk song “Grossvater Tanz” (Grandfather Dance) in the finale of Papillons. The same tune also appears in Carnaval for a programmatic purpose. These two pieces are a clear illustration that Schumann applies pre-existing music, and in addition they represent the spirit of literary reference. Liszt is well known for his superb transformations of other composers’ works into glorious piano compositions. Liszt drew his inspirations from different genres, including both vocal and instrumental music. His ability to turn earlier musical materials into virtuosic solo piano pieces that demonstrate his brilliance in creating imaginative keyboard sounds is remarkable. Among those pieces composed by Liszt, terms such paraphrase, reminiscence, or fantasy frequently appear as titles. I selected two such pieces: Rigoletto: Paraphrase de concert, S. 434 and Rondeau fantastique sur un thème espagnol, S. 252. In addition, Liszt also uses variation form to explore the possibilities of pre-existing themes. The piece I chose to represent this is Variations on the Theme “Weinen, Klagen, Sorgen, Zagen” and Crucifixus from the Mass in B minor by J.S Bach, S.180. This dissertation comprises three piano recitals that were performed in 2010 and 2011 in Ulrich Recital Hall and Gildenhorn Recital Hall of the Clarice Smith Performing Arts Center of the University of Maryland. The recordings are documented on compact discs that are housed within the University of Maryland Library System.

Move, for string quartet, piano, percussion and electronics

MOVE is a composition for string quartet, piano, percussion and electronics of approximately 15-16 minutes duration in three movements. The work incorporates electronic samples either synthesized electronically by the composer or recorded from acoustic instruments. The work aims to use electronic sounds as an expansion of the tonal palette of the chamber group (rather like an extended percussion setup) as opposed to a dominating sonic feature of the music. This is done by limiting the use of electronics to specific sections of the work, and by prioritizing blend and sonic coherence in the synthesized samples. The work uses fixed electronics in such a way that allows for tempo variations in the music. Generally, a difficulty arises in that fixed “tape” parts don’t allow tempo variations; while truly “live” software algorithms sacrifice rhythmic accuracy. Sample pads, such as the Roland SPD-SX, provide an elegant solution. The latency of such a device is close enough to zero that individual samples can be triggered in real time at a range of tempi. The percussion setup in this work (vibraphone and sample pad) allows one player to cover both parts, eliminating the need for an external musician to trigger the electronics. Compositionally, momentum is used as a constructing principle. The first movement makes prominent use of ostinato and shifting meter. The second is a set of variations on a repeated harmonic pattern, with a polymetric middle section. The third is a type of passacaglia, wherein the bassline is not introduced right away, but becomes more significant later in the movement. Given the importance of visual presentation in the Internet age, the final goal of the project was to shoot HD video of a studio performance of the work for publication online. The composer recorded audio and video in two separate sessions and edited the production using Logic X and Adobe Premiere Pro. The final video presentation can be seen at geoffsheil.com/move.

Temporal variations of IEEE 802.11b signal strengths in an in-building environment

Recent popularity of the IEEE 802.11b Wireless Local Area Networks (WLANs) in a host of current-day applications has instigated a suite of research challenges. The 802.11b WLANs are highly reliable and wide spread. In this work, we study the temporal characteristics of RSSI in the real-working environment by conducting a controlled set of experiments. Our results indicate that a significant variability in the RSSI can occur over time. Some of this variability in the RSSI may be due to systematic causes while the other component can be expressed as stochastic noise. We present an analysis of both these aspects of RSSI. We treat the moving average of the RSSI as the systematic causes and the noise as the stochastic causes. We give a reasonable estimate for the moving average to compute the noise accurately. We attribute the changes in the environment such as the movement of people and the noise associated with the NIC circuitry and the network access point as causes for this variability. We find that the results of our analysis are of primary importance to active research areas such as location determination of users in a WLAN. The techniques used in some of the RF-based WLAN location determination systems, exploit the characteristics of the RSSI presented in this work to infer the location of a wireless client in a WLAN. Thus our results form the building blocks for other users of the exact characteristics of the RSSI.

The Development of Piano Variations in the Romantic Era

The purpose of this study is to illustrate the development of piano variations as a genre during the Romantic era. In order to facilitate this examination of piano variations techniques, a brief look at the types of variation procedures used by composers of previous eras will assist in understanding developments that later occurred in the Romantic period. Throughout the Baroque era, composers preferred the fured-bass, fixed-melody, and harmonic forms of variation. The crowning achievement of Baroque keyboard music, Bach's Goldberg Variations (1725), contains examples of the "constantharmonic" method in its collection of 30 variations, each of which maintains both the bass and harmonic structure of the themes. While most composers of the classical period favored the "melodic-outline" form of variation, Haydn developed hybrid variation procedure that exhibits recurrence of material rather than repetition, alternating variation (ABABA), rondo variation (ABACA), and ternary variation (ABA). Haydn, Mozart and early Beethoven variations also exhibit simpler textures than do their Baroque predecessors. The nineteenth century produced numerous compositions that display variation techniques, some based on such older, classical models as melodic-outline variation and hybrid variation, others in the style of the character variation or fiee variation. At the beginning of the nineteenth century, Beethoven and Schubert used such classical variation techmques as melodic-outline variations and hybrid variations. Beethoven's late sonatas displayed such new means of expression as variation, fugue, and dramatic recitatives. The third movement of the Sonata in E major, Op. 109 (1820) has a theme and six variations of the melodic-outline type. Johannes Brahms was particularly fond of composing variations for piano. Among the best known examples of formal-outline variations are those found in the Variations and Fugue on a Theme of Handel, Op. 24 (1861). Character variations, in which styles are characterized by the retention and variability of particular elements, also flourished during the Romantic period. Cesar Franck's Variations Symphoniques (1885) are, perhaps, among the most important examples of free variations. This composition is a one-movement work consisting of three sections, Introduction, Variations, and Finale (all movements played "attaca"). This work combines two independent classical formal structures, the concerto and the variation.

THE PIANO MUSIC OF ROBERT SCHUMANN (1810-1856) AND JOHANNES BRAHMS (1833- 1897): A SURVEY OF CONCERTI, VARIATIONS, AND CHARACTER PIECES

Robert Schumann (1810-1856) and Johannes Brahms (1833-1897), in some ways Robert Schumann's artistic descendant, are the most important and representative German piano composers during the Romantic period. Schumann was already a mature and established musician in 1853 when he first met the young Brahms and recognized his talents, an encounter that had a long-lasting affect on the lives and careers of both men. After Schumann’s mental breakdown and death, Brahms maintained his admiration of Schumann’s music and preserved an intimate relationship with Clara Schumann. In spite of the personal and musical closeness of the two men, Schumann’s music is stylistically distinct from that of Brahms. Brahms followed traditions from Baroque and Classical music, and avoided using images and expressive titles in his music. Brahms extraordinarily intermingled earlier musical forms with multicolored tones of German Romanticism. In contrast, Schumann saw himself as a radical composer devoted to personal emotionalism and spontaneity. He favored programmatic titles for his character pieces and extra-musical references in his music. While developing their own musical styles as German Romantic composers, Schumann and Brahms both utilized the piano as a resourceful tool for self-realization and compositional development. To investigate and compare the main characteristics of Schumann and Brahms’s piano music, I looked at three genres. First, in the category of the piano concerto, I chose two major Romantic works, Schumann’s A minor concerto and Brahms’s B-flat major concerto. Second, for the category of piano variations I included two sets by Brahms because the variation framework was such an important vehicle for him to express his musical thoughts. Schumann’s unique motivic approach to variation is displayed vividly in his character-piece cycle Carnaval. Third, the category of the character piece, perhaps the favorite medium of Romantic expression at the piano, is shown by Schumann’s Papillons and Brahms’s sets of pieces Op.118 and Op.119. This performance dissertation consists of three recitals performed in the Gildenhorn Recital Hall at the University of Maryland, College Park. These recitals are documented on compact disc recordings that are housed within the University of Maryland Library System.