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.

SELECTED VARIATIONS BY COMPOSERS IN GERMANY AND FRANCE

The Haward of Dictionary of Music (1983), defines variation as "a technique modifying a given musical idea." From the Baroque period on, the form and the techniques of variation were developed and enriched in Germany and France. Therefore, I presented the works of composers from these two nations. Even though there was a vast number of possibilities, I wanted to be scholastically fair and interesting in making my selections by choosing well-known pieces along with lesser-known ones. Haydn's well-known Variations in F minor consist of two sets of double variations which break into an improvisation fantasy. The first movement of Beethoven Sonata in A flat major, Op. 26, is a set of five variations on the composer's original theme. The variations are positioned in the first movement instead of Sonata-Allegro form. In 1861 Brahrns composed the Variations and Fugue, Op. 24, on the theme of Handel. Brahms displays a wealth of rhythmic, harmonic and textural contrasts in the variations. Chopin's E Major Variations without opus number are written on a Swiss influenced German folksong. Faure's Theme and Variations in C sharp minor, Op. 73, includes eleven variations. The work displays the composer's subtlety, grace and reticence. 12 Variationen iiber ein eigenes Thema were written by Alban Berg as a composition study with Schonberg. The Finale of Dutilleux's Piano Sonata, titled "Chorale with Variations", is written in an impressionistic style. A rich expressiveness is well blended in a classical form. In 1742, the remarkable Aria and thirty variations known as the Goldberg Variations were composed by J. S. Bach. The thirty Variations are unified by the bass line, which forms the foundation of the Aria. The pieces discussed above were presented in three recitals. Compact disc recordings of these recitals are available in the Michelle Smith Performing Arts Library of the Clarice Smith Performing Arts Center at the University of Maryland.

3D Ionospheric Effects on HF Propagation and Heating

The thesis uses a three-dimensional, first-principles model of the ionosphere in combination with High Frequency (HF) raytracing model to address key topics related to the physics of HF propagation and artificial ionospheric heating. In particular: 1. Explores the effect of the ubiquitous electron density gradients caused by Medium Scale Traveling Ionospheric Disturbances (MSTIDs) on high-angle of incidence HF radio wave propagation. Previous studies neglected the all-important presence of horizontal gradients in both the cross- and down-range directions, which refract the HF waves, significantly changing their path through the ionosphere. The physics-based ionosphere model SAMI3/ESF is used to generate a self-consistently evolving MSTID that allows for the examination of the spatio-temporal progression of the HF radio waves in the ionosphere. 2. Tests the potential and determines engineering requirements for ground- based high power HF heaters to trigger and control the evolution of Equatorial Spread F (ESF). Interference from ESF on radio wave propagation through the ionosphere remains a critical issue on HF systems reliability. Artificial HF heating has been shown to create plasma density cavities in the ionosphere similar to those that may trigger ESF bubbles. The work explores whether HF heating may trigger or control ESF bubbles. 3. Uses the combined ionosphere and HF raytracing models to create the first self-consistent HF Heating model. This model is utilized to simulate results from an Arecibo experiment and to provide understanding of the physical mechanism behind observed phenomena. The insights gained provide engineering guidance for new artificial heaters that are being built for use in low to middle latitude regions. In accomplishing the above topics: (i) I generated a model MSTID using the SAMI3/ESF code, and used a raytrace model to examine the effects of the MSTID gradients on radio wave propagation observables; (ii) I implemented a three- dimensional HF heating model in SAMI3/ESF and used the model to determine whether HF heating could artificially generate an ESF bubble; (iii) I created the first self-consistent model for artificial HF heating using the SAMI3/ESF ionosphere model and the MoJo raytrace model and ran a series of simulations that successfully modeled the results of early artificial heating experiments at Arecibo.

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.

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.

Resonant and Secular Orbital Interations

In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.