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.

Lifetime and distribution of ozone and related pollutants in the eastern United States

Most major cities in the eastern United States have air quality deemed unhealthy by the EPA under a set of regulations known as the National Ambient Air Quality Standards (NAAQS). The worst air quality in Maryland is measured in Edgewood, MD, a small community located along the Chesapeake Bay and generally downwind of Baltimore during hot, summertime days. Direct measurements and numerical simulations were used to investigate how meteorology and chemistry conspire to create adverse levels of photochemical smog especially at this coastal location. Ozone (O3) and oxidized reactive nitrogen (NOy), a family of ozone precursors, were measured over the Chesapeake Bay during a ten day experiment in July 2011 to better understand the formation of ozone over the Bay and its impact on coastal communities such as Edgewood. Ozone over the Bay during the afternoon was 10% to 20% higher than the closest upwind ground sites. A combination of complex boundary layer dynamics, deposition rates, and unaccounted marine emissions play an integral role in the regional maximum of ozone over the Bay. The CAMx regional air quality model was assessed and enhanced through comparison with data from NASA’s 2011 DISCOVER-AQ field campaign. Comparisons show a model overestimate of NOy by +86.2% and a model underestimate of formaldehyde (HCHO) by –28.3%. I present a revised model framework that better captures these observations and the response of ozone to reductions of precursor emissions. Incremental controls on electricity generating stations will produce greater benefits for surface ozone while additional controls on mobile sources may yield less benefit because cars emit less pollution than expected. Model results also indicate that as ozone concentrations improve with decreasing anthropogenic emissions, the photochemical lifetime of tropospheric ozone increases. The lifetime of ozone lengthens because the two primary gas-phase sinks for odd oxygen (Ox ≈ NO2 + O3) – attack by hydroperoxyl radicals (HO2) on ozone and formation of nitrate – weaken with decreasing pollutant emissions. This unintended consequence of air quality regulation causes pollutants to persist longer in the atmosphere, and indicates that pollutant transport between states and countries will likely play a greater role in the future.