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The notion of closure pervades mathematics, especially in the fields of topology and projective geometry. Demonstrating this pervasiveness in the field, this graduate-level book provides a complete introduction to closure systems. With an emphasis on finite spaces and algebraic closures, the text covers graph theory, ordered sets, lattices, projective geometry, and formal logic as they apply to the study of closures. Each chapter presents a vignette to illustrate the topic covered. The author also includes numerous exercises as well as concrete examples to support the material discussed.
An extraordinary prodigy of Mozartean abilities, Felix Mendelssohn Bartholdy was a distinguished composer and conductor. Now, in the first major Mendelssohn biography to appear in decades, Todd offers a remarkably fresh account of this musical giant.
During the 1830s and 1840s the remarkably versatile composer-pianist-organist-conductor Felix Mendelssohn-Bartholdy stood at the forefront of German and English musical life. Bringing together previously unpublished essays by historians and musicologists, reflections on Mendelssohn written by his contemporaries, the composer's own letters, and early critical reviews of his music, this volume explores various facets of Mendelssohn's music, his social and intellectual circles, and his career. The essays in Part I cover the nature of a Jewish identity in Mendelssohn's music (Leon Botstein); his relationship to the Berlin Singakademie (William A. Little); the role of his sister Fanny Hensel, herself a child prodigy and accomplished composer (Nancy Reich); Mendelssohn's compositional craft in the Italian Symphony and selected concert overtures (Claudio Spies); his oratorio Elijah (Martin Staehelin); his incidental music to Sophocles' Antigone (Michael P. Steinberg); his anthem "Why, O Lord, delay forever?" (David Brodbeck); and an unfinished piano sonata (R. Larry Todd). Part II presents little-known memoirs by such contemporaries as J. C. Lobe, A. B. Marx, Julius Schubring, C. E. Horsley, Max Mller, and Betty Pistor. Mendelssohn's letters are represented in Part III by his correspondence with Wilhelm von Boguslawski and Aloys Fuchs, here translated for the first time. Part IV contains late nineteenth-century critical reviews by Heinrich Heine, Franz Brendel, Friedrich Niecks, Otto Jahn, and Hans von Blow.
Granddaughter of the philosopher Moses Mendelssohn and sister of the composer Felix Mendelssohn Bartholdy, Fanny Hensel (1805-1847) was an extraordinary musician who left well over four hundred compositions, most of which fell into oblivion until their rediscovery late in the twentieth century. In Fanny Hensel: The Other Mendelssohn, R. Larry Todd offers a compelling, authoritative account of Hensel's life and music, and her struggle to emerge as a publicly recognized composer.
Examines Mendelssohn's relationship to the past, shedding light on the construction of historical legacies that, in some cases, served to assert German cultural supremacy only two decades after the composer's death.
This biography traces Mendelssohn's development from dazzling child prodigy to renowned composer and conductor.
Exploring many aspects of Felix Mendelssohn's multi-faceted career as musician and how it intersects with his work as composer, contributors discuss practical issues of music making such as performance space, instruments, tempo markings, dynamics, phrasings, articulations, fingerings, and instrument techniques. They present the conceptual and ideological underpinnings of Mendelssohn's approach to performance, interpretation, and composing through the contextualization of specific performance events and through the theoretic actualization of performances of specific works. Contributors rely on manuscripts, marked or edited scores, and performance parts to convey a deeper understanding of musical expression in 19th-century Germany. This study of Mendelssohn's work as conductor, pianist, organist, violist, accompanist, music director, and editor of old and new music offers valuable perspectives on 19th-century performance practice issues.
With their insistence that form is a dialectical process in the music of Beethoven, Theodor Adorno and Carl Dahlhaus emerge as the guardians of a long-standing critical tradition in which Hegelian concepts have been brought to bear on the question of musical form. Janet Schmalfeldt's ground-breaking account of the development of this Beethoven-Hegelian tradition restores to the term "form" some of its philosophical associations in the early nineteenth century, when profound cultural changes were yielding new relationships between composers and their listeners, and when music itself-in particular, instrumental music-became a topic for renewed philosophical investigation. Precedents for Adorno's and Dahlhaus's concept of form as process arise in the Athenäum Fragments of Friedrich Schlegel and in the Encyclopaedia Logic of Hegel. The metaphor common to all these sources is the notion of becoming; it is the idea of form coming into being that this study explores in respect to music by Beethoven, Schubert, Mendelssohn, Chopin, and Schumann. A critical assessment of Dahlhaus's preoccupation with the opening of Beethoven's "Tempest" Sonata serves as the author's starting point for the translation of philosophical ideas into music-analytical terms-ones that encourage listening "both forward and backward," as Adorno has recommended. Thanks to the ever-growing familiarity of late eighteenth-century audiences with formal conventions, composers could increasingly trust that performers and listeners would be responsive to striking formal transformations. The author's analytic method strives to capture the dynamic, quasi-narrative nature of such transformations, rather than only their end results. This experiential approach to the perception of form invites listeners and especially performers to participate in the interpretation of processes by which, for example, a brooding introduction-like opening must inevitably become the essential main theme in Schubert's Sonata, Op. 42, or in which tremendous formal expansions in movements by Mendelssohn offer a dazzling opportunity for multiple retrospective reinterpretations. Above all, In the Process of Becoming proposes new ways of hearing beloved works of the romantic generation as representative of their striving for novel, intensely self-reflective modes of communication.
Since about 1970 there has been a veritable renaissance in scholarship and performances concerning the works of Felix Mendelssohn Bartholdy and Fanny Hensel. The essays in this book, presenting the findings of three generations of members of the international community of Mendelssohn/Hensel scholars, constitute a compendium of cutting-edge research relating to these two important representatives of nineteenth-century musical culture.