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How is the Beatles' "Help!" similar to Stravinsky's "Dance of the Adolescents?" How does Radiohead's "Just" relate to the improvisations of Bill Evans? And how do Chopin's works exploit the non-Euclidean geometry of musical chords? In this groundbreaking work, author Dmitri Tymoczko describes a new framework for thinking about music that emphasizes the commonalities among styles from medieval polyphony to contemporary rock. Tymoczko identifies five basic musical features that jointly contribute to the sense of tonality, and shows how these features recur throughout the history of Western music. In the process he sheds new light on an age-old question: what makes music sound good? A Geometry of Music provides an accessible introduction to Tymoczko's revolutionary geometrical approach to music theory. The book shows how to construct simple diagrams representing relationships among familiar chords and scales, giving readers the tools to translate between the musical and visual realms and revealing surprising degrees of structure in otherwise hard-to-understand pieces. Tymoczko uses this theoretical foundation to retell the history of Western music from the eleventh century to the present day. Arguing that traditional histories focus too narrowly on the "common practice" period from 1680-1850, he proposes instead that Western music comprises an extended common practice stretching from the late middle ages to the present. He discusses a host of familiar pieces by a wide range of composers, from Bach to the Beatles, Mozart to Miles Davis, and many in between. A Geometry of Music is accessible to a range of readers, from undergraduate music majors to scientists and mathematicians with an interest in music. Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory. The book also contains exercises designed to reinforce and extend readers' understanding, along with a series of appendices that explore the technical details of this exciting new theory.
Biomateriomics is the holistic study of biological material systems. While such systems are undoubtedly complex, we frequently encounter similar components -- universal building blocks and hierarchical structure motifs -- which result in a diverse set of functionalities. Similar to the way music or language arises from a limited set of music notes and words, we exploit the relationships between form and function in a meaningful way by recognizing the similarities between Beethoven and bone, or Shakespeare and silk. Through the investigation of material properties, examining fundamental links between processes, structures, and properties at multiple scales and their interactions, materiomics explains system functionality from the level of building blocks. Biomateriomics specifically focuses the analysis of the role of materials in the context of biological processes, the transfer of biological material principles towards biomimetic and bioinspired applications, and the study of interfaces between living and non-living systems. The challenges of biological materials are vast, but the convergence of biology, mathematics and engineering as well as computational and experimental techniques have resulted in the toolset necessary to describe complex material systems, from nano to macro. Applying biomateriomics can unlock Nature’s secret to high performance materials such as spider silk, bone, and nacre, and elucidate the progression and diagnosis or the treatment of diseases. Similarly, it contributes to develop a de novo understanding of biological material processes and to the potential of exploiting novel concepts in innovation, material synthesis and design.
Why would Gustav Mahler (1860-1911), modernist titan and so-called prophet of the New Music, commit himself time and again to the venerable sonata-allegro form of Mozart and Beethoven? How could so gifted a symphonic storyteller be drawn to a framework that many have dismissed as antiquated and dramatically inert? Mahler's Symphonic Sonatas offers a striking new take on this old dilemma. Indeed, it poses these questions seriously for the first time. Rather than downplaying Mahler's sonata designs as distracting anachronisms or innocuous groundplans, author Seth Monahan argues that for much of his career, Mahler used the inner, goal-directed dynamics of sonata form as the basis for some of his most gripping symphonic stories. Laying bare the deeper narrative/processual grammar of Mahler's evolving sonata corpus, Monahan pays particular attention to its recycling of large-scale rhetorical devices and its consistent linkage of tonal plot and affect. He then sets forth an interpretive framework that combines the visionary insights of Theodor W. Adorno-whose Mahler writings are examined here lucidly and at length-with elements of Hepokoski and Darcy's renowned Sonata Theory. What emerges is a tensely dialectical image of Mahler's sonata forms, one that hears the genre's compulsion for tonal/rhetorical closure in full collision with the spontaneous narrative needs of the surrounding music and of the overarching symphonic totality. It is a practice that calls forth sonata form not as a rigid mold, but as a dynamic process-rich with historical resonances and subject to a vast range of complications, curtailments, and catastrophes. With its expert balance of riveting analytical narration and thoughtful methodological reflection, Mahler's Symphonic Sonatas promises to be a landmark text of Mahler reception, and one that will reward scholars and students of the late-Romantic symphony for years to come.

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