The Harmonicon


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Music and Mathematics


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From ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This work links these two subjects in a manner that is suitable for students of both subjects, as well as the general reader with an interest in music.




Number to Sound


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Number 10 Sound: The Musical Way 10 the Scientific Revolution is a collection of twelve essays by writers from the fields of musicology and the history of science. The essays show the idea of music held by Euro th pean intellectuals who lived from the second half of the 15 century to the th early 17 : physicians (e. g. Marsilio Ficino), scholars of musical theory (e. g. Gioseffo Zarlino, Vincenzo Galilei), natural philosophers (e. g. Fran cis Bacon, Isaac Beeckman, Marin Mersenne), astronomers and mathema ticians (e. g. Johannes Kepler, Galileo Galilei ). Together with other people of the time, whom the Reader will meet in the course of the book, these intellectuals share an idea of music that is far removed from the way it is commonly conceived nowadays: it is the idea of music as a science whose object-musical sound--can be quantified and demonstrated, or enquired into experimentally with the methods and instruments of modem scientific enquiry. In this conception, music to be heard is a complex, variable structure based on few simple elements--e. g. musical intervals-, com bined according to rules and criteria which vary along with the different ages. However, the varieties of music created by men would not exist if they were not based on certain musical models--e. g. the consonances-, which exist in the mind of God or are hidden in the womb of Nature, which man discovers and demonstrates, and finally translates into the lan guage of sounds.




John Wallis: Writings on Music


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John Wallis (1616-1703), was one of the foremost British mathematicians of the seventeenth century, and is also remembered for his important writings on grammar and logic. An interest in music theory led him to produce translations into Latin of three ancient Greek texts - those of Ptolemy, Porphyry and Bryennius - and involved him in discussions with Henry Oldenburg, the Secretary of the Royal Society, Thomas Salmon and other individuals as his ideas developed. The texts presented in this volume cover the relationship of ancient and modern tuning theory, the building of organs, the phenomena of resonance, and other musical topics.







Catalogue


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Sing Aloud Harmonious Spheres


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This is the first volume to explore the reception of the Pythagorean doctrine of cosmic harmony within a variety of contexts, ranging chronologically from Plato to 18th-century England. This original collection of essays engages with contemporary debates concerning the relationship between music, philosophy, and science, and challenges the view that Renaissance discussions on cosmic harmony are either mere repetitions of ancient music theory or pre-figurations of the ‘Scientific Revolution’. Utilizing this interdisciplinary approach, Renaissance Conceptions of Cosmic Harmony offers a new perspective on the reception of an important classical theme in various cultural, sequential and geographical contexts, underlying the continuities and changes between Antiquity, the Middle Ages and the Renaissance. This project will be of particular interest within these emerging disciplines as they continue to explore the ideological significance of the various ways in which we appropriate the past.




The Musical Language of Italian Opera, 1813-1859


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Though studying opera often requires attention to aesthetics, libretti, staging, singers, compositional history, and performance history, the music itself is central. This book examines operatic music by five Italian composers--Rossini, Bellini, Mercadante, Donizetti, and Verdi--and one non-Italian, Meyerbeer, during the period from Rossini's first international successes to Italian unification. Detailed analyses of form, rhythm, melody, and harmony reveal concepts of musical structure different from those usually discussed by music theorists, calling into question the notion of a common practice. Taking an eclectic analytical approach, author William Rothstein uses ideas originating in several centuries, from the sixteenth to the twenty-first, to argue that operatic music can be heard not only as passionate vocality but also in terms of musical forms, pitch structures, and rhythmic patterns--that is, as carefully crafted music worth theoretical attention. Although no single theory accounts for everything, Rothstein's analysis shows how certain recurring principles define a distinctively Italian practice, one that left its mark on the German repertoire more familiar to music theorists.




The Literature of Music


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