The Euclidean Division of the Canon PDF Download
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Author: Andrä Barbera
Publisher: U of Nebraska Press
ISBN: 9780803212206
Category : Music
Languages : en
Pages : 332
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Book Description
The Division of the Canon is an ancient Pythagorean treatise on the relationship between mathematical and acoustical truths. Euclidean in style, sectional in nature, and essentially Pythagorean, the Division has been susceptible to quotation since antiquity and has attracted the attention of many musicologists, classicists, mathematicians, and historians of science.
Author: Andrä Barbera
Publisher: U of Nebraska Press
ISBN: 9780803212206
Category : Music
Languages : en
Pages : 332
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Book Description
The Division of the Canon is an ancient Pythagorean treatise on the relationship between mathematical and acoustical truths. Euclidean in style, sectional in nature, and essentially Pythagorean, the Division has been susceptible to quotation since antiquity and has attracted the attention of many musicologists, classicists, mathematicians, and historians of science.
Author: Euclides
Publisher:
ISBN: 9780803212206
Category :
Languages : en
Pages : 316
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Book Description
Author: Henry Wylde
Publisher:
ISBN:
Category : Music
Languages : en
Pages : 254
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Book Description
Author: Flora R. Levin
Publisher: Cambridge University Press
ISBN: 0521518903
Category : History
Languages : en
Pages : 365
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Book Description
In this book, Flora Levin explores how and why music was so important to the ancient Greeks. She examines the distinctions that they drew between the theory of music as an art ruled by number and the theory wherein number is held to be ruled by the art of music. These perspectives generated more expansive theories, particularly the idea that the cosmos is a mirror-image of music's structural elements and, conversely, that music by virtue of its cosmic elements - time, motion, and the continuum - is itself a mirror-image of the cosmos. These opposing perspectives gave rise to two opposing schools of thought, the Pythagorean and the Aristoxenian. Levin argues that the clash between these two schools could never be reconciled because the inherent conflict arises from two different worlds of mathematics. Her book shows how the Greeks' appreciation of the profundity of music's interconnections with philosophy, mathematics, and logic led to groundbreaking intellectual achievements that no civilization has ever matched.
Author: Benjamin Wardhaugh
Publisher: Princeton University Press
ISBN: 0691235767
Category : Mathematics
Languages : en
Pages : 416
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Book Description
A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.
Author: Leonid Zhmud
Publisher: Oxford University Press
ISBN: 0191626384
Category : History
Languages : en
Pages :
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Book Description
Pythagoras (c. 570 - c. 495 BC), arguably the most influential thinker among the Presocratics, emerges in ancient tradition as a wise teacher, an outstanding mathematician, an influential politician, and as a religious and ethical reformer. He claimed to possess supernatural powers and was the kind of personality who attracted legends. In contrast to his controversial and elusive nature, the early Pythagoreans, such as the doctors Democedes and Alcmaeon, the Olympic victors Milon and Iccus, the botanist Menestor, the natural philosopher Hippon, and the mathematicians Hippasus and Theodorus, all appear in our sources as 'rational' as they can possibly be. It was this 'normality' that ensured the continued existence of Pythagoreanism as a philosophical and scientific school till c. 350 BC. This volume offers a comprehensive study of Pythagoras and the early Pythagoreans through an analysis of the many representations of the Teacher and his followers, allowing the representations to complement and critique each other. Relying predominantly on sources dating back to before 300 BC, Zhmud portrays a more historical picture of Pythagoras, of the society founded by him, and of its religion than is known from the late antique biographies. In chapters devoted to mathematical and natural sciences cultivated by the Pythagoreans and to their philosophies, a critical distinction is made between the theories of individual figures and a generalized 'all-Pythagorean teaching', which is known from Aristotle.
Author: Thomas Christensen
Publisher: Cambridge University Press
ISBN: 1316025489
Category : Music
Languages : en
Pages : 1033
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Book Description
The Cambridge History of Western Music Theory is the first comprehensive history of Western music theory to be published in the English language. A collaborative project by leading music theorists and historians, the volume traces the rich panorama of music-theoretical thought from the Ancient Greeks to the present day. Recognizing the variety and complexity of music theory as an historical subject, the volume has been organized within a flexible framework. Some chapters are defined chronologically within a restricted historical domain, whilst others are defined conceptually and span longer historical periods. Together the thirty-one chapters present a synthetic overview of the fascinating and complex subject that is historical music theory. Richly enhanced with illustrations, graphics, examples and cross-citations as well as being thoroughly indexed and supplemented by comprehensive bibliographies of the most important primary and secondary literature, this book will be an invaluable resource for students and scholars alike.
Author: Don Michael Randel
Publisher: Harvard University Press
ISBN: 9780674011632
Category : Music
Languages : en
Pages : 1020
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Book Description
This classic reference work, the best one-volume music dictionary available, has been brought completely up to date in this new edition. Combining authoritative scholarship and lucid, lively prose, the Fourth Edition of The Harvard Dictionary of Music is the essential guide for musicians, students, and everyone who appreciates music. The Harvard Dictionary of Music has long been admired for its wide range as well as its reliability. This treasure trove includes entries on all the styles and forms in Western music; comprehensive articles on the music of Africa, Asia, Latin America, and the Near East; descriptions of instruments enriched by historical background; and articles that reflect today’s beat, including popular music, jazz, and rock. Throughout this Fourth Edition, existing articles have been fine-tuned and new entries added so that the dictionary fully reflects current music scholarship and recent developments in musical culture. Encyclopedia-length articles by notable experts alternate with short entries for quick reference, including definitions and identifications of works and instruments. More than 220 drawings and 250 musical examples enhance the text. This is an invaluable book that no music lover can afford to be without.
Author: James Evans
Publisher: Princeton University Press
ISBN: 0691187150
Category : Science
Languages : en
Pages : 346
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Book Description
This is the first complete English translation of Geminos's Introduction to the Phenomena--one of the most important and interesting astronomical works of its type to have survived from Greek antiquity. Gracefully and charmingly written, Geminos's first-century BC textbook for beginning students of astronomy can now be read straight through with understanding and enjoyment by a wider audience than ever before. James Evans and Lennart Berggren's accurate and readable translation is accompanied by a thorough introduction and commentary that set Geminos's work in its historical, scientific, and philosophical context. This book is generously illustrated with diagrams from medieval manuscripts of Geminos's text, as well as drawings and photographs of ancient astronomical instruments. It will be of great interest to students of the history of science, to classicists, and to professional and amateur astronomers who seek to learn more about the origins of their science. Geminos provides a clear view of Greek astronomy in the period between Hipparchos and Ptolemy, treating such subjects as the zodiac, the constellations, the theory of the celestial sphere, lunar cycles, and eclipses. Most significantly, Geminos gives us the earliest detailed discussion of Babylonian astronomy by a Greek writer, thus offering valuable insight into the cross-cultural transmission of astronomical knowledge in antiquity.
Author: Paul T. Keyser
Publisher: Taylor & Francis
ISBN: 113429803X
Category : History
Languages : en
Pages : 1073
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Book Description
The Encyclopedia of Ancient Natural Scientists is the first comprehensive English language work to provide a survey of all ancient natural science, from its beginnings through the end of Late Antiquity. A team of over 100 of the world’s experts in the field have compiled this Encyclopedia, including entries which are not mentioned in any other reference work – resulting in a unique and hugely ambitious resource which will prove indispensable for anyone seeking the details of the history of ancient science. Additional features include a Glossary, Gazetteer, and Time-Line. The Glossary explains many Greek (or Latin) terms difficult to translate, whilst the Gazetteer describes the many locales from which scientists came. The Time-Line shows the rapid rise in the practice of science in the 5th century BCE and rapid decline after Hadrian, due to the centralization of Roman power, with consequent loss of a context within which science could flourish.
