Plainchant is the oldest substantial body of music that has been preserved in any shape or form. It was first written down in Western Europe in the eighth to ninth centuries. Many thousands of chants have been sung at different times or places in a multitude of forms and styles, responding to the differing needs of the church through the ages. This book provides a clear and concise introduction, designed both for those to whom the subject is new and those who require a reference work for advanced study. It begins with an explanation of the liturgies that plainchant was designed to serve. It describes all the chief genres of chant, different types of liturgical book, and plainchant notations. After an exposition of early medieval theoretical writing on plainchant, Hiley provides a historical survey that traces the constantly changing nature of the repertory. He also discusses important musicians and centers of composition. Copiously illustrated with over 200 musical examples, this book highlights the diversity of practice and richness of the chant repertory in the Middle Ages. It will be an indispensable introduction and reference source on this important music for many years to come.

Fully revised and updated, this text adds coverage of mashups and auto-tune, explores recent developments in file sharing, and includes an expanded conclusion and bibliography.

Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.

Discusses how European scientists from the High Middle Ages through the Enlightenment used wonders, monsters, curiosities, marvels, and other phenomena to envision the natural world.

Close readings of ostensibly “blank” works—from unprinted pages to silent music—that point to a new understanding of media. In No Medium, Craig Dworkin looks at works that are blank, erased, clear, or silent, writing critically and substantively about works for which there would seem to be not only nothing to see but nothing to say. Examined closely, these ostensibly contentless works of art, literature, and music point to a new understanding of media and the limits of the artistic object. Dworkin considers works predicated on blank sheets of paper, from a fictional collection of poems in Jean Cocteau's Orphée to the actual publication of a ream of typing paper as a book of poetry; he compares Robert Rauschenberg's Erased De Kooning Drawing to the artist Nick Thurston's erased copy of Maurice Blanchot's The Space of Literature (in which only Thurston's marginalia were visible); and he scrutinizes the sexual politics of photographic representation and the implications of obscured or obliterated subjects of photographs. Reexamining the famous case of John Cage's 4'33”, Dworkin links Cage's composition to Rauschenberg's White Paintings, Ken Friedman's Zen for Record (and Nam June Paik's Zen for Film), and other works, offering also a “guide to further listening” that surveys more than 100 scores and recordings of “silent” music. Dworkin argues that we should understand media not as blank, base things but as social events, and that there is no medium, understood in isolation, but only and always a plurality of media: interpretive activities taking place in socially inscribed space.

Musical notation has not always existed: in the West, musical traditions have often depended on transmission from mouth to ear, and ear to mouth. Although the Ancient Greeks had a form of musical notation, it was not passed on to the medieval Latin West. This comprehensive study investigates the breadth of use of musical notation in Carolingian Europe, including many examples previously unknown in studies of notation, to deliver a crucial foundational model for the understanding of later Western notations. An overview of the study of neumatic notations from the French monastic scholar Dom Jean Mabillon (1632–1707) up to the present day precedes an examination of the function and potential of writing in support of a musical practice which continued to depend on trained memory. Later chapters examine passages of notation to reveal those ways in which scripts were shaped by contemporary rationalizations of musical sound. Finally, the new scripts are situated in the cultural and social contexts in which they emerged.