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The Cambridge History of Western Music Theory Hardcover – May 13 2002
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"This first single-volume history of music theory in English is a significant addition to literature about music. [...] It should be part of all academic music collections" Choice
"[This] work is an extremely valuable contribution to the history of music theory...the essays are of high quality, and the scholarship is impeccable...Nearly every reader will find something of value herein. The book can serve both as a reference work and as a snapshot of current theoretical opinion. It belongs on the shelf of every scholar who has a serious interest in music theory and its development." Isis
This remarkable book not only offers the reader a detailed account of the entire history of theoretical writing about Western music from the ancient Greeks to modern times, but also provides an incisive critique of the original objectives and ultimate significance of such writing. The various contributors are all specialists well able to encapsulate as well as clarify the essence of complex materials. In addition, the excellent selection of plates, tables and examples, coupled with comprehensive bibliographies, provides rich and vivid contexts for subject-matter that is never merely abstract, but satisfyingly linked to the particulars of musical works. All teachers, researchers and students who take music seriously will find The Cambridge History of Western Music Theory enormously stimulating.--Arnold Whittall, Professor Emeritus of Music Theory & Analysis, King's College London
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. Richly enhanced with illustrations, graphics, examples and cross-citations, as well as being thoroughly indexed and supplemented by comprehensive bibliographies, this book will be an invaluable resource for students and scholars alike.See all Product Description
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The article entitled "Music Theory and Mathematics" written by Catherine Nolan naturally begins with a discussion of the Pythagorean influence and its going beyond merely numerical ratios to sophisticated mathematical models incorporating geometry, combinatorics, and algebra. And although the author does not give discuss it, the Pythagorean and neo-Pythagorean influence has found its way into efforts to automate musical composition in the field of artificial intelligence. These efforts have yielded impressive results, and have produced musical pieces that are definitely satisfying to the human ear. The author though gives a highly interesting discussion of the developments over the centuries since the days of the Pythagoreans, particularly the influence of the advances in both physics and mathematics. This was especially true in the seventeenth century, where physics really began to take off, and offered a more realistic foundation for musical theory. There are many other gems to be found in this article, where the reader for example will read about the contributions of Gioseffo Zarlino, the Italian musical theorist and composer who in 1558 extended the Pythagorean `tetractys' to what he called the `senario' and which provided in his view a theoretical justification for the imperfect consonances. The reader will also be exposed to the use of combinatorics to build musical compositions, such that when carried to extreme where are possibilities are considered, one obtains according to the author compositions that go beyond the usual harmonic and melodic syntax. Mersenne's table of possible melodies from 1 to 22 notes is illustrated is illustrated in this article. One also encounters the use of modular arithmetic in the equal temperament scale. The most interesting discussion though in this article is the one David Lewin's use of transformation theory in defining what he calls the `generalized interval system' and `transformation network' The author points to the Lewin musical models as giving an uncountable(!) number of conceivable musical spaces available to music theorists.
Another very interesting article in the book is the one entitled "The Role of Harmonics in the Scientific Revolution" by Penelope Gouk. At first glance one might think that this article is written from the odd "postmodern" viewpoint that to a large extent still permeates historical criticism. It is not however, and the author details a fascinating account of the impact of `harmonics' in the scientific revolution of the sixteenth and seventeenth centuries. Most interesting is her assertion that the application of mathematics before the seventeenth century was thought of as `natural magic', which is defined as essentially the use of "occult" forces to bring about changes or effects. Natural magic is to be distinguished from "demonic" magic that makes use of immaterial and intelligent beings or "demons." Thus the phenomenon of "sympathetic resonance" between two bodies was integrated into the new experimental sciences. Readers will remember that Isaac Newton was severely criticized for his universal theory of gravitation due to the belief by some at the time that it's action-at-a-distance property had an "occult" quality to it. But the physics of vibrating strings was developed in due time, and this along with the reaction of Enlightenment philosophers against any traces of the "occult" in experimental science was a reason for the acceptance of harmonics as reasonable and scientific. Extreme views of sympathy were elaborated however proposed, one due to Robert Fludd and discussed by the author in this article. Parts of the universe he thought were "sympathetically interrelated" with actions in one part having influence on another. It is fascinating to contemplate in retrospect that the physical behavior of the pendulum and the vibrating string held so much sway in the minds of philosophers, scientists, and mystics. This continues to this day of course, but in a much more elaborate manner, going by the name of string theory. Any vestiges of the occult are not present in any modern physical theory, and action-at-a-distance has been essentially replaced by the curvature-of-spacetime paradigm of Albert Einstein. Very loosely speaking however, the combination of the (quantized) vibrating string and the Einstein notion of gravity as being curvature of spacetime is what string theory is all about. Harmonics in this sense is therefore alive and well and is deeply integrated into the physics community at the present time.
Surely it is a bit pricey, but it is a treasury of information and is necessary, I think, to every researcher in the field of music theory and related (interdisciplinary) areas. It also covers psychology of music, and methodology of teaching music. Every chapter tries to give a complete, if brief, overview of the subject, and bibliography is simply great. You won't regret buying it!