A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) (英語) ハードカバー – 2011/3/21
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Most listeners prefer tonal music to atonal music, but what exactly is the difference between them? In this groundbreaking work, author Dmitri 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. Tymoczko creates for the reader a new framework for thinking about music, one that emphasizes the commonalities among styles from Medieval polyphony to contemporary jazz.
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 the relationships among familiar chords and scales. This gives readers the tools to translate between the musical and visual realms, revealing surprising degrees of structure in otherwise hard-to-understand pieces.
Tymoczko uses these theoretical ideas 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. Using analysis to make his argument clear, he discusses a host of familiar pieces by Bach, Mozart, Chopin, Debussy, Stravinsky, Shostakovich, Miles Davis, Bill Evans, and others.
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.
a tour de force, a rich and suggestive summation of an exciting new perspective, a jumping-off point for further explorations. (Peter Pesic, Times Literary Supplement)商品の説明をすべて表示する
This work adds additional ways of seeing music that are not clearly apparent with standard notation.
I was surprised that so many of the composers artists and works were ones that I had noted to be significant in there avant-garde expansion of musical boundaries.
A joke punchline is achieved by misdirecting the audience to believe that the joke is taking them in one direction when it is actually taking them where they did not expect.likewise, many of the clusters of tones in jazz, Tristan, Shostakovich, Debussy, Chopin and others, create ambiguity about the intended direction and resolution and these clusters may contain many possible future paths, thus making anticipation difficult and surprise likely.
It explains music theory in a unique way that I have yet to see from any other source (if there is another book out there that offers such an approach, I would like to know about it). Music is in many respects a mathematical language and basing the study of it around including its geometrical forces is a great way of finding a new understanding.
Maybe many of his ideas aren't (completely) new as some reviewers have asserted, but they are presented in a way that is accessible and understandable to those of us without a higher education (I would also think that many with music degrees would ALSO benefit from this book as well though).
Having said that, the novice -should- study a traditional harmony book- such as Piston's Harmony -before- reading this book. Had I not done that, much of the terminology, ideas and principles would not have made sense to me.
This book has made me want to re-tackle my old Piston Harmony book and others yet this time, with a fresh insight and a new perspective. I will be studying this book alongside the old standard curriculum such as Piston's for a very long time to come. It has already helped my learning and my teaching as well (I teach beginner and intermediate piano students).
I have read some of the egg-headed reviews that cast aspersions on this book and I completely disagree with them, so much so that I chose to write this review, something that I do not normally do.
My response to them would be that if you are that learned, that smart, that all-knowing, then why are you even bothering to read this book or any other book for that matter?
Great book, get it, study it and it will give you a fresh view on many old ideas perhaps some that you have been already been studying for many years prior.
I would like to add that this book is most helpful with regards to the study of harmony and chords in classical music though it is ALSO very insightful for the study of 20th century music and jazz as well. The last couple of chapters are about these more contemporary genres and it has sparked my interest in music that I don't generally care for or seek out.
I would love to sit in on the Professor's classes one day, though I live in Louisville, and I doubt that will ever happen! But, who knows, at least I have this book!
Despite the originality and the level of abstraction, the content is kept to the level of undergraduate music majors (or music lovers) with a modest fund of mathematics. Once the key ideas of "equivalence class", already familiar to musicians because of octave equivalence, and "quotient space" are grasped, the rest is fairly plain sailing.
The book is especially useful because of the large number of musical examples on-line, in both score and audio format. I wish all theory books had such examples. The examples do convince me that the geometric approach provides a unifying approach to Western music over the past five or six hundred years. For example, the geometric approach helped me to understand how and why chromatically altered chords work in a way that I never could before.
However, the geometric approach is not complete, it does not cover everything we hear in musical structure, and it would have been nice if the author had provided more help in understanding its limitations, e.g. what the heck is a cadence anyway? Also the "counterpoint" in the book's title covers only the rudiments of what most people would think of as counterpoint, e.g. there is no discussion of imitative forms.
As a composer myself, who uses algorithms to generate scores, the geometric approach offers a highly promising avenue to automatically generating listenable chord progressions and voice-leadings, and not just in 12-tone equal temperament.
It also would have been nice if the book had clearly situated itself in its context of contemporary mathematical music theory, with more discussion of relations to neo-Riemannian theory and such. But it would probably be more appropriate if this were addressed in a new book aimed at the graduate school level of readership.