A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) 1st Edition

Several years ago I happened to see one of Dmitri Tymoczko's Science articles. I was hoping to find an introduction to that paper's ideas that would be suitable for a course aimed at students with an undergraduate background in both mathematics and music theory, but none existed at that time. When OUP published A Geometry of Music, I was excited to see it; however, when I saw that half of the original six reviews here were strongly negative, I hesitated to buy it.Unfortunately, some previous reviewers seem to feel an animus toward the author and insist on using the book's dust jacket and introduction against him. But plainly OUP selected the blurbs it did to emphasize the book's potentially broader appeal, and it's hard to see how the author's account of his undergraduate music theory education in the introduction can be regarded as an affront to his alma mater. One has only to turn to the author's acknowledgments and read his copious footnotes to see that he has given ample credit where credit is due. The homoousian claims that most of the book is trivial, that much of the work has been purlioned, and that the remainder is useless are easily seen to be ludicrous. Reviewers who claim to have written books on "Algorithmic Computer Music" which don't seem to be available or claim that "[d]efining an all-encompassing numerical or spatial model is easy (and, honestly, trivial)" should make their works available for all to see. Perhaps their papers will appear in the journal Science - right after the next article on crafting a perpetuum mobile.After using A Geometry of Music as the basis for teaching a course, I find myself in agreement with those previous reviewers who praised its strengths; however, I do have two criticisms to offer. The book's most significant shortcoming from my perspective is its paucity of exercises. Unfortunately, there are only 38 of them, and those are relegated to Appendix F. Of those exercises only eight relate to the entire second half of the book, and four of those concern one of the topics of Chapter 7. While I understand that the book is intended to serve as an introduction for music theorists, composers, and amateurs, it seems likely that its main audience is going to be music students. In order to better serve students future editions of this book should include many more exercises, and the exercises should appear as an integral part of the book, not in an appendix. More casual readers can skip the exercises as they see fit. Kostka's text on twentieth-century music seems like a good model for the breadth and depth of musical analysis exercises that I would like to see, and the workbook for Cadwallader and Gagne's text on Schenkerian analysis could serve as a model for the level of difficulty that would be appropriate for this book.One other shortcoming of A Geometry of Music is its general avoidance of the underlying mathematics, even in the more technical appendices. I think many more computational examples and exercises should be included in a book at this level, and the general level of computational difficulty I would like to see in future editions would meet or exceed those of Straus's text on post-tonal theory. The material currently in Appendices A through E, together with additional examples and exercises, would enhance the body of the book. More technical appendices could then explore topics along the lines of the author's on-line supplements to his Science papers. This additional material would also demonstrate the falsehood of homoousian claims that the book is "trivial," that it lacks original ideas, and that topology adds nothing to our understanding of music.All in all, I highly recommend this book to anyone interested in seeing where music theory is going in the twenty-first century.

For those of us that did not go to music college and who are self taught and study music daily, this book is an invaluable resource.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!