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

An interesting academic read with little practical utility imo. While technically very accurate, tediously mapping voice leading onto multidimensional graphs isn't overly superior than just looking at the notation or other easier methods. And while geometry validates rules of thumb that are already common practice (no pun intended), those rules of thumb are still a lot easier than the analysis methods presented in this book. A lot of "lecturing birds on flying" i'm afraid. So yes as an academic work, pretty good. But for the "ideal composer" as the book was intended...meh. Theory with little practical application.

Tymoczko is undeniably right about the mathematics here. You could choose to represent a four-note voice-leading as a fourth dimensional orbifold. But, by the end of the book, it's still unclear why you would. E.g., the symmetries that exist in these geometries are mathematically valid, but is a composer working in a major key likely to value the suggestion they invert it into the Locrian mode? Read this if you want some interesting mathematics, but don't expect it to be practical.

The utility of this book is highly overstated, IMHO. As someone who has taught college math I am not intimidated by the 'multi-dimensional space' concept, and I've been a composer for decades (a film for which I wrote the score is doing fairly well on Amazon Prime). I find his explanation of tonality wanting (really, the augmented and diminished chords are more 'natural' than the major and minor?), and I found nothing in here that inspired me with fresh approaches to composition. All the diagrams look pretty, but once I got past all the flash, at its core I found myself asking: "where's the beef?"

I'm working my way through this. So far every page has been fantastic. Extremely practical approach; much deeper than just a geometric analysis. The quality of the physical hardcopy itself is quite a bit better than average as well. I buy and read many books on music theory and information. This is one to buy.

Truly thought provoking, very abstract concepts. Being honest I had to read some sections more than once, but the concepts are mind opening once understood.

Nice

The author shows how harmony and counterpoint can be described as efficient movements in higher dimensional space. And then he uses this as a model to show how music from different eras are actually related. Which was very interesting and I learned a lot through the discussion, but it fails to explain much about the nature of music that hasn't already been stated by other authors. And it's certainly not the new revolution in music theory that he hypes it up to be. It's simply a really nifty new tool to analyze music.It's a good read and I recommend it to anyone interested in theory or composition but it's not offering a practical working theory by any stretch of the imagination. I seriously question the usefulness of this new model for composition and I suspect the constraints of space and time a person experiences through the use of a physical instrument such as a piano may render this model completely redundant for making music. As an analytical tool it seems useful.

The tip of the iceberg. An exciting analysis and synthesis of musical styles and development, hopefully this work will become the progeny of many future works as it is rich in ideas.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.

a very interesting perspective on how music is constructed. however for a person not versed in music theory( even the basics) might find this book heavy going. but having said that the auther goes out of his way to make a complex subject as accessible as possiblecomposers will probably find intersing material here.

I've been waiting 30 years for a book like this.... Quite hard work but definitely worth it. The vision to link all these types of tonal music is amazing. As a composer who went through university in the serial wasteland of the late 1970's the recognition of the place of jazz (and rock) as a beacon of hope for tonality strikes a (consonant) chord. I can't recommend this book highly enough.

A thought provoking book - well worth the read.

Easy to understand, and would recommend for anyone learning how to compose music, or have an interest in the subject.

まだ邦訳が出版されていないネオリーマンセオリーの本です。いわゆるバークリーメソッドやクラシック和声学では捉えづらい印象派のような調性間の薄い、しかし無調ではない音楽を分析／創作するにあたって非常に有用です。ネオリーマンセオリーはヨーロッパではそれなりに流行っているようです。