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I got this book because I wanted to learn about the next level of music theory and had heard about Cohn from my professor at the time. When I completed my formal study of classical music theory, it left me wondering what else there was to learn, because there were so many different techniques and sounds that only got glossed over by classical harmony as either 'coloristic' chord progressions or endless tonicizations. I think this strictly tonal idea of music is probably influenced a lot by Schenker, and there are aspects of it that have become outdated. Jazz theory, on the other hand, is to a large degree about finding the right scale and chord tones to improvise over any chord and thus largely based on practice and practical application.
This book is totally different. It takes what you know about harmony and flips it on its head, in the greatest way possible. If you've never read anything by Cohn or don't know about the Tonnetz, then you are in for a wild ride! While the writing is extremely academic and at times I found myself looking up a word every couple of pages, the tone of the writing is pleasant and fun. There is no snobbery here; he is simply laying down every discovery that he has made about a different way that triads can relate to each other. Also, as he says, you only need to have a very basic understanding of theory to understand what he is explaining here. There are moments when the sentences get dense with information but once you take it in slowly for a second time you will probably understand it. I think that having a background in music theory sometimes slowed me down because he explains things in a new way.
Every anomaly that has ever tickled the edge of your awareness pertaining to music theory, 'borrowed' chords or scale degrees, and chord progressions that twinge the ear and drive curiosity (chromatic mediants, anyone?) are all opened wide and explained so thoroughly (with maps to navigate!) that you will become aware of a whole new system of thinking about consonance and dissonance; and, better yet, of controlling them to a much larger degree than the tonal (or jazz) system allows for. This theory of how triads relate is on another level, and completely explains many anomalies from classical theory when applied to popular music, or the music of the 19th century- Debussy, Wagner, etc.
I found myself reaching profound understandings that the Beatles used this mode of relation, it is what composers for film use, it is that 'surprising' sound that is becoming less and less foreign to us as time goes on. They used this subconsciously, but this explains how they got there- and explains a way to take it in any direction that you want. Just like tonally classical theory explains how classical composers composed to create their specific system of music, this explains how lots of composers who have veered away from classical rules and dogma have chosen to compose.
This is a harmonic realm where consonance and dissonance is temporarily suspended, allowing more subtle control between the two and it really is a beautiful realm of huge possibilities. If you are a composer or a musician of any kind, I highly recommend this book to you, as a tool to write more beautiful and "new" sounding songs. This is another system to use as a tool, like classical or jazz theory.
I myself am not a huge proponent of strictly following any theory, but learning tonal theory has led me to some of my most satisfying songs, and I anticipate that mastering the ideas of this type of music theory will lead to me create even more beautiful music which is expressive of life on a deep level. Already, learning this has allowed me to "spin" out of tonally-controlled compositions, into harmonic realms of an almost alien beauty, like a controlled but seemingly chaotic orbit on the edge of perfection and complete wreckage, and then without missing a beat, drop into a completely new tonality. It's freaking mind-blowing, and for that experience alone, I highly recommend it!
As the book points out, very intuitively, in one of the earlier chapters, there are basically 3 different ways of organizing music: Tonal, Not strictly tonal- using tonal ideas like triads and such to skip around to different tonics and tonalities (jazz probably falls somewhere in this second category as as well), and Atonal. While tonal music is great I think there may be too many rules to still be entirely relevant. While atonal music can be beautiful in its own way, the "structure" of that can literally be determined by rolling dice, so that's just not good enough for me yet. The cutting edge type of theory here straddles the boundaries between these two PERFECTLY.
Using this system allows composers a way to flirt with or have a lengthy affair with dissonance- while using concepts that are familiar to them (like triads) and being in TOTAL CONTROL. That, to me, is the biggest part of this book. It gives me a way to be in total control of where I am going and to understand what I am going to do next. If you want to spice up your compositions- get this! If you want to have a system for understanding non-traditional harmonies, then GET THIS!! I can't recommend this enough, it is an amazing book, and if you don't have it already then you are missing out on tons of possibilities which you probably aren't even aware of right now.