Firstly, I think the most glaring omission is Louis Andriessen, who not only co-wrote The Apollonian Clockwork, but has also composed some of the most important and exciting non-Webernian music around. What is especially important about Andriessen is that his own 'minimal' style is fully aware of the Modernist heritage at the same time as it critiques or refutes it, as oppoesed to others who just dismiss it outright and have no real understanding of post-Webernian serialism. Also, Andriessen's continuing political ideals make him an interesting study in current musico-poltical relations (now that most are dead: Nono, Cardew; or just write rubbish: Henze).
In fact, while I am no authority on comtemporary Dutch music, I certainly know no more about it through reading this book. Which brings me to my second point: the Anglo-West Europe-American-centricity.
Not only does he leave out the Netherlands, Finland, Scandinavia, South America, as well as the bizarre history of post-war Polish music, but also Australia and (South East) Asia. Now while I am no doubt partisan, his only mention of Australia is one line about the Elision Ensemble in relation to Richard Barrett, Chris Dench, and Finnissy. I think Australia has some of the best composers anywhere (Liza Lim, for instance), writing from a variety of perspectives and a fuller account of these
place-specific musics would have interesting, for instance examination of Australia's liminal position between Europe and Asia and how that affects attitudes to composition.
While his bit on Part is a witty piece of pomo gaming, he sometimes trips himself up in his pomo considerations (as other reviewers have pointed out): for instance, he says that the postmodern condition entails the loss (both through desire and circumstance) of the dominant-central figures crucial to the Modernist project (eg. Boulez) because there are now 'many streams' instead of a river, but he then later complains that no new 'Generals' have stood up to replace the these old ones in terms of central importance to the musical world. In this way, he doesn't really trace many new paths in his last section, but simply rings up his old mates (Boulez, Birtwistle, Berio, Stockhausen, Ligeti, etc) and asks them what they've been up to recently. But, then again, that is really what the book is for and it does it admirably.
And not only is his championing of Barraque timely, but Bill Hopkins too, whose music I was unaware of until reading his bit.
One hopes there will be a 3rd edition after most of the 'peace-time Generals' are gone and a final summation of the lasting effects of the immediate post-war project can take place. Until then this is the book to read if you want to know about the good-old music with no tunes that we all love.
Also the Strings and Knots is organised in reverse alphabetical (very postmodern!)