Is that a textbook? If so, I'm afraid I'd dismiss it based on the poor writing that it probably contains, based on all the other history books that contain poor writing.
Instead, I'd read selected biographies about composers since it will describe the world in which the composer lived as he lived it, as opposed to a description to how it appeared.
I'm not familiar with Headington's book. I started with Music in the Western World - A History in Documents (P. Weiss, R. Taruskin). It was meant as a companion book to a music history course and was passed on to me. It covers the usual Ancient Greece to contemporary music. What makes it unique is that most of it is quotes from contemporaries of each age. It shows us that at any time, any change or innovation was controversial and engendered heated discussion or frantic letter writing. It made the periods remarkably alive, and I thoroughly enjoyed this book.I then got A History of Western Music (Burkholder, Grout, Palisca) on the recommendation of someone in the forums. Apparently it's often referred to as "the Grout book". It is very thorough and in depth. I haven't gotten past Ars Nova and the 14th century even before the Renaissance. The publisher provides a companion site with examples for the hearing, and also quizzes and such for those who have a penchant for them. I find that in North America we don't get a lot of history other than the perpetual "discovery of America" and Henry's wives. So I studied history along with it, using the Web.I like the idea of studying composers, but find that history also gives a context to those composers. Or is it the other way around?