This book starts well, with a lively journey around musical styles, including a brief visit to the promised Chinese zither music. Cook correctly embraces far more than Western art music in his analysis.
However, it drops into a rather protracted midsection on composition- and reception-based models ... "we need both" ... you don't say! And then you're soon into an extraordinary chapter on Music and Gender, or more specifically, the sex act. So Beethoven's masculine style is aggressive thrusting, and Schubert's more feminine offering is gay. This is exactly the kind of highfalutin agenda-laden balderdash which fixes a great divide between the intelligentsia and ordinary folk, both middle and working class. Not ideal for A Very Short Introduction!
I would also question his summarising point that music is "not a phenomenon of the natural world but a human construction". Your average songbird may question this, not to mention any human who happens him/herself to be a phenomenon of the natural world. Hmm. Have another think for the second edition.
I hoped for something on melody, harmony, rhythm, around the world. And there was some, but other things predominated. An interesting book, but ultimately frustrating.