The Music of the Spheres is a not-completely worthless history of the inter-relation of music (and to an extent, art in general) and science. If James had stopped at providing a simple survey of his materials, he might have done well in providing a brief history of Western civilization's evolving attitudes toward music and science up to the 18th century. James, unfortunately, fails to prove his thesis, and as science becomes more complex, shrinks from that part of his discussion.
James posits that science has failed modern society in a way that it did not fail ancient civilizations through the Romantic era. Philosophy and science, bound together, provided mankind with a sense of place in the universe, and this was not only reflected in the development of art, but this philosophical understanding derived, in portion, from understanding of music. While that may be true, the understanding that the ancient philosophers gathered from their musical experiments was the foundation for centuries of fallacious thinking about the nature of the universe which, when it clashed with empirical observation during the Renaissance, led to the arrest of Galileo, among others. In defending this short-sighted view of the importance of music, James is left in the awkward position of supporting a philosophical view of the world that is not supported by our observations of the world. James never gives us this defense, and instead discusses the elevation of the status of the artist as the meaning-maker in the Romantic era at length, without ever really stopping to consider that science's contributions to society since the mid-1800s could be anything but a bad thing.
All this seems to be because James has fundamentally misunderstood the project of philosophy, and the project of science as a sub-discipline of philosophy. Philosophers have been tasked for millennia with helping us understand everything from the best form of government to our place in the universe, and in the 1660s, the "experimental program" of philosophy began diverging into modern science: a form of philosophy that examines the world around us the way it actually is, and attempts to draw conclusions from observations.
The experimental program of philosophy was a marked difference from the inductive approaches that led the ancients to rationalize about the music of the spheres, but just because the work of science has branched off from the work of philosophy does not mean that philosophers have stopped asking questions of grand importance. James here seems to be lamenting the passage of an era when it was possible for someone to make wild rationalizations about the function of the universe from the banging of pots.
While it is not clear that James does not understand modern science well enough to discuss it in relation to music, he refrains from that discussion as his history approaches the modern day. He shifts the conversation away from his original theme by simple dismissals that theories of evolution and quantum mechanics have left us nothing but a spiritual sense of ennui as the universe ceases to have any inherent meaning. Even as James discusses more recent musical developments (like 12-tone composition) and the increasing diversity within musical tastes, he fails to grasp that our rich musical landscape is possible, in part, because science has helped give us the philosophical means to understand that we all get to decide what the universe means for us.
Unable or unwilling to engage with poly-structuralist modes of meaning-making, James leaves the reader with a wish for a moment of silence in a cacophonous landscape. Unable to perceive the singular song that would give us all meaning in the noise, James covers his ears, and invites the reader to do the same.
James' reach exceeds his grasp in The Music of the Spheres. While James' understanding of music history is beyond dispute, this book would have been much better had he as complete an understanding of science or philosophy. Instead, The Music of the Spheres reads like an undergraduate essay on a complex topic. James is capable of telling part of the story, and if he stuck to the part that he knew about, this would have been a much better book.