I have to admit that Barker is the preeminent writer on Ancient Greek music theory. I can't fault this book on technical grounds, or really on any of the content. And if someone told me they really wanted to know all they could about how Ancient Greeks thought about musical pitch, I'd probably point them here.
However, my ranking is lowered because of its incomprehensible density and dryness. As much as I'm used to dense academic texts, even this was a slog.