Reddit reviews The Power of Music: Pioneering Discoveries in the New Science of Song

It's not really limited in research, plenty of neurologists have done studies into the subject. There are schools where you can study music therapy which isn't a bunch of pseudoscience, it's built on solid research.

This book is a good laymen's summary but it gets a bit preachy near the end.

Another post recommended This is Your Brain on Music which is also a great book as well.