Most glaringly, the author assaults Helmholtz without acknowledging the fact that people who study this topic in academia are way past that. It's like if I were to tell you that I've got an amazing new theory of physics and justify it by referencing Newtonian mechanics -- every academic knew it to be incomplete a century ago. Pointing that out is not a novel idea.
If you're interested in understanding how music works on a psychological level, "music theory" is the wrong thing to search for. The fields you're interested in are psychoacoustics and music perception.
Music theory is the study of compositional practice. It's a field that collects a whole bunch of descriptive theories on how composers in different periods and genres tend to work. You can use it to help yourself compose pieces in a given paradigm.
Psychoacoustics and music perception are the study of how we actually understand sound and music. The theories therein are what gave us things like lossy compression (e.g. "exactly what raw sound data can we discard and still preserve a perceptually identical recording?"). This is an incredible achievement in that it only works if we have a thorough understanding of how the brain processes sound and music. Psychoacoustics has little to say about what makes something qualitatively musical, but that's where study of music perception picks up.
In the overlap between these two fields, there are a bunch of people working on unified theories of harmonic/Western/tonal music. The author fails to reference the most interesting work done in this area. The ones I've found most convincing are:
- Dmitri Tymoczko's Geometry of Music: http://dmitri.tymoczko.com/geometry-of-music.html
- Bill Sethares's Tuning Timbre Spectrum Scale approach: http://sethares.engr.wisc.edu/ttss.html
- Andrew Duncan's Combinatorial Music Theory: http://andrewduncan.net/cmt/
Some of this work is pretty old at this point. Granted, it's surprisingly difficult to do a full literature review in this area. I know from experience, because I studied this topic in grad school. Someone could probably earn a Ph.D. by properly synthesizing all of these idea into a music theory that combines the analytical power of Tymoczko's approach with the first-principle work of Setheres.