My new interest is how Music Novatory dismisses the importance of overtones in pitch structure, and only speaks of their value in acoustics. This is something I'm not fully understanding yet, and I would love it if someone gave me a brief explanation of this reasoning (if that's possible :). Many contemporary music theorists try to explain everything with overtones.

Overtones, sometimes called natural harmonics, or upper partials, exist as a property of sound in the physical universe. Sound is the medium through which music is externally expressed. As an analogy, consider poetry. The medium for a poem may be the human voice, if it is spoken aloud, or ink on paper, if it is written down, or just the memory and thoughts of one who is reciting internally. We cannot expect to understand the MEANING of a poem by studying the tonal properties of the human voice, nor by studying the physical characteristics or chemical make-up of ink and paper, nor by analyzing the neurological responses in the brain of the thinker. Instead, we must understand the LANGUAGE in which the poem was composed.
Likewise, if we wish to understand a piece of music, we must understand the LANGUAGE of music. The language of music blossoms from generative mathematical structures that are perceived and understood intuitively by human beings. In the World of Pitch, these structures are generated with simple ratios that relate one fundamental frequency, or tone, to another. The presence and relative strength of the various overtones will change the timbre of each tone, but not its fundamental frequency or its function within the world of pitch. A piece of music, whether performed on a piano, guitar, orchestra, electronically with pure sine waves, or just in the mind and thoughts of someone hearing internally, will remain essentially the same piece of music. Manipulating the overtones of the various pitches in a performance will change the external, superficial sound of a particular performance, but will have no bearing upon the internal structure of the piece, or, for that matter, upon the generative structures of the musical language itself.
To summarize, and try to put this in perspective: Harmonic overtones are a property of sound in the physical universe, and as such they belong to the domain of Performance, which is more superficial and external than the domain of Generative Structure, which is where the language of music in born. Generative structure in the world of Pitch is based upon simple ratios. The harmonic overtone series is also based upon simple ratios (which gradually become more and more complex). Though they are both based upon simple ratios, it does not follow that one is based upon the other.
Note: There may be some types of music that rely more upon harmonic overtones than has been implied in the above paragraphs. This would include music for drone instruments, such as bagpipe, that is essentially static in harmony. In these cases, there is no harmonic movement, and the horizontal or linear aspects of harmony, namely voice-leading and chord patterns, are for all intents and purposes non-existent. In cases such as these, it would make sense for all pitches to be tuned as harmonic overtones of the fundamental drone. However, let us not forget that tuning is itself an aspect of the more superficial domain of Performance, so it is still not clear whether the overtone series is indeed involved in the generation of the musical structures of such music.