Moving along, working my way through Tchaikovsky's Guide to the Practical Study of Harmony. I'm already feeling that I understand harmonic structure a bit more now.

That's not too surprising really, chapters I through IX really cover most of harmonic exploration. Chapters X through XVII cover special cases and how to deal with certain dissonant chords, chapters XVIII through XXII are about modulation, and XXIII through XXXIV are about other ways to present chords to make the melodies and voices more interesting. So it's really about learning a groundwork, then acquiring some 'new options' involving non-harmonic harmonies to spice up (but not Jazz up - that would be a whole different book!) the sound.