If anyone has interest in harmonic theory and why I/IV/V progressions are so pervasive, I highly recommend "The Harmonic Experience" by W.A. Mathieu. He really gets into the harmonic series, and how intervals are really low prime ratios. I read this book after being a professional musician for 15 years and it was an ear opening experience. there are lots of great singing exercises for really hearing the overtone seri…
That book looks really interesting - thanks for the recommendation. What still twists my melon about harmony is the Pythagorean Comma. Harmony equating to integer ratios seems so right... But the fact that a perfect 5th on a piano isn't really a perfect 5th troubles me at some existential level.
The fifths in equal temperament are completely fine, but the thirds are really quite a ways off from the harmonic 5/4 major third. I would recommend experimenting with the traditional meantone tuning system if you're interested in this -- it offers almost as much flexibility as equal temperament (with 6 adjacent keys on the circle of fifths being free of wolf intervals), and it lets you play with "real thirds".