Thank you to all for the high quality of the discussion. I am particularly taken with MTed's reference to pulling out subordinate melodies from the possible chords, which really helps explain counterpoint and some of voice leading. I assume that one way of tricking the brain is by linking up chords that gradually imply another key while they are still supporting the notes in the original key. I can't imagine doing it, but I can see the potential.

I found, in a book of Jazz Theory by Stanton (can't remember his first name, but it is easily the best and clearest book I have ever read), a really simple idea that I had never heard, and which will be obvious to all you music scholars, which is that one reason why a chord like C. a chord like Am, and a chord like Em (the I, VI, III chords in the key of C) can be often substituted for each other is that they share a couple of notes with each other!!!!! like C-E-G for C, E-G-B for Em, A-C-E for Am; just as the II and the IV can substitute on occasion. I know that sounds really infantile, but it was news to me!!

yours, Peter T.