The golden age of American popular music - not just jazz, but the popular songs even people who didn't like jazz listened and danced to, and which were often then taken as vehicles by jazz players - (Jazz is omnivorous) was the first half of the twentieth century. A common feature of these songs is daring harmony; quite often the melody note is accompanied by a chord to which it doesn't even belong. I first noticed this - though I must have semi-consciously enjoyed it thousands of times before; most people are not conscious of more than the melody, though the harmonies are working on them - in Kurt Weill's 'September Song', but yesterday I was looking at 'Some of these Days' (incidentally a favourite of Jean-Paul Sartre's, though that may not be a recommendation) and saw it again. Here's the melody line, with the chords (I have left out a few inessential ones) marked above:
People such as myself and, I hope, a few others of an analytic (did someone say 'pedantic'?) turn of mind like to know, as far as it's possible, (which admittedly isn't very far) just why the music that sounds great does so. I have heard even accomplished musicians say that such an analytic approach must surely reduce one's true enjoyment of the music. Keats, who with his medical training ought to have known better, made a similar complaint about Newton's analysis of the rainbow. No; knowing how things work increases one's joy in them.