I am volunteering as a mentor for a non-profit which puts less experienced players into bands in an 8 week session leading up to a performance. My group is doing jazz, and I felt as if they needed a bit of background on basic jazz theory. So -a disclaimer:
WARNING THE FOLLOWING CONTAINS THEORETICAL CONCEPTS WHICH MAY BE OF ABSOLUTELY NO INTEREST TO NON-MUSICALLY MINDED PEOPLE.
1st. A jazz song is just a song, any song can be a jazz song.
2nd. The thrust of the evolution of jazz has been primarily in two directions -chord extensions and chord substitutions.
In a practical sense there are only really 3 types of chords -major, minor, and dominant seventh. Now, these chords do begin to overlap and this is where chord substitutions come into play. For example: a C-major chord is spelled C-E-G, an A-minor chord is spelled A-C-E. Two of those notes are the same, no? So it is possible that an A-minor chord could potentially work in place of C-major. We extend chords just by adding thirds on top of the three note chord -the 'triad.' So C-major becomes C-major 7th when we spell it C-E-G-B. It become C-major 9th when we spell it C-E-G-B-D. We could continue this (11th &13th chords), or we could sharpen or flatten the 'natural' notes that would be in that chord -each time creating a different 'color' for the basic C-major chord. Experienced jazz players just have a lot more colors in their Crayola box than the rest of us..
But, no matter how much one extends or substitutes chords, the melody requires the basic tonalities to be present in order for it to sound like the song. The most common jazz arrangements go beyond the melody and underlying harmonic structure by adding in the arranger's chosen substitution/extended chords, which does a disservice to people who are interested in learning the basic song and playing it their own way.
