Just thought I'd chime in here...since I see where you're going.
I-major triad or major 7th
II-minor triad or minor 7th
III-minor triad or minor 7th
IV-major triad or major 7th
V-major triad with dominant 7th
VI-minor triad or minor 7th
VII-half diminished 7th or minor flat 5th 7th
Although I prefer to relate to the C scale, in the context of Wolfran it would be
Eb major 7th, F minor 7th, G minor 7th, Ab major 7th, Bb dominant 7th, C minor 7th, and D half dim or minor flatted 5th 7th.
Bear in mind that is by no means a comprehensive scope. This is only the beginning. I imagine the next step would be to learn the inversions of those chords. I would learn it in C and not try to overwhelm myself with all keys just yet.
Jazz is like a language. One must learn what to do before learning how to do it. Learn the letters, then words, syllables, sentences, then passages.
In other words, learn the notes, then intervals like thirds, sixths, fifths...then 10ths later, and notice I said later. After intervals, comes chords. Start with simple triads then add the major and minor or dominant 7ths. Once chords are mastered then progressions follow. Ok...I'll quit for now...cause it gets better....
