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"I Will Survive"

The functionality of seventh chords depends on two things: whether it is a flat 7 or a natural 7, and whether the 3rd is major or minor. Dominant 7th chords are major 3rd/flat 7th, as you know. This is as you describe, "functional" in that it resolves up a fourth to the tonic. In the cases of Major and minor 7th chords (1,3,5,7) and (1,flat 3,5,flat 7) respectively, the 7th is there for color. If you played 7th chords up the scale you would have 1 Major 7th, ii minor 7th, ii minor 7th, 4 Major 7th, **5 Dominant 7th **, vi minor 7th, 7 dim 7th. Only the dominant 7th and the dim 7th are "functional" 7ths. (The dim 7th IS a dominant 7th just omitting the root.) Going further, you can add the ninth as well as the seventh. Same thing with regard to the major or minor 3rd, and the flat or natural 7th, in that there are major and minor ninths as well as dominant ninths. To complicate things Debussy uses whole tone scales which is c,d,e,f#,g#,a#(Bb), and C. This chord is major 3rd/flat 7, but is only for color. I would encourage you to read some popular music, from any period, that uses chord symbols as shorthand to the player. You will see exactly what I'm talking about.