Now then. All sorts of interesting ideas proposed and some useful approaches spun off. But can we use a bit of detective work, apply Occam’s razor and come up with a simpler way of thinking about this? Did Brecker really magically invent a way of adding a major third to a minor chord?
The late great MB was many things, but before he was anything else he was an utterly fluent classic bebop player. Bear in mind that the lines Nick analyses here are certainly scalar. Consider also that it was always common in classic bebop (and funk) to treat II-Vs or even IIs as just Vs. Where does that get us?
I’d say that Brecker is possibly just playing A7/E (I’ll stick to Nick’s usage of tenor transposition), using the bebop scale and just hanging daringly on the “passing tone” of the scale. (Maybe even straphanging…) A classical analyst might refer to this as a (very) extended appogiatura.
So is this a mode of the A7 bebop scale or Em7 add major 3rd?
E F# G G# A B C# D
Make up your own mind as always, and what matters most is how you make sense of things, but I’d add a few other thoughts.
1. I’ve seen plenty of charts with eg A7/E written instead of Em7 (or 9 or 11). I don’t know whether that’s a deliberate intention to convey this “mode of bebop scale” approach or just the way things happen to have been notated. And the tendency of early jazz and bop to think of just V-Is (with the elaboration to II-V-I as an option that came along later) is borne out by musicians’ playing and by charts they wrote themselves.
2. Brecker certainly did produce some amazing and often technically very intriguing solos. But all I know about the guy indicates that there was usually an underlying simplicity. He was once asked how he came up with his lines (or something like that) and just remarked that “pretty much everything I play is a tritone substitution”. I’d suggest that there’s a man who exhaustively explored simple principles rather than inventing new ones. Such as a sort of “magic” major third on a minor chord.
3. It’s always struck me that the bebop scales seem preordained to add the wackiest possible “passing tone” so as to flow best. Taken in isolation, the #5th freaks out a tonic chord, whether major or minor. The major 7th is added to a V chord – what, so you get both a dominant and major 7th? And of course, the weirdest thing we could add to a II chord is the major 3rd…
Remember also that Brecker is being slightly unorthodox here – in general we use the bebop added notes as a passing tone. I have a bit of a problem speaking about “bebop scales” at all and prefer to regard them as scales with passing tones.
4. Even so, playing eg E7 instead of Em7 is common in jazz. Both modally, as here (where we can recall that Dorian and Mixolydian are just one shade apart) and as substitutes in functional harmony.
5. And as ever – ain’t what you do, it’s the way that you do it.
I suppose it had to happen… Thank you TH (aka “confused of Bristol”) for asking about the en vogue topic of negative harmony. I completely understand your confusion.
A charming story related to me recently by Russell Occomore, one of the directors of 
Interesting piece in 
And of course, if you make it a policy not to lie, you’ll have a much easier life. No need to remember or concentrate – you can just get on and do your thing. Sadly, nowadays that isn’t a recipe for success, but you’ll sleep soundly. And fame often ain’t worth the candle anyway.
Jason Lyon on Music 