Yes, add#9 definitely exists and is common in jazz. Let's go through some background info first.
The nomenclature of chord naming works like this: If the chord has a 7th of any type (or something from the 7th family like the 6 or b6) then we can have 9ths, 11ths and 13ths in a chord.
ex) Cadd2 is CEG and D. This chord does not have a 7th (or 6th, which is a replacement for the 7th) so we would call the D a 2nd, rather than a 9th.
ex) Cadd9 requires us to have some sort of 7th as well. It could be CEGBD or CEBD (we don't need the 5th) or even CEGBbD, etc.
So, a true Cadd#9 would involve a B of some sort.
Upper Structure(US) Chords
To form all sorts of #9 (or 11th and 13th) chords we can use a concept called Upper Structures. These are a class of amazing chords that are generically defined as a polychord (a dom 7th shell, which is R3b7, plus some combination of 9, 11 and 13). I'm speaking purely from a piano standpoint. We can think of US chords as two chords in two different hands. The left hand(LH) will have the dominant 7th, while the right hand(RH) will have the 9th, 11th and 13th (the "colour" notes).
Here's an example of an US chord with a #9. Let's say we're talking about Cadd#9. The LH will have the notes C E and Bb. The RH will have the rest. #9 is essentially D# (or Eb if we rename it enharmonically). Let's call it Eb as it will be easier to understand the next part. We have 2 avoid notes (notes we're not allowed to include) in any US chord. These are always a perfect 4th from the root (F in this case) and a major 7th from the root (B in this case) because the 4th clashes with the 3rd of our Cdom7 and the B clashes with the b7 of our Cdom7 chord.
To fill in the rest of the chord, choose any major or minor chord that includes Eb, but does not include our avoid notes (F and B). Here's a list:
- Eb major (Eb as the root...Eb G Bb)
- Eb minor (Eb as the root...Eb Gb Bb)
- C minor (Eb as the third...C Eb G)
- Ab major (Eb as the fifth...Ab C Eb)
Cb major (Cb Eb Gb) wouldn't work because Cb is the same as B and that's an avoid note. Neither would Ab minor because it contains a Cb (avoid note).
Now that we have these 4 chords, we can combine our LH chord with any of these and we will get a #9 chord. If we use the Eb major chord, since it's a minor 3rd from our root (C), we would call the chord C USbIII (pronounced as C upper structure flat 3). For the Ab major example, we would call the chord C USbVI since Ab is a minor 6th above the root. If we choose C minor we would get C USi. Notice the use of large roman numerals for major chord upper structures and the use of lower case roman numerals for minor chord upper structure chords. Here are some example of what we would call the intervals in these chords:
ex) LH: C E Bb with RH: Ab C Eb gives us a C#9b13 chord a.k.a. C USbVI
ex) LH: C E Bb with RH: C Eb G gives us a C#9 chord a.k.a. C USi
In general, forming chords based on using upper structures allows us to not have to worry about figuring out b9, 9, 11, #11, etc intervals. We can simply view the chord as a polychord.
Using Upper Structure Chords
In jazz, you can use them to replace dominant 7th chords or you can use them as passing chords that are used to get to a certain chord.
Here's an example of a typical "turn around" in jazz using the pattern I - VI - II - V (one, six, two, five). In the key of C major, I is CEG, VI is ACE, II is DFA and V is GBD. In jazz, we would use the 7th versions of those chords: I is CEGA or CEGB, VI is ACEG, II is DFAC and G is GBDF. No jazz musician worth their salt would play GBDF for the V chord, it's just too tame, hence upper structures! For your case, let's say we wanted to have the #9 interval in the chord.
For the V chord, #9 would be A# (G is the root).Let's call it Bb for simplicity. Our avoid notes in this case are 4 (C) and 7 (F#). What major and minor chords have a Bb, but do not contain C or F# (or their enharmonic equivalents which are B# and Gb respectively)?
- Bb major
- Bb minor
- G minor
- Eb major
So, we could play the V chord as an Eb/G7 chord, which means we have the notes G B F Eb and Bb. That's a very nice and lush chord to use in place of the typical GBDF!
Check out the wikipedia entry on Upper Structure chords for more details: enter link description here