Theory behind a 4th inversion G7#9 chord with a dropped 5th?

[datroof]

*Which* #9 chord does it not work on?

G7#9 was given; G Ab A# B C# D E F; 1 b9 #9 3 #11 5 13 7
[...]

now the other symmetrical octatonic.
A7: A Bb B# C# D# E F# G; same relation to the chord.
[...]

Symmetrical octatonic is a go-to if you want b9 and #9 in the same chord. Literally necessarily true.
Unless one doesn't get the whole 0 1 3 or 0 2 3 basis for the scale, then you do have a 50% chance at the mistake.

Yes, the Ab dim (whole-half) would be the go-to for G7b9, or G7alt. Not so much for G7#9, especially if you want the classic #9 sound. D dim (as CTurner said) would only work as half-whole, which is usually not the default. That's why I say "not necessarily".

Well, it was there in the scale given. G Ab A#. Everyone doing it in jazz knows from G Ab A# or Bb for G7b9 #9 (#11 13) with no worries. The application for a dominant 7th in that usage is necessarily true. G A Bb C Db Eb E F#: you would almost never want C or F# over a G B F so it's kind of a moot point for 'chord/scale theory' tbh.

I was right though in the fact that only one of the two possible D dim scales contains the Bb/A#. So, I'm back to "not necessarily".

[jancivil]

Well for further gainsaying we could argue the meaning of the word 'the'.

[datroof]

go-to

The real go-to scale for G7 altered would Ab melminor, which contain almost all of the alterations you could want (I know you know this). Followed by C harm minor scale, which has nice gravity toward Cmi. Ab dim (scale) is on the list, but not top of the list.

[jancivil]

Ab Bb 'Cb Db' Eb F G vs Ab Bb B C# D E F G; 'the' go-to over the other? [G7] b5 b13 vs #11 major 13th.

So I like the article 'a' [go-to).

[jancivil]

"Ab melodic minor" is typically seen as "Db Lydian Dominant", its 4th mode. So in the sense of 'altered dominant' being 'flat five substitution principle', Db is a flat 5 literally vs the #11 in the symm. octatonic along with a regular P5 D. It depends on what you want to do. I don't care much about it as an academic kind of a deal: you can't think and play at the same time.

but an argument for symm. octatonic would now contain b9 for the Db7.

[cturner]

D dim (as cturner said) would only work as half-whole, which is usually not the default. That's why I say "not necessarily".

Although in the history of Chord/Scale, half-whole seems the first one presented. This from George Russell's Lydian Chromatic Concept:

[jancivil]

It's Messiaen's 2nd mode of limited transposition, in "Technique de mon langage musical" - 1944.

"it's usually not the default" is doing too much, frankly. I've never heard anyone talk like that.
It appears originally starting with a semitone, but who cares. There's two ways of ordering it, it's a 50/50 proposition.

Chord/scale theory is pretty academic. What does your ear want in the moment.

[cturner]

If your performance is short enough, you can play anything. John Cage understood this when he composed 4’33”, and not 43’30”.