I understand about the relationship between run-of-the-mill suspended chords and inverting them. For example, I know a Gsus2 (
GAD) is an inversion of Dsus4 (
ADG ought to be called, other than Gsus2 in 1st inversion or Dsus4 in 2nd inversion, I'm not sure.
Now Wikipedia insists that a chord in 1st inversion must have a third as the lowest note and the root a sixth above it, which has implications for my assumptions. If there's an unusual chord like this...
...would it be correct to say it's in 1st inversion or not? Granted there is no third—E—so, by the Wikipedia definition, it falls short. Intuitively, though, it is. At least to me.
So if the answer is no, that's not 1st inversion, would I have to name that chord Fsus2add♭9,♯11,13? Or F13♭9,♯11sus2omit7? Or Fsus2,♯4add♭9,13?
Or what if the D were lowered one octave? Would it now be Cmaj9♯11sus4 in 4th inversion? Or would that also require E to be present?
(I know, I know... context. Please remember this question is purely about formal theory and the example chord is just an example.)