WHEN IS ♯11 THE SAME AS ♯4?
For my ears, never.
Go to a piano and play c + e + f♯ + g as a block chord. Now move the f♯ up an octave. Sonically, honestly, are they the same? I don't think they are.
Functionally, the f♯ is an augmented fourth from c. But Cadd♯4 has different harmonic implications to C(♯11); the relation between the chromatic and diatonic notes is different. The language is descriptive, not functionally reductive, so if you want a certain sound, you owe it to yourself to describe it as accurately as you can.
There will be those who will assume a minor seventh and a major ninth in C(♯11) but I feel that assumption is an over-complication, as I can happily describe C7(9,♯11) and leave no doubt, consistently.
The knock-on of this is that this allows the composer to accurately and consistently describe more exotic chords. Let's look at c + d + e:
Should the musician add a g and call the chord Cadd2 or C(9) the intention of the sonority might be lost; perhaps the composer wanted that specific harmony without the perfect fifth. So now, after writing the chord, the composer has to think: how do I represent this harmony accurately, simply and consistently?
If you didn't want to stray too far away from what people know you could use "omit 5" or "no 5":
But this symbol still states the chord as a major chord, which may not be desirable. It's also possible to describe the intervals from the tonic – a form of figured notation, really. You could stay within the tonal system:
Or use a bastardised form of pitch set theory:
But the idea here is that you are now not confined by a tonal system that may have nothing to do with the harmonies in your work. You can thus write things like
44 d[4,♭5] F♯maj7(♭5) | C♯maj7(♭5) C7(♭9) | Fm c[♭2, ♭9] | c[♭2, ♭9] ||
which might look like this in a score:
All the harmonic information is preserved in the chord symbols.
WHY USE A CHORD WHEN YOU ACTUALLY WANT A SCALE?
The purpose of a chord symbol is to show the harmony. In chord-scale theory, a musician will use a chord as a function of a scale, to represent the scale. So you hear things like this:
The score has a D7(♭9,♭11)... so I'm on the D reversed diminished scale!
Did the composer intend to hear that for the melody? Or in fact, was this meant purely for the harmony?
Simply put, there is no reason to play a diminished scale on that chord if you do not say that's what you want. If you're just describing the harmony then a soloist could play any scale they wanted as long as it sounded right to him/her. So if you really want that scale, just write it.
Here, I am using a lower case letter to denote the tonic, and have superscripted the type of scale (diminished, semitone interval first). How it's done doesn't matter, but in this case, there is no real need for a chord as a scale is intended. This has the consequence of allowing you to write a different chord – potentially, the chord you actually want.
If in fact you intended a tritone mix then a polychord might do it:
A♭/D or A♭+D
The upper-case D is a chord, not a bass note - that would be A♭/d.
As harmonic symbols these choices are distinct, and give the tonally-based soloist different choices – ddim.(s) precludes c♯ and g which are present in both dmaj. and a♭maj..
All that remains is for the writer to be consistent with the abbreviations of scales (for example, I have a personal list). It's easy enough to write a piece with absolutely no references to chords at all, just indicating the scale desired. For a soloist of any capability the intention of the composer is clearer.