If I get this right, from what you're saying the major 9th would need both the G# and the B...i.e A C# E G# B?
1 3 5 7 9
Yes - a Major 9th is a Major 7th with the 9th added (the next "stacked triad")
To have its "own name" it needs to conform to the "stacked triad" rules
The next logical steps are 11th and 13th chords but on guitar it is obviously more difficult to include all of the theoretically required notes
These tend to get built on the "dominant 7th" (b7) chords so the "rules" are not so important as you are likely to have to sacrifice a tone or 2 to get the fingering correct
Other variations work this way, which is why we get chords like F#m7b5
The more notes that get thrown into the mix the more chance of dissonance within the chord itself
Also, with so many notes in the mix any "inversions" make it really difficult to identify the proper chord - hell, we came up with loads of options with just 4 notes!!!!
what about a chord that is 1 3 5 9 or any inversions of that? (A C# E B)
If the chord does not contain the 7th then this is where you use "add9", so a chord in A Major containing 1 3 5 9 would be A add9
If it is 1 3 5 7 9 it is A Major 9th
If it is a true inversion in the same key then it remains A add9
If the inversion means that you prefer to use a different "root note" you simply work through the variations like we have done in this thread to decide what name best describes the chord in context
