Does an A13 chord include the 11th? Here's why I'm asking... If you google this chord for piano, sometimes the third (C#) is omitted and sometimes the 11th (D) is omitted -- but sometimes they are both included. In a theory video I watched a chord played as A - G - B - D - F# (Gmaj7/A) was referred to as an A13sus. This makes sense if the D (the 11th) is not included in a "standard" A13. But if it is, I'm confused as to why it is referenced this way.
Theoretically speaking, thirds are stacked sequentially, until the quoted one is reached.
So, 1, 3, 5, 7, 9, 11, 13 are the notes that 'should' go into a 13th chord. That 13th chord is generally going to be a dominant 13th, so the 7th part will be m7, (b7). So, note-wise on C: C E G Bb D F A.
There are potential clashes here, with notes being so close (in name). When kept away from each other, as in more than an octave apart, the clashes can be avoided. C E G is the basic major triad. C E G Bb is dominant 7th. C E G Bb D is dominant 9th.
The F (11th note) is often omitted, but the 13th is pretty important - it's the one that names the chord ! In busier chords, it's often the 5th that gets left out - there are shades of that note frequency in the root. The root generally stays - it names the chord - although guitarists playing alongside a bass player can usually leave that out. The 3 has to be there - defining major or minor.
It's established that most chords with a number attached that's larger than 7 keep that 7th not. BUT - that 7th note here is b7, as it is NOT a major 7th type chord.
As said previously, the F gets left out, and the D can too. On guitar (I know it's only a theory question!) leaving out the D and F still constitute a 13th chord. I work on the premise that 7+6=13, so with the b7 and the 13 notes on board, along with the basic triad, it works on guitar - where some notes are not easily reachable. On piano, the voicing is all important, making sure, if indeed you want to play all notes, that where they're played is taken into account.
I suppose this is another bit of theory that really needs the practical to make it make sense!