OK, here's my $0.02 on 9, 11 and 13 - which Jeff sensibly avoided...
(OK, I'm going in... if I'm not back in 24 hours, call a search party...)
9ths can generally be added to any chord type, if they are
major 9ths (whole step above the root). If the 7th is omitted - as is very common in rock, folk and pop - they are called "add9".
This is an inconsistency in chord symbol shorthand. The original idea was that the most common chord types would get the shortest symbols (by assuming vatious default intervals); but that was at a time when full "9" chords were an extension on a 7th chord. Now, in rock music, it's a lot more common to add a 9th to a triad. So a "9" chord has more notes in it than an "add9" chord.
"A(add9)" = A C# E B; "Am(add9)" = A C E B.
The "9" doesn't have to go on top of the chord. It can go low in the chord. E.g., A B C# E is still "A(add9)" not "A(add2)". (Calling it "9" is another hangover from the 1 3 5 7 9 11 13 stacking principle).
IOW, as with
all chord symbols (except slash chords), it only tells you the notes you need to include in the chord; not the order you have to arrange them. I.e.,
in theory "A(add9)" means "A C# E B"; but
in practice you can stack those notes in any way you like - except with B on the bottom (because that makes it sound like a different chord.
In jazz, you sometimes get b9s on V7 chords - as mentioned in the last post. It's a strong dissonance (with the root), but dissonance is kind of the point with V7s, so it's OK.
"11" and
"13". In theory, these just indicate the last note added to the complete stack, making 6-note or 7-note chords. But - as Jeff says - in practice they are almost never complete, for various reasons. Obviously with a 7-note chord there is the practical issue for 6-string guitarists! But even a pianist is highly unlikely to play every note of a "13" chord. (There is an exception, which I'll come to.)
11ths. The one kind of 11th chord that can be a complete stack is a "m11" chord. Am11 = A C E G B D. The 9 (B) is optional, but if you can get it in there it sounds fine. As many of you will know, the open strings of the guitar form an "Em11" chord, missing the 9th (E G B D A); you could add the 9th (F#) as 2nd fret on the 1st string. But as you see, EGBDA is 5 notes from Am11 too! (Technically A9sus4, but it shows how chord identities start to become blurred the more notes you add...)
Adding 11ths to
major chords means (almost always) omitting the 3rd. So "A11" - technically A C# E G B D - is often used as shorthand for A9sus4 (A E G B D), because everyone knows (or should...) that "A11" will not include the C#. The interval C#-D is known in jazz as an "avoid note", because of the awkward (unhelpful or confusing) dissonance it makes. So you leave out one or the other.
On a maj7 chord, an 11 causes an additional issue. A C# E G# B D makes an E7 chord on top of an A major chord! A V chord and I at the same time! I.e., a harmonic mess.
13ths. With either "13" or "maj13", the 11th will be omitted (for the above reasons). The 9th is also optional. And in jazz, seeing as perfect 5ths are also often omitted, a "13" chord only needs 4 notes: root-3rd-7th-13th. An "A13" chord might only contain A C# G F#. Of course, the E helps confirm the root (if you can get it in there), while the B will help fill it out. But on guitar, x-0-5-6-7-x makes a perfectly good "A13".
Maj13" chords are rarer, but still possible. "Amaj13" = A C # E G# B F#. Try this: x-0-6-6-7-7 (add the open 6th if you want to include E).
13ths can be added to m7 chords, but it's very rarely done. E.g., in theory you can have a complete 7-note "Am13" chord: A C E G B D F#. (F#, notice, not F. Added 6ths and 13ths are always
major.) But the problem - as with any chord using the whole scale!
- it could be almost any other chord! But even if you left out the B and D, so it was more clearly Am7 with F# added, it sounds too close to the chord most likely to follow, which would be D7. IOW, when we use Am7-D7, one of the most important moves is from G on Am7 to F# on D7. If we add the F# to Am7, obviously it spoils that resolution. That doesn't mean that m13 chords sound bad in themselves; try x-0-5-5-7-7.
13sus4 chords are quite possible, and not uncommon. "A13sus4" = A D E G B F#. Think of it as "Em9/A" if you like, or "Gmaj7/A" if you miss the E (which is not essential). x-0-5-7-7-7, or x-0-2-0-3-2. (follow that with Dmaj9, x-x-0-2-2-0.) The 9th is also optional.
Getting back to 11ths, the "avoid note" issue can be "avoided" not only by omitting the 3rd, but by keeping and 3rd raising the 11th.
Here are some
#11 chords:
Amaj7#11 = A C# E G# D#
Amaj9#11 = A C# E G# B D#
Amaj13#11 = A C# E G# B D# F#
A7#11 = A C# E G D#
A9#11 = A C# E G D# B
A13#11 = A C# E G D# B D#
So, there are two potential 7-note chords which work (in theory anyway)! Of course, as with other 13th chords, we can omit the optional 9th (B), and maybe the 5th. These shapes are a little tricky on guitar - and rarely useful anyway! but try these:
Amaj13#11 = x-0-6-8-7-9 (A G# D# F# C#)
Amaj13#11 = 5-4-4-4-4-4! (A C# F# B D# G#)
I've not been able to find a shape for A13#11, even omitting the B and E. The issue is that the G needs (ideally) to be below the F#, and you need both C# and D#. (There is probably a really stretchy one, but who needs it?)
9#11 shapes are not too hard, and occasionally useful, for those occasional serious jazz moments... x-1-0-1-1-0 (Bb9#11) to x-3-2-4-3-x (Cmaj9). I'm sure you can work out moveable options for the 9#11 shape if you want.
Questions welcome...