Why do some extended chords have three added notes?

Question

As I understand it, a basic chord is built of three notes, which can be harmonized in different octaves. It's always the first, third, and fifth to make up a basic chord.

An extended chord then adds a note. A ninth extended chord, for example, adds the ninth note in the scale to the chord. So I would assume that the chord C9(13) would have the first, third, fifth, ninth, and thirteenth notes of the C-major scale in the chord. I would assume the notes in the chord should be:

CEGDA. Because the D is the ninth note from the root, and the A is the thirteenth from the root.

But in the description it says CEBbDA.

So, why are there three added notes when the name of the chord only has two added notes? And why Bflat? And why is the G not there?

Answer 1

There are two different types of extended chords being conflated here:

"Add" chords

An "add" chord is some chord to which a particular note or notes are explicitly added. For example, a C(add9) chord, would be CEGD — C major with an added 9th.

Extended seventh chords

When the "add" is left off, the chord symbol indicates a seventh chord with extensions. So a C9 chord, for example, could be CEGBbD — a C7 (C dominant 7) chord plus the 9th, also sometimes called a "C dominant 9".

In the case of seventh chords, it's usually acceptable to leave off the fifth of the chord, in which case, for C9, the spelling would be CEBbD.

The chord in the question

The chord C9(13) would mean "C dominant ninth with an added 13": CEGBbDA or, dropping the fifth, CEBbDA.

The chord C13 would mean CEGBbDFA or CEBbDFA

C(add9,add13) would mean CEGDA

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See the linked questions for additional or more specific information on chord symbol meanings, chord voicings, and which pitches are required or optional in particular chords.

Answer 2

A C major triad contains the notes C, E, and G; add a Bb to get a C7 chord, which is often called a dominant 7th chord. Extended chords are usually thought of as extending a 7th chord.

Now, a C9 chord is understood to be a C7 chord with an added D, or 9th. To form a C11 chord, add an F (the 11th) to a C9; to form a C13 add an A (the 13th) to a C11. So, a complete C13 chord contains the notes C, E, G, Bb, D, F, and A (the 1, 3, 5, b7, 9, 11, and 13).

Generally speaking, it is considered fine to omit the 5th of any chord with a perfect 5th (diminished and augmented triads should probably keep their diminished or augmented 5ths, though). As a rule of thumb it is fine to omit the lower extensions, too; so a C11 might omit the 9th, and a C13 may omit either or both of the 9th and 11th. Following a comment from @user1079505, the 11th is usually omitted from major chords in any case because the 11th clashes with the major 3rd. All of this is subject to the conditions of an actual musical context.

In addition, the guitar has its own constraints. It can be difficult to play some chords in 6-note voicings, or it may be difficult or impossible to find a playable voicing that sounds good. Guitarists routinely abbreviate chords because the abbreviated chords are easier to play, and often sound better than their more fully-voiced cousins. Playing with other musicians also provides plenty of reasons for leaving notes out of your chord voicings to leave space for other players, but that is not what is at work here.

Here is one extremely common voicing for C13. Note that I am showing two "grips", i.e., two fingerings, for the same voicing (arrangment of notes):

%8/1.X/X.8/2.9/3.10/4.X/X[C13]       %X/X.3/1.X/X.3/2.5/4.5/4[C13]

This voicing is C, Bb, E, A. Both of these voicings have the root first, then the 7th, then the 3rd of the chord. This configuration of 1-7-3 is called a shell voicing, and it contains the essential notes to communicate 7th chord quality: the root, the third (is it major or minor?), and the seventh (is it a major 7th chord, a dominant 7th chord, or a diminished 7th chord?). After getting those three notes down, you can plunk down a 13th and you have the skeleton of a 13th chord.

Or you can try adding more extensions, and here is another version that manages to fit both a 9th and a 13th on top of the shell voicing:

%8/2.7/1.8/3.7/1.10/4.X/X[C13]       %X/X.3/2.2/1.3/3.3/3.5/4[C13]

This voicing is C, E, Bb, D, A, and it is the voicing described in the OP post. The first three notes of this voicing also form a shell voicing, this time 1-3-7. Note that this 13th chord is related to what is probably the most common voicing for a 9th chord on guitar:

%8/2.7/1.8/3.7/1.8/4.X/X[C9]       %X/X.3/2.2/1.3/3.3/3.3/3[C9]

The first one is usually seen with the 5th (the G on top) omitted because otherwise it is a bit of a finger-squisher (and it doesn't really need the 5th); the second chord shape is seen all the time, and it is not uncommon for the 5th to be omitted on this one, too. This second shape for C9 can be turned into a C13 by placing the pinky on the 5th fret (A), replacing the G on the 3rd fret, i.e., by replacing the 5th of the chord with the 13th.

Any musician might abbreviate chords for a variety of reasons, and there is nothing wrong with that; unless one is being pedantic or very particular about a specific voicing, one would still call a C13 which was missing the notes as described above a C13 and be done with it. There are a lot of circumstances when even the root of the chord is omitted, and it is still called a C13.

Usually when a composer or transcriber wants particular voicings, they write them explicitly on the staff. Coming across a mouthfull like C9(omit 5, add13) is rough when you read a chart, where C13 is a lot easier to digest. Chord symbols are really just indicators of the prevailing harmony in a piece of music. Interpret them under the constraints of your instrument, abilities, and musical context, and everything will be fine.

Answer 3

Attempting to add a little more to the already great existing answers-

The basic triads comprise 1, 3 and 5. They need the 1 (root) as without that they have no name! The 3 can either be major or minor, which is of paramount importance for many reasons.The 5 (P5) is actually present in the overtones of 1, and will be the first, usually, to be omitted in extended chords.

When 'stacking thirds', the next will be the 7th note. In the OP's situation, it's ♭7, although it could easily be ♮7, more on that later.

Any other chords above that 7th, like 9th, 11th, 13th, are duty bound to include that 7th. So far, we have 1 and 3, 7 and 9 that need to be in a 9th chord. On piano, that's not a problem, as we can find each in several octaves, and produce a chord where no notes clash with each other - there's sufficient space sonically between each. On guitar, so far, it's not too problematic, although voicing and fingering both need consideration.

It's when even more extension notes are added that it's awkward - sometimes more than awkward - impossible. Let's take C13. In theory, it should contain C, E, G, B♭, D, F and A. In fact, every note from the F major scale (C13 emanates from key F). On piano, one could simply use several fingers, and play an F scale, all notes simultaneously. It doesn't sound good. So, that's where we consider taking out some less important notes, but still retain the more important ones. On guitar, it's impossible anyway - only 6 strings!

So this is where we need to think about what else is happening around. If there's a bass, that'll almost inevitably play C - that can go. 3 and ♭7 need to stay, and for C13, the A (13th) needs to be there - otherwise it's not going to be a 13th chord. Experience usually tells a player which stay and which go.

As said earlier, on guitar, voicing will need to be judicious, for fingering and voicing reasons. On piano (not tagged) life's much easier.

Now onto the last part of the question. The chord itself belongs far more to the key F than key C - yes, it's found in both, but diatonically, the B♭ puts it into key F.It's the dominant chord in that key.

As promised earlier, it could be B♮, which keeps it in key C - C E G B is C major 7 (C▵7), and with further extensions becomes, for example, Cmaj9 - (C E G B D). Same rules apply. Anything above '7' needs to retain that 7, and the 3 needs to be M3. There's also minor chords, as in Cm7, Cm9, which will contain m3 (E♭) instead of note E.