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Tutorial: How chord naming works

JimGtr

Platinum Supporting Member
Messages
997
I've been handed charts and seen stuff in threads with chord progressions written like this: Cmaj Fmaj Gmaj, when what they mean is C F G. Technically "C" and "Cmaj" are synonymous, however in practice it's confusing because you would normally only see "maj" explicitly written out when it's a "maj7". So when you see "Cmaj" you're not sure if the composer meant "Cmaj7" and it's just a typo/omission or if they actually just meant "C"... not to mention that you're eyes may play tricks on you thinking that it actually said "maj7."

The number one rule when doing a chart or lead sheet that someone else will read (often cold) is to make it as easy as possible for the musician to get it right.

Taking the above scenario to a ridiculous extreme, we obviously want to avoid writing: "C triad with a major third and natural fifth to an F with a major third and natural fifth and major seventh to a G with a major third and natural fifth and a dominant seventh." That was a bitch to write and basically impossible to read, not to mention the amount of physical space on the page/screen that it occupies.

There are certain conventions that make things easier and clearer which is what the rest of this post is about.

With chord symbols we want to write the bare minimum we need to get the intention across. Easier to read, less confusion. So it works like this:

Unless written differently:
3rd is assumed major,
5th is assumed natural (correct term is "perfect"),
6th is assumed natural (correct term is "major"),
7th is assumed dominant (correct term is "minor"),
9th is assumed natural (correct term is "major"),
11th is assumed natural (correct term is "perfect"),
13th is assumed natural (correct term is "major").

(Note: Using the term "natural" in this context is not the correct naming convention, just trying to illustrate a concept as simple as possible.)

They all are assumed natural, except for the 7th as the only exception. Only when it's different than above do you need to notate it as such.

With the exception of the 6th, every extension (7th, 9th, 11th, and 13th) assume that all the extensions below it are present. Examples: 9th chords assume the 7th is present, 11th chords assume the 7th and 9th are present, and 13th chords assume that 7th, 9th, and 11th are present.

Examples:

Triads:
Root: is always written, obviously.
Third: Assumed major unless explicitly written as minor. I.e.- C = major, Cm = minor. You don't write Cmaj when you mean C.
Fifth: Always assumed natural unless altered. I.e. - C, Cm = all natural fifths. Only altered fifths need to be written, i.e. - Caug, Cdim (diminished assumes minor as well), and Cmin7b5.

Note: All chords have a Root, third and fifth. The 7ths, 9ths, etc are added on top of this foundation.

7th chords are dominant unless you specify it as a major 7th. Seventh chords assume the root, 3rd and 5th and the same rules apply: it's major unless you say minor, and it's a natural 5th unless you say different.
C7, Cm7, etc = dominant 7th. You don't write Cdom7 when you mean C7.
Cmaj7 CmMaj7, etc = major seventh (need to specify "maj" here since it's not dominant).

9th chords are natural 9th unless you specify it as a #9 or b9. 9th chords assume the root, 3rd and 5th, and 7th and the same rules apply: it's major unless you say minor, and it's a natural 5th unless you say different, and it a dominant 7th unless you say different.
C9= R, 3rd, 5th, dominant 7th, natural 9th.
Cm9 = R, minor3rd, 5th, dominant 7th, natural 9th (have to specify minor).
C7#9 = sharp 9th (major 3rd assumed). (Technically you don't need to write the "7" since that assumed, but if you didn't in this case then C7#9 would be written as C#9 which reads "C# with natural ninth" -- not what we want. With altered extensions -- #9, b9 , #11 and b13 -- we always write the "7" as well to avoid confusion.)
Cmaj9 = major 7th, natural 9. Since it's a major 7th you have to specify it. (See why writing Cmaj when you mean C is confusing?)

11th chords are natural 11th unless you specify it as a #11. 11th chords assume the root, 3rd and 5th, 7th, and 9th and the same rules apply: it's major unless you say minor, and it's a natural 5th unless you say different, and it a dominant 7th unless you say different, and it's a natural 9th unless you say different.
This explains the difference between C11 and Csus4. C11 means root, 3rd, 5th, 7th, 9th and 11th while Csus4 means root, 4th, 5th.
Also explains why Bb/C and C11 are often considered functionally synonymous since the Bb/C (Bb triad over a C bass note) gives you R, 7th, 9th, and 11th which defines all the upper extensions (though you lose the 3rd).
Cmaj7#11 is R, 3rd, 5th, maj7th, #11th. Since it's a major 7th it has to be specified.

13th chords are natural 13th unless you specify it as a b13. 13th chords assume the root, 3rd and 5th, 7th, 9th, and 11th and the same rules apply: it's major unless you say minor, and it's a natural 5th unless you say different, and it a dominant 7th unless you say different, it's a natural 9th unless you say different, it's a natural 11th unless you say different. This explains the difference between C13 and C6. C13 means root, 3rd, 5th, 7th, 9th 11th and 13th while C6 means root, 3rd, 5th and 6th.
C7b13 - R, 3rd, 5th, dom7th, 9th, 11th, b13th. (Again, we write the "7" to avoid confusion.)
Note that in practice you almost never play the 11th as part of a 13th chord, but the 11th is still a part of of the chord.

Sus chords replace a tone rather than add one. Csus4 replaces the third with the "suspended 3rd" which is the fourth (root + fourth + fifth). Csus2 replaces the third with the 2nd (root, 2nd, fifth). The difference between Csus2 and C(add9) is C(add9) has a 3rd and Csus2 doesn't (see below).

"Add" chords add a tone. Where C9 is root, 3rd, 5th, 7th, and 9th .... C(add9) is root, 3rd, 5th, 9th (skips the 7th). Because when you say "9th" you assume all the extensions below that are present, i.e. - the 7th. Likewise if you say 11th you also assume the 7th and 9th; and if you say 13th you also assume 7th, 9th, and 11th. Using "add" removes that assumption.

6th chords are its own thing. It's a triad with a 6th on top. 6th chords assume the root, third and fifth and the same rules apply: it's major unless you say minor, and it's a natural 5th unless you say different.
C6 = R, 3rd, 5th, 6th (C,E,G,A).
The difference between C6 and C13 is that C13 assumes the 7th, 9th and 11th as well (C,E,G,Bb,D,F,A).

"Alt" chords mean that all of it's extensions (7th, 9th, 11th and 13th) are altered. You still need to specify minor/major, and dominant 7th is assumed. It's a shorthand. G(alt) or more commonly G7(alt) is shorthand for a G7 with both a #9 and a b9, and a #11, and a b13. In practice you could play a C7+9 or C7-9 or C7b13 or C7#11 or C7b9b13 aka C7#5b9, etc... just make sure any extensions you play are altered and you're good.

Augmented chords means that the 5th is raised. C,E,G#

Diminished chords means minor 3rd and flat 5th. If there's a 7th it's double-flatted. C,Eb.Gb and C,Eb,Gb,A (actually the "A" is "B double flat").

Two things:
1. In practice just because you see C13, which is r, 3rd, 5th, 7th, 9th, 11th, 13th, doesn't mean you have to play a 7 note chord. It just defines the tonality and as a player you build a partial chord that supports that. The theory behind that would be a whole 'nother post, but as a brief example you'll get the 13th sound if you play R, 3rd, 7th, 13th (root is root, 3rd defines major vs minor, and without the 7th it would sound like a 6th chord).

2. If you get handed a poorly written chart don't say anything. ;) Do ask for clarification where you need it, but pointing out someone's mistakes or lack of formal knowledge doesn't make for a good vibe. Just be glad you got anything at all! That doesn't mean that YOU shouldn't write good charts, however.

And... one last thing actually. A lot of this is interpretation. If you want to tell someone exactly what to play you'd write it out in great detail. A chord chart on the other hand is just a roadmap with hints. So if you have this chord progession:

| C | Am | F | G |

..which is diatonic to the key of C, that could mean a couple things. On one hand it could mean 'please play simple triads" or it could mean "here's the basic changes do your thing." In the latter case you could add extensions yourself; the 7ths, 9ths, etc as you see fit. If you stay in key, that G could be a G7 or a G9 or a G11 (or F/G) or a G13 and it would all be in key.

But if the composer went to the trouble to actually specify G13 instead of just G... why? It could mean that there's an "E" in the melody and want some chordal support for that. Could be a voice-leading hint, could mean he just wants a 13th sound to that chord, or could just mean be jazzier/hipper. Take this for example:

| C | Am | Fmaj7 | G13 |

You could put an "E" drone on all the chords, and maybe that's what the composer was hinting at. I might play that C chord with the "E" on top, Am with the same "E" on top, Fmaj7 with the same "E" on top and the G13 with the same "E" on top, emphasizing that common tone. On guitar you could play simple triads with the open E ringing out the whole time, for example. Or avoid it completely (you could still just play triads). It could just mean that the melody hovers around the E so you might want to avoid F notes in the same octave. Just ask yourself what you think the composer is conveying and then make your own decision on what to play.
 
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JonR

Member
Messages
15,678
Good summary of the conventions, but - in the same spirit of information and clarification ;) - I'm going to get pedantic on a couple of terms....
(Your facts are all correct, but there are problems mostly with your interval terminology.)
Unless written differently:
3rd is assumed major,
5th is assumed natural,
"perfect"
6th is assumed natural,
"major"
7th is assumed dominant,
"minor".
The phrase "dominant 7th" describes a chord, not an interval.
The word "dominant" means "5th step of scale", and hence the chord built on that step (V).
The V chord in either major or harmonic minor has a major 3rd and a minor 7th.
This is a unique combination, which gives rise to the term "dominant 7th" to describe that chord type wherever it might occur.
9th is assumed natural,
"major"
11th is assumed natural,
"perfect"
13th is assumed natural.
"major"
They all are assumed natural, except for the 7th as the only exception. Only when it's different than above do you need to notate it as such.
Right (given above corrections ;)).
It's as if the default scale for building chords is mixolydian mode. It isn't of course, it's just that the V chord is the most likely one to have a 7th added, so that minor 7th interval is written as plain "7".
Also, there are 5 minor 7th intervals in the major scale and only two major 7ths. So it makes sense for the most common kind of 7th to have the shortest symbol.
With the exception of the 6th, every extension (7th, 9th, 11th, and 13th) assume that all the extensions below it are present.
Well, the 6th does too. It assumes 1-3-5 are present.
But it's true (arguably) that the 6th is a different kind of chord. Others are built on the "tertian" principle, adding alternate steps of the scale ("stacking 3rds").
Examples: 9th chords assume the 7th is present, 11th chords assume the 7th and 9th are present, and 13th chords assume that 7th, 9th, and 11th are present.
In theory, yes. In practice, not always. [As you go on to explain below ;)]
7th chords are dominant unless you specify it as a major 7th. Seventh chords assume the root, 3rd and 5th and the same rules apply: it's major unless you say minor, and it's a natural 5th unless you say different.
C7, Cm7, etc = dominant 7th.
See above. Only C7 is a "dominant" 7th, because it derives from the dominant degree of F major (or F harmonic minor).
C7 and Cm7 both have "minor 7th" extensions. The difference is the 3rd, as you say.
Cmaj7 CmMaj7, etc = major seventh (need to specify "maj" here since it's not dominant).
Since the 7th is not the usual minor (b7), yes.

Corrections shown in red below:
9th chords are natural 9th [have a major 9th extension] unless you specify it as a #9 or b9. 9th chords assume the root, 3rd and 5th, and 7th and the same rules apply: it's major unless you say minor, and it's a perfect 5th unless you say different, and it a minor 7th unless you say different.
C9= R, 3rd, 5th, minor 7th, major 9th.
Cm9 = R, minor 3rd, 5th, minor 7th, major 9th (have to specify minor 3rd only).
C7#9 = sharp 9th [technically an "augmented 9th"] (major 3rd assumed). (Technically you don't need to write the "7" since that assumed, but if you didn't in this case then C7#9 would be written as C#9 which reads "C# with natural ninth" -- not what we want. With altered extensions -- #9, b9 , #11 and b13 -- we always write the "7" as well to avoid confusion.)
Cmaj9 = major 7th, major 9. Since it's a major 7th you have to specify it. (See why writing Cmaj when you mean C is confusing?)

11th chords are perfect 11th unless you specify it as a #11. 11th chords assume the root, 3rd and 5th, 7th, and 9th and the same rules apply: it's major unless you say minor, and it's a perfect 5th unless you say different, and it a minor 7th unless you say different, and it's a major 9th unless you say different.
This explains the difference between C11 and Csus4. C11 means root, 3rd, 5th, 7th, 9th and 11th while Csus4 means root, 4th, 5th.
Also explains why Bb/C and C11 are often considered functionally synonymous since the Bb/C (Bb triad over a C bass note) gives you R, 7th, 9th, and 11th which defines all the upper extensions (though you lose the 3rd). [you also lose the 5th, which is not critical.]
Cmaj7#11 is R, 3rd, 5th, maj7th, #11th. Since it's a major 7th it has to be specified.

13th chords are natural 13th [have a major 13th interval] unless you specify it as a b13. 13th chords assume the root, 3rd and 5th, 7th, 9th, and 11th [but see below] and the same rules apply: it's major unless you say minor, and it's a perfect 5th unless you say different, and it a minor 7th unless you say different, it's a major 9th unless you say different, it's a perfect 11th unless you say different. This explains the difference between C13 and C6. C13 means root, 3rd, 5th, 7th, 9th 11th and 13th while C6 means root, 3rd, 5th and 6th.
C7b13 - R, 3rd, 5th, dom7th, 9th, 11th, b13th. (Again, we write the "7" to avoid confusion.)
Note that in practice you almost never play the 11th as part of a 13th chord, but the 11th is still a part of of the chord.
Yes, this is important; In practice, perfect 11ths are not added to chords with a major 3rd, because of the "nasty" b9 interval introduced (the famous jazz "avoid note").
This is why "C11" can be used to stand for C9sus4, because a full C11 (including the E) is never likely to be used.
If the 3rd is minor, then a perfect 11 is fine. "Cm11" = C Eb G Bb (D) F. (9ths are optional in 11th and 13th chords.)
Sus chords replace a tone rather than add one. Csus4 replaces the third with the "suspended 3rd" which is the fourth (root + fourth + fifth).
In fact, it's the 4th that is the "suspension" - the word refers to carrying over a note from a previous chord.
Classically, an F note on a C chord would have been part of the previous chord (say F, Dm, Bb or Gm7), and is then "suspended" over the C before being resolved down to E.
In modern music, of course, sus chords are used without any need for the suspension to be part of a previous chord, or for it to be resolved.
"Alt" chords mean that all of it's extensions (7th, 9th, 11th and 13th) are altered. You still need to specify minor/major, and dominant 7th is assumed. It's a shorthand. G(alt) or more commonly G7(alt) is shorthand for a G7 with both a #9 and a b9, and a #11, and a b13. In practice you could play a C7+9 or C7-9 or C7b13 or C7#11 or C7b9b13 aka C7#5b9, etc... just make sure any extensions you play are altered and you're good.
Right.
#11 and b13 are in practice the same as b5 and #5. IOW, an altered dominant chord has no perfect 5th.
"7alt" can mean any combination of b5 or #5, and b9 or #9.

It's important not to confuse these chords with lydian dominant chords: 7#11, 9#11, 13#11.
Augmented chords means that the 5th is raised. C,E,G#

Diminished chords means minor 3rd and flat 5th. If there's a 7th it's double-flatted. C,Eb.Gb and C,Eb,Gb,A (actually the "A" is "B double flat").
There are two kinds of diminished chord, built on the dim triad:
Diminished 7th, or "full diminished": root, minor 3rd, diminished 5th, diminished 7th (bb7).
Half-diminished, or m7b5:: root, minor 3rd, diminished 5th, minor 7th (b7) - so-called because it only has one diminished interval, not two.

The m7b5 chord comes from the vii degree of the major scale. Bm7b5 = B D F A = vii in C major (used more often as ii in A minor).
The dim7 chord comes from the vii degree of the harmonic minor scale. Bdim7 = B D F Ab = vii in C minor. (But enharmonic with 3 other dim7 chords, which can all stand for each other.)
Two things:
1. In practice just because you see C13, which is r, 3rd, 5th, 7th, 9th, 11th, 13th, doesn't mean you have to play a 7 note chord. It just defines the tonality and as a player you build a partial chord that supports that. The theory behind that would be a whole 'nother post, but as a brief example you'll get the 13th sound if you play R, 3rd, 7th, 13th (root is root, 3rd defines major vs minor, and without the 7th it would sound like a 6th chord).
Right - important point.
Root, 3rd, 7th, plus last named extension will give the essential sound (function) of the chord. 5th and 9th (if unaltered) don't really affect the sound, other than filling it out a little.
As mentioned above, 11th (if not mentioned) should be omitted.
2. If you get handed a poorly written chart don't say anything. ;) Do ask for clarification where you need it, but pointing out someone's mistakes or lack of formal knowledge doesn't make for a good vibe.
Quite ;). No offence intended here :).
And... one last thing actually. A lot of this is interpretation. If you want to tell someone exactly what to play you'd write it out in great detail. A chord chart on the other hand is just a roadmap with hints. So if you have this chord progession:

| C | Am | F | G |

..which is diatonic to the key of C, that could mean a couple things. On one hand it could mean 'please play simple triads" or it could mean "here's the basic changes do your thing." In the latter case you could add extensions yourself; the 7ths, 9ths, etc as you see fit. If you stay in key, that G could be a G7 or a G9 or a G11 (or F/G) or a G13 and it would all be in key.
Yes, but the choice would be governed by context (style or genre), taste and common sense...;)
But if the composer went to the trouble to actually specify G13 instead of just G... why? It could mean that there's an "A" in the melody
You mean "E". (typo ;))
 

DavidS

Silver Supporting Member
Messages
716
Wow, that is one of the most concise and straightforward explanations I've ever read. Thanks for taking the time for spelling it all out
 

JimGtr

Platinum Supporting Member
Messages
997
Thanks for the replies everyone.

JonR, thanks for the corrections and clarifications (and the detail!). This is important stuff so much appreciated. And yes, the "A" in the second to last paragraph should have been "E". :)

Nice concise explanation above. Although i think there should be a mention of slash chords as well.
Yes, good idea:

Slash chords are a way of specifying a bass note in a chord. The symbol above the slash is the chord and the symbol below the slash is the bass note. For example F/G is an F chord with a G in the bass (G,F,A,C). And a C/G chord is C chord with a G in the bass (G,E,G,C). Note with the C/G example I used an inversion on the top chord (E,G,C instead on C,E,G), any inversion is fine.
The bass note can be a part of the chord written above the slash, but it doesn't have to be.
All of the rules outlined in the original post apply to the chord above the slash, but the bass note should be strictly adhered to.
Slash chords are also used to show bass line movements through a chord progression, for example: C G/B Am Am/G. In this case the chords are C G Am Am and the bass notes are C B A G.
The chord can be on top doesn't have to be a triad, for example: Dm11/A is perfectly valid.
Another example: Am AmMaj7 Am7 D7 is often played as, and sometimes written as: Am Am/G# Am/G Am/F#.
In an ensemble the bass player may cover the bottom note leaving the guitar or piano free to just play the top portion. It's situation dependent, sometimes a slash chord is a way of specifying a complete chord where the guitar or piano would play both the top and bottom portion; or it could be a way to hint at a bass line as in the chord progressions above.
Take the original post's example of C Am Fmaj7 G13 where there's an "E" note common to all the chords. And I mentioned that you may want to voice that with the E on top of all the chords. You could also specify a bassline to go along with that:
| C C/B | Am Am/G | Fmaj7 | G13/D G13 |
Slash chords are also used to show bass pedal tones, like this:
A D/A G/A D/A.
In this case the A is just chugging along in the bass while the chords move on top. The slash notation makes it easy to convey that pedal tone in a clear way.
 

JimGtr

Platinum Supporting Member
Messages
997
"Alt" chords mean that all of it's extensions (7th, 9th, 11th and 13th) are altered. You still need to specify minor/major, and dominant 7th is assumed. It's a shorthand. G(alt) or more commonly G7(alt) is shorthand for a G7 with both a #9 and a b9, and a #11, and a b13. In practice you could play a C7+9 or C7-9 or C7b13 or C7#11 or C7b9b13 aka C7#5b9, etc... just make sure any extensions you play are altered and you're good.
Right.
#11 and b13 are in practice the same as b5 and #5. IOW, an altered dominant chord has no perfect 5th.
"7alt" can mean any combination of b5 or #5, and b9 or #9.

It's important not to confuse these chords with lydian dominant chords: 7#11, 9#11, 13#11.
Yes, that's important to note and it wasn't clear in the OP. Alt chords alter the 5th as well, there's no perfect 5th in alt chords. Root, 3rd and then everything else is intentionally f--ked up after that ;). (In a beautiful way, mind you... I love alt chords.) Actually the spelling is Root, 3rd, b5, #5, b7, b9, #9, #11, b13. It's just that b5 and #11 are the same note, and b13 and #5 are the same as well so they are synonymous. Probably a better spelling is Root, 3rd, b5 (aka #11), #5 (aka b13), b7, b9, #9. Or C Db Eb E(natural) Gb G#Bb.

"7alt" can mean any combination of b5 or #5, and b9 or #9.
That's probably the most practical way to think about it.

Ok enough smarts for me today, off to watch some Three's Company reruns... :p
 

stevel

Member
Messages
15,205
(Your facts are all correct, but there are problems mostly with your interval terminology.)
"perfect"
...
Agreed. Should go with "traditional" terminology when identifying those intervals or put a footnote in that "natural" means "diatonic to any major key" - which could probably be more confusing.

Also Jim, 6/9 chords are relatively commonplace and while your rules would be applicable, like the m7b5 I didn't see them specifically mentioned.

Steve
 

stevel

Member
Messages
15,205
Also, I know you're being conversational (a whole 'nother...) but you may want to fix up the agreement in places like:


"6th chords are its own thing"

are THEIR own thing.

Happens again right after with "Diminished chords is" which of course should be "are" (and earlier you did use "are" with "9th chords" - so just for the sake of consistency).

Steve
 

Clifford-D

Senior Member
Messages
17,045
My understanding is the word minor is talking about the flattened quality of the 3rd.

The word major talks to the raised quality of the 7th

A C triad is just that, C.
To put major on the C chord infers the major 7th.

C says a lot. It says there is a major 3rd and a perfect 5th.

The chord C6 works hand in hand with a Cmaj7 I chord
But the word maj or major is not needed because maj only means major 7th
Ps; maj and min talk about the guide tones, the most discriptive tones in basic functional harmony
 

JonR

Member
Messages
15,678
My understanding is the word minor is talking about the flattened quality of the 3rd.

The word major talks to the raised quality of the 7th
In chord symbol terminology yes.

IOW, many intervals or extensions can be major minor, but "m" or "min" in a chord symbol refers to the 3rd alone, while "maj" refers to the 7th alone.
Ps; maj and min talk about the guide tones, the most discriptive tones in basic functional harmony
Nice point.
To be precise, 3rd and 7th are (at least in jazz) the "guide tones", and they're the ones where the "major-minor" confusion can arise, and where the symbols use the neat system of assuming major 3 and minor 7, unless otherwise stated ("m" or "maj" respectively).
 

Clifford-D

Senior Member
Messages
17,045
C E G B
Real quick: What is the "9" in the C major scale?
What is a 9th?

Chords are made in 3rds
So C major scale in 3rds
C E G B D F A
R 3 5 7 9 1113



The 9th is D,

The rule is "if the C chord has a 7th, the D will be 9th
If the C chord doesn't have a 7th, the D will be the 2nd.

If there is a 9th then there must be a 7th in the chord.
 
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lhallam

Member
Messages
17,447
C E G B
What is a 9th?

Chords are made in 3rds
So C major scale in 3rds
C E G B D F A
R 3 5 7 9 1113



The 9th is D,

The rule is "if the C chord has a 7th, the D will be 9th
If the C chord doesn't have a 7th, the D will be the 2nd.

If there is a 9th then there must be a 7th in the chord.
Not what I was taught for my classical music degree which is very concise. Folks tend to abbreviate full names, especially in jazz:

If you have C-E-G-D -- called a C major add 9 - implies no 7th.

If you have C-E-G-B-D -- C major major 7th major 9th AKA C major 9th

If you have C-D-G -- C suspended 2nd (no 3rd) AKA a C 2 chord (Can also be a G sus 4th) depending on context.

It's the 6th that requires a 7th.

C-E-G-A = C major 6th
C-E-G-Bb-D-A = C major minor 7th major 9th 13th AKA C dominant 7th 13 AKA C13th
 

JonR

Member
Messages
15,678
Not what I was taught for my classical music degree which is very concise. Folks tend to abbreviate full names, especially in jazz:

If you have C-E-G-D -- called a C major add 9 - implies no 7th.

If you have C-E-G-B-D -- C major major 7th major 9th AKA C major 9th

If you have C-D-G -- C suspended 2nd (no 3rd) AKA a C 2 chord (Can also be a G sus 4th) depending on context.

It's the 6th that requires a 7th.

C-E-G-A = C major 6th
C-E-G-Bb-D-A = C major minor 7th major 9th 13th AKA C dominant 7th 13 AKA C13th
Right.

"9" on its own means there should be a 7th present, because the system simply adds 3rds: 1-3-5-7-9, and we only need to show the last number. That's why we use "add9" to indicate the absence of a 7th.

"Sus2" is different because it derives from the idea of replacing the 3rd - before you ever get to adding a 7th.

The "2" and the "9" are the same note, of course, and could actually be voiced in the same position in the chord. It's the idea of how they're derived that explains the inconsistency (kind of...).
 




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