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Which name is better, more correct?

C13 is C E G Bb D F A.

If we remove the third, ninth, and eleventh, we get C G A Bb.

Would C13 no 3, 9, 11 be an correct name? I've found that same chord named as C7/6 no 3 (dominant seventh, added sixth, no third).

Which one makes more sense?

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I wouldn't go with either of the names you suggested. When you use "no" chord notation typically you are changing the intended harmony of a chord to something the chord symbol was not ment to represent.

Let's look at what we have:

 C G A Bb 

I'm assuming the C is the bass note. It would be a stretch to call this any type of C chord because not only is there no 3rd, but there is also no 2nd or 4th. There is very rarely a chord with an omitted 3rd that is not suspend.(Besides a power chord which this is not.)

If we look at this chord as some kind of A chord it makes much more sense because we can stack the chord in thirds now and have it make sense:

A C _ G Bb

We still have no 5th, but the 5th is commonly omitted in larger chords. A to C makes a minor 3rd, the G is a minor 7th and the Bb is a b9. Because the C is in the bass, we will have to notate the chord in slash notation so we get:

Am7b9/C

Still a lengthy name, but it describes the function of the chord better than C13 no 3, 9, 11 where it is very odd to omit 3 notes in a chord.

Another thing to note is it is typical in a 13th chord to omit the 9th and 11th as they are optional. So the suggested name could be reduced to C13 no 3, but still it is odd to omit a 3rd without some kind of sus.

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If we remove the third, ninth and eleventh from C13 we get C G Bb A,

so I guess the most correct term would be C13 no 3, 9, 11 or just C13 no 3(I think that a C13 chord doesn't necessarily have a 9th or 11th,but I'm not sure).

But C G A Bb would be C6/7 no 3, because the A here is the 6th, not the 13th. It would have to be one octave higher in order to be the 13th.

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Given the notes C G A Bb, I would think of it as a Gmadd2 (no5)/C or taking the notes in the order which would come from C13 removing the third, ninth, and eleventh [C G Bb A] I would think of it as a Gm add9 (no 5)/C.

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There's no "correct" way to exactly name this chord using the standard nomenclature.

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1  
Did you mean there's no single correct way, or that the chord cannot be named? A bit more explaining would make the answer more valuable. – joseem Jun 27 at 14:53
    
I meant that there's no nomenclature (as far as I know) that names this chord in any useful way, other than simply spelling it out as C G A Bb. But if I had to name what it sounds like to me, I'd say Cb7 plus 6. The feeling of b7th chords doesn't really need a third, and the A just sounds to me to be the sixth degree thrown in for a bit of dissonance. I don't think you can get away with calling that "C 13". But of course that's just my personal take. I don't see any point in trying to define the "best" way of describing this chord in a very oversimplified system. – Scott Wallace Jun 27 at 15:44
1  
Must disagree that dom7 chords don't need a 3. 5 can be dispensed with, but not 3 - that tells if it's maj. or min. – Tim Jun 27 at 15:48
    
"I don't see any point in trying to define the "best" way of describing this chord in a very oversimplified system." The asker probably sees a point to it, since they went to the trouble to ask. It seems like this answer is really saying, "I don't want to answer this question and I don't think anyone else should either". – Todd Wilcox Jun 27 at 19:22
    
@Tim- we'll just have to agree to disagree. Whether the third of a chord is major or minor is almost always implied by the scale. If you have the chord progression, spelled out from below in C major, of cge'g'/Ggd'f'/cgc'e', doesn't the second chord sound like a dom7 to you? – Scott Wallace Jun 28 at 10:59

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