I saw this from @ingolee - This is really good. 
However -
It is possible to have an E13 chord voicing where the C# is NOT 13 or more intervals from the root (E).
So the chord C13 (lets use mostly white keys on the piano) could be spelled (from bottom to top)
C - A - D - E - Bb
This IS still a C13 chord - Yet the A is only 6 intervals from C (the root).
Can someone tell me WHY this is STILL a C13 chord and NOT a C6???
Fun fun fun!!!
Do you know the answer? I donāt. As far as Iām concerned, two notes that are an octave apart are the same note with a different flavor. If you are going to go into so much detail as to write c13 instead of c6, then just write the bloody notes on the staff.
And it can be useful information in certain situations. I have some ideas about this question but letās let others get involved here.
I think 11th and 13th are also defined as adding a 3rd to the 9 and 11th chords respectively. I believe it comes down to the predominant guide tones for the two chords. the E6 is a 4 note chord and has a different tonal characteristic vs the 13th when played on a guitar. As far as theory goes, anything goes. As someone mentioned above, just write out the sheet music lol
Isnāt it intended to show the inversion, like where to place the top note relative to the root?
What would you call the same chord on guitar if you played C A D E between frets 1 and 3 and Bb at the 17th fret with your right hand index finger fretting it?
Iāve always thought of a 13th chord as being the same as a sixth but with the 7th added. At least thatās the way it works out on guitar. Doesnāt speak to the inversions, but thatās the way it works out.
Same type of thing with a 9 chord. The difference between, say, a D add 9 vs D9 is the 7th. The 9 chord has it, the add 9 does not.
Same with a Dsus4 vs D11. D11 has the 7.
9, 11, 13 chords always contain the 7th.
Thatās a different system called āfigured bass notationā where the numbers show inversions. And its rarely used anymore because its super clunky and cumbersome to read.
But Iāll explain it anyway because Iām a official music nerd.
Remember that inversions are:
C chord - C E G - Written as ā1ā
C chord first inversion - E G C - Written as ā1 superscript 6ā
C chord second inversion - G C E - Written as ā1 superscript 6, subscript 4ā
Likewiseā¦
C minor chord - C Eb G - Written as āiā
C minor chord first inversion - Written as āi superscript 6ā
C minor chord second inversion - Written as āi superscript 6, subscript 4ā
So āfigured bass notationā, if you look closely at it, is specifying intervals. Consider:
C second inversion - G C E- '1 superscript 6, subscript 4.
The the superscript defines the interval from the lowest note (which is not the root in this case). G up to E is 6 intervals. Then the subscript 4, because G up to C is 4 intervals
As long as you hit a Bb and not a Bā® then its still a C13.
Pretty close! In the ballpark and getting warmer!! lolā¦
This parts 100% correct
So youāre suggesting the 13 chord must always contain the 7th?
Consider this:
A āCā chord that has 1, 3, 5, 9, 11, 13. Literally everything BUT the 7th, are you sure you still wouldnāt consider that a 13?
What then would you call it?
C2+add6+sus4+add9?
C2sus4plus6add9?
ā¦Donāt get me wrong, the point isnāt to argue over the spelling or semantics of a chord.
I believe where all this is most relevant, is when there are groups of musicians that have to use these symbols to efficiently read the same roadmap. Personally Iāve found (for me anyway) that its a little easier to diagnose and solve conflicts in orchestrations and rehearsals when thereās a shared understanding at times.
So which tones in this example are āpredominantā? And how do we distinguish which are predominant enough to be required in the voicing vs which ones could be omitted within the scope of the chord label?
If E6 and E13 have different tonal characteristics on guitar, wouldnāt this mainly be because theyāre a different combination of notes?
Yeahā¦ but Iāve found myself having to experiment with the best way to explain it lately. Reading what people said is really really helping me understand where possible breakdowns in communication between band members reading leadsheets and composers mislabeling chords in first draft rough-copies of transcripts can occur.
@ingolee - Yeah man - itās really nice to see this many people curious enough to chime in! Wanna take a shot at it?
I would say that a C6 is a major chord in the key of C. The C13 chord is usually the dominant chord in the key of F. Dominant chords often contain a minor 7th interval which for a C chord is Bb and you have that note listed here so that makes it sound like a dominant chord.
A C13th chord can be voiced many different ways but the 3rd (E) and the 7th (Bb) are necessary to give this chord a dominant sound, and of course it needs the A note to be called a 13th. Without the Bb it could be a C6/9 chord with the notes you have listed.
Well, hereās my take on it. One of the reasons itās not a 6th chord is cuz of the presence of the 7th. 9, 11 and 13 chords (well, 7 chords as well) are dominant chords. Always contain the 7th.
So with that example (above), the 6th and 13th are the same note, but usually the 13th would be played up top, not in the 6 position. The idea is that youāre stacking thirds on top of the major (1-3-5) triad. Take the major, add a third for the 7th, another for the 9th, then also for the 11th and 13th. So the āAā ideally would not be in the 6th position, but would be above the 7th (which is why itās called a 13th).
Yeah, I would say that. Cuz itās a dominant chord. The 7th ā and Iād also say the 3rd, but esp the 7th ā is necessary to make it a 13th (well, or a 9th or 11th). You could lose the 5th. Could lose the 11th. āCouldā lose the 9th (not essential, but it does add flavor), but not the 7th. Lose the 7th and itās no longer a dominant chord.
Or as @ingolee put it:
Spot on.
Yaaaaay! Woot Woot.
Ding Ding Ding - We have a winner lol.
Yup - Anytime a 13 is noted (Say C13), a dominant base chord voicing is automatically assumed. In the instance of a 6 chord (C6) it is not.
There are 2 types of voicings in the anatomy of a chord. The base (not bass) voicing, and the upper structures. The base voices are 1 through 7, and upper structures are 9 through 11
If the chord does NOT contain a dominant voicing in a bass, which by definition is a major 3rd and a flat 7th, the 13th chord BY DEFINITION is not a 13th.
If the 3rd is raised and the 7th is also raised, it is a Cmaj13
If the 3rd is lowered and the seventh is lowered it is a Cmin13
If the 3rd is raised and the seventh is lowered it is a C13
If the 3rd is lowered and the 7th is raised it is a very ugly chord that doesnāt really have a name (but it would not be a 13 chord, since it does not meet the criteria of a 13 chord by definition).
This parts technically incorrect, but you seem to have understood the other part anyway.
Just to clarify, C is indeed the ādominantā chord in F like you said. However thereās a difference between a dominant chord, and a dominant chord voicing.
If you are in the key of C, then F is your subdominant chord. Lets say we play an F7 in the key of C. Then we are playing a dominant voicing, on a subdominant chord.
So the 13th voicing doesnāt have anything to do with the Tonic, Superonic, Mediant, Subdominant, DOMINANT, and Subtonic, and Tonic Leading (Degrees 1 2 3 4 5 6 7 respectively).
It only has to do with the intervals within the base voicing of the chord 
There you go. You got it. Yes, you can āomitā the 5th, but you can not alter it. Interestingly enough, you may also omit the root. And this is done often in Jazz. So you could have a C13 with the notes E, Bb, D, A, D. See - no root, no 5th, but still a C13. Thatās possible because the root voicing is built off the dominant understructure of an natural 3rd and lowered 7th. Good job!
Did I win anything? Did Ingolee win anything? I want stuff! 
On a more serious note, thanks for posting this, Jonathan. Good stuff. Great discussion.
If I needed to know all that to play I would have been a ditchdigger.
When ever we talk about theory I always think of the late songwriter Bob Merrill.
āSeventeen hits in his first three years was pretty good hitting for an Atlantic City-born fellow who could not read music or play a musical instrument. Everything was composed on a toy xylophone that had numbers on the keys. It cost him $1.98 at the five-and-dime. Heād tap out a tune and take the numbers heād written down to someone who could play the piano to transcribe. When his royalties reached $250,000, he treated himself to a $6.98 toy xylophone, which he used for the remainder of his careerā
Well he did have to read the numbers, thatās kind of like theory right? 
Such a way with words you have, Bob! 
My thoughts exactly!