Showing Your Work: The Difference Between 6 and 13

Find out how to easily avoid a common error when referring to 13 chords on the guitar.

Ultimate Guitar
Were you ever discouraged in math class when you were deducted points for not adequately showing all of your work? It seemed like a trivial thing. The answer to 1 + 1 is 2. The answer would always be the answer - and that's all it can be! It's a finite scenario - what difference does it make how you get there?

Until today, somewhere around 95% of you have never encountered a real-life scenario where the answer to a simple question based in the addition and subtraction of small integers became dependent upon how one arrived at the answer. What is the difference between a 6 chord and a 13 chord?

If we were to follow primal logic, we would say the difference between 6 and 13 is 7. Back in math class, this would be accepted as correct, and the finite truth. Music however, is not specifically finite; therefore, it is not always safe to assume the same types of logic will always work in any given scenario. Many times it will, but an unknown number of times it will not. The 13 chord is a case of the latter. When working with guitar chords, the difference between 6 and 13 is not 7, but 9 + (-2). This is the hidden work behind the answer to the math equation. In chord world, negative 2 would be equal to the dominant seventh note, and 9 is equal to the second interval from the root of the chord - typically, but not always, played one or two octaves higher than the lowest notes in the chord.

Below are two voicings of the same chord stepping down from a dominant seventh, to a sixth chord. You can put the red note (root) anywhere you like on the neck, but for the purpose of academics, A is a nice place to play these chords. Use the shapes to move this chord to other notes, such as F#. Slide the whole shape and grip of the chord chord up or down the neck until the red note is the root note of the chord you wish to play. No matter what note the root is, the difference between a 7 chord and a 6 chord is one fret.

You could play both the 7 and 6 tones together, like in the second 6 chord, but you will begin to hear the sixth tone as the dominant feature, thereby making the seventh tone unnecessary for ultilizing the harmonic function of the 6 chord. While adding the seventh tone is audibly pleasing, and it could be included just for the sake of convenience (i.e. ease of grip for the chord), one can choose to add this note, or not, to a 6 chord. The dominant seventh tone alone will not alter the harmonic trajectory of the chord.

While showing our work when using our chord formula for a 13, we have discovered that while 13 = 6 + 7; 7 = 9 - 2. In this particular scenario, the number seven becomes a variable string array with contents of 9 - 2. The equation contains a variable inside another variable. 

In terms of practical reality, what this all means is: a dominant sixth chord becomes a thirteen chord when the conditions of 6 + 9 - 2 are met.

The tones contained in the string array defining the 13 chord are: 6 - 9 - 5 - R - 3 - 7. In some cases, it can become possible to eliminate the third interval from the chord because the interval between 9 and (-2) is a major third, accomplishing the task of defining the harmonic structure of the chord as a dominant. This point is illustrated through the chords below. Note how the chord becomes minor sounding when the third tone is removed. Played in this fashion, A 13 (no 3) becomes a substitute for Em-9. Then depending on the context of the whole progression, the name of the chord could possibly be changed to Em9 /A.

About the Author:
Dealey is a Vancouver, Canada based guitarist, songwriter, recording engineer and producer. He is the author of the forthcoming independent book, "The Relative Nature Of Chords: A Street-Smart Field Guide for Guitar." Watch for exclusive excerpts on Ultimate-Guitar! You can support his music here - or talk to him about collaborating on your project by email to info(a.t.)

10 comments sorted by best / new / date

    The difference between 6th and 13th chords is simply the 7th. A 6th chord doesn't have a 7th in it, a 13th chord does. This just seems too complex.
    Also octave is not mentioned. Now in guitar specifically to get all the notes I understand they can not all stack like a piano, BUT the easiest way to tell 6 from 13 is the octave. In writing the chords on a staff you would stop at the 6 for the 6th chord or continue up to the 13. I felt this langue was talking too high for no more gleaned from the content. Sorry but reading this article was more trouble than it was worth and I don't think would help a musician outside of a theory students study guide.
    The octave doesn't really make a difference. Extensions tend to sound better the higher they are played (if you play them lower, it may make the chord sound muddy) but it doesn't need to be a 13th higher than the bass note. It can be played in any octave. The chord name doesn't really tell about the voicing you should use. It only tells the chord tones and the bass note. But not the order of the notes. A chord that has notes C E G Bb and A in it in any order is a C13 chord. C7add6 doesn't really exist. If you add an A to a C7 chord, it is always the 13th. And if you add an A to a C major chord, it is always the 6th.
    The Harvest
    A 13 chord will not accomplish the complete harmony in the chord without the inclusion of the 9th. Without the 9th, it is just a 6 chord. Placing the 6th higher in the order is simply an inversion of a 6th chord, it doesn't change the actual intervallic relationships within the chord and key.
    A 13th chord doesn't really need a 9th in it, it needs a 7th. Actually if the chord has a 6th and 9th but not a 7th, we call it a 6/9 chord. For example C6/9. A 13th chord is an extended chord. Extended chords are always 7th chords.
    you guys in the comments really cleared up a lot of things for me, but all of your examples have been in major. what about minor-related chords, like D A C F B (which ive used in a song before)? would that be a Dmin13?
    Yes. Dm13 = Dm7 + 13. The other notes (9 and 11) are optional. It is also good to remember that the 6th/13th are assumed to be major. This means Am6 is A C E F#, not A C E F. You can alter the 13th and make it minor. For example E7b13 is possible.
    ive heard that before. also, while we're on the topic of extensions, is it true that the 4th in 11th chords are usually raised?
    Sorry for a bit late reply. It depends on the chord. Minor chords usually have natural 11ths (I don't think a m7#11 chord even exists - I mean, it's possible in theory, but it will sound like a m7b5 chord, unless it also has a natural fifth which just makes it sound horrible). Dominant chords can have natural 11ths - though it's pretty common to raise the 11th. If a maj7 chord has an 11th, it's pretty much always a raised 11th.
    Okay, all of the above looks completely clear, but what about the difference between the 6th and added 13th chords, e.g. A6 vs Aadd13 - both having the same notes: A-E-C#-F#?