Major Thirteenth chord

Some Review

Recall from lesson on building a context that we've defined a chord as being 3 or more distinct notes, usually played at the same time. (C and D are considered distinct, but C# and Db are not, nor are octaves of the same note).

Recall that chords come in two basic parts, a letter name (C, C#, etc.) also known as a root note (tonic, 1), and a descriptive part that abbreviates the name of the chord (is a short-hand for all the intervals of each distinct note from the root note).

Recall that an interval is the distance between two notes, and that we are using numbers (with accidentals) to describe these intervals.(ex. 5 = perfect fifth, etc.) For more info on intervals see July19's lesson. to convert letters to numbers and numbers to letters, see the link below (bottom of page) on transposition.

Recall, we've previously defined the following chords:
major = 1,3,5
minor (m)= 1,b3,5
diminished (o)= 1,b3,b5
power chord (5) = 1,5,8(1)
dominant seventh chord as (7) = 1,3,5,b7
dominant ninth chord (9) = 1,3,5,b7,9
minor seventh chord (m7) = 1,b3,5,b7
minor ninth chord (m9) = 1,b3,5,b7,9
major seventh chord (maj7) = 1,3,5,7
major ninth chord (maj9) = 1,3,5,7,9
major eleventh chord as (maj11) = 1,3,5,7,9,11

Now we shall define the major thirteenth chord as:
maj13 = 1,3,5,7,9,11,13
Sometimes we write major thirteenth chords as maj13 or (delta)13. (Ex. Cmaj13, D(delta)13, etc.)

Here are some open maj13 chords to get you started:
Amaj13=002122, Cmaj13=X32203,
Dmaj13=X40000, Emaj13=001122, Gmaj13=332202.

We should note from our definition (maj13=1,3,5,7,9,11,13) that a major thirteenth chord contains a major eleventh chord (maj11=1,3,5,7,9,11) within it.
We can think of a major thirteenth chord as a major eleventh chord with an added major thirteenth.

If we don't know how to play a maj13 chord, we could substitute a major chord, major seventh chord, or a major ninth chord, or a major eleventh chord with the same root. We will no longer have the full flavor of the maj13 chord, but the substitution should work.

We also note that a chord synonym for for Imaj13 is iii11b9b6.
In the key of C:
Cmaj13 = C,E,G,B,D,F,A = Em11b9b6/C

So you could use as a substitute for a maj13 chord, a minor eleventh flat nine flat thirteen chord a major third higher than the maj13 chord. (you could substitute Em11b9 for Cmaj13)

Recalling how the chromatic scale maps out on a fretboard in standard tuning ( see July19's lesson). We can map out the maj13 chord on the fretboard (shown here in F) ( we note that the M6 and the M13 intervals are octaves of each other and have written in the 13, the same way any and all 8s have been written as 1s).


Those familiar with the fretboard will note that the same intervals make up the major scale (1,3,5,7,9,11,13 = 1,3,5,7,2,4,6)

We can cut this up into zones of one sort or another. In previous lessons, we've been looking at shapes based on octave patterns. (A-shape, E-shape, etc.). So below are the 5 shapes along with some voicings in TAB that go along with the shape. All of these are for Fmaj13. To change to to another maj13 chord, we use the same process as for other moveable chords (barre chords, etc.).

Fmaj13 "E-shape"(root note on the 6th string)

  0   1   2   3 


Fmaj13 "D-shape" (root note on the 4th string)

  3   4   5   6 


Fmaj13 "C-shape" (root note on the 5th string)

  5   6   7   8


Fmaj13 "A-shape" (root note on the 5th string)

  7   8   9  10  11  12


Fmaj13 "G-shape" (root note on the 6th string)

 10  11   12  13  14


Ok. So we can make many different voicings out of a given chord (many more than shown here). Choosing for ourselves just what voicing we're going to use to interpret a chord is one part of developing our own style.


Probably the most common way of hearing chords with notes not all played at once would be the playing of arpeggios. We notice from above that we see more possibilities for note choices on a single string in a given position.

Here is another example of an arpeggio based on Fmaj11 (in E-shape, 1rst position) Compare shape with notes in TAB.

  0   1   2   3


You need not play all the notes, nor play them in order or only once. Consider the following from the same chord, shape, etc.


Ok so we can play maj13 chords several ways, but what do we do with them? Are there any general rules? (yes. Can we break them? you bet.)


We often see maj13 chords written in songs, but there is a way to understand why they pop up where they do? Usually.

Recall, that we harmonized the major scale to get the chords (triads):
I-ii-iii-IV-V-vi-viio (in the key of C: C-Dm-Em-F-G-Am-Bo)
and the seventh chords:
Imaj7-ii7-iii7-IVmaj7-V7-vi7-vii7b5 (in C:
Cmaj7-Dm7-Em7-Fmaj7-G7-Am7-Bm7b5) and the ninth chords:
Imaj9-ii9-iii7b9-IVmaj9-V9-vi9-vii7b9b5 (in C:

In eleventh chords:
Imaj11-ii11-iii11b9-IVmaj9#11-V11-vi11-vii11b9b5 (in C:

In thirteenth chords the major scale harmonized becomes:

We can see here that the chords in the major scale with a major 13th chord are the 1.

Where else does the maj13 chord turn up?
Without getting into the modes of these scale systems as well, we find maj13 chords in the natural minor (also in its modes).

In the natural minor (minor scale, or aeolian mode), the maj13 is the bIIImaj13 (in the key of Am: bIIImaj13= (Cmaj13= C,E,G,B,D,F,A), Am= (A,C,E)).

In the harmonic minor scale, the melodic minor scale, the gypsy minor scale, the pentatonic minor scale, the hungarian scale, and the enigmatic scale, the maj13 chord does not naturally occur.

In fact the maj13 chord is synonymous with the major scale (the ionian mode). There are no other 7 note or smaller scales with the maj13 chord in them (as the root chord). In order to find another scale outside of the modes of the major scale with a maj13 chord in it, we will need to find an 8-note or higher scale to find one.

For some progressions. See maj7 lesson for notes on progressions with maj chords, substitute the maj13 for maj7.


We can invert 7 note chords, just like 3 or 4 or 5 or 6 note chords. When we do so, we see a breakdown of the usefulness of inversions. Every 13th chord harmonized from the major scale inverts into every other 13th chord harmonized from the major scale. In practice, voicings are of more use to the composer/improviser than inversions.

We have been using inversions to look at chord synonyms, and for the sake of completness, we can say the following:

Cmaj13= C,E,G,B,D,F,A (root position, 1 is in the bass)

Cmaj13 = Dm13 = Em11b13b9 = Fmaj13#11 = G13 = Am11b13 = Bm11b13b9b5

Speaking of substitutions, Some extensions and alterations often found on the maj13 chord are listed below for the intermediate/advanced student to work through and explore:

maj13 = 1,3,5,7,9,11,13
maj13#5 = 1,3,#5,7,9,11,13
maj13b5 = 1,3,b5,7,9,11,13
maj13#11#5 = 1,3,#5,7,9,#11,13
maj13#11b5 = 1,3,b5,7,9,#11,13

If you don't know how to play one of these chords, there's a good chance you could get away with substituting a maj6/7 or maj7 for it (of course, you'll lose part of the flavor, but in a jam...). it might be helpful to learn some maj13 shapes without 5's in them (so it doesn't clash when substituted for a major chord with an altered 5).

Here are some in F (Fmaj13(no5))
Fmaj13 = 1XX333 (E-shape, root on 6th string)
Fmaj13 = 1X223X (E-shape, root on 6th string)
Fmaj13 = XX3755 (D-shape, root on 4th string)
Fmaj13 = X8X755 (C-shape, root on 5th string)
Fmaj13 = X8X9 10 10 (A-shape, root on 5th string)
Fmaj13 = X 12 12 12 X 12 (G-shape, root on 6th string, omitted)

Larger Extended Chords and Omited Notes
As we create larger and larger chords, we note that some of the new tones create dissonances with the other tones. In the maj11 chord the 11th creates dissonances with the 3rd, and the 7th, which are the most important intervals for defining a majX chord (maj7, maj9, maj11, maj13). So, often in larger chords a tone or two will be omited. This can happen to clarify the sound although there are other reasons. the guitar typically has 6 strings. an 11th chord has 6 tones, and a 13th chord has 7 tones. Since 6 string chords can sound overly full or awkward, especially if switched between smaller chords, it can be desirable to have smaller 4-string or 5-string chords.

So which tones to omit?
The most common tone to omit 1st is the 5th. If you're playing with a group, it is common for the bassist to emphasize the root and the 5th. Next most common tone to omit is the 4th, but this should not be omited if the chord you're playing names the tone in the chord (11th chords, 7/11, add4, sus4, etc.).
Likewise in 11th or 13th chords, the 9th can be omited.

If you're playing in a group, you might try omitting the root, if another player is playing/emphasizing the root.

So, for the maj13 chord I would suggest learning voicings that contain the root,3rd,7th,13th.
1,3,7,13 = maj7/6 (no5)
and also the root,9th,11th,13th.
1,9,11,13 = Imaj13 (no3,no5,no7) = ii7

Next lesson is on Dominant thirteenth Chords.

Christopher Roberts

How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart

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Last updated February 5, 2004
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