Dominant Thirteenth chord


Some Review

Recall from May 3rd's lesson 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 as (9) = 1,3,5,b7,9
dominant eleventh chord as (11) = 1,3,5,b7,9,11

Now we shall define the dominant thirteenth chord as:
13 = 1,3,5,b7,9,11,13
Sometimes we write dominant thirteenth chords as dom13 or 13. (Ex. C13, Ddom13, etc.)

Here are some open 13 chords to get you started:
A13=X00032, B13=X22224,
E13=000122, G13=333200.

We should note from our definition (13=1,3,5,b7,9,11,13) that a dominant thirteenth chord contains a dominant eleventh chord (11=1,3,5,b7,9,11) within it.
We can think of a dominant thirteenth chord as a dominant eleventh chord with an added major thirteenth.

If we don't know how to play a 13 chord, we could substitute a major chord, or a dominant seventh chord, or a dominant ninth chord, or a dominant eleventh chord. We will no longer have the full flavor of the 13 chord, but the substitution should work.

We also note that a chord synonym for for I13 is iii11b9b5b6.
In the key of F:
C13 = C,E,G,Bb,D,F,A = Em11b9b5/C

So you could use as a substitute for a 13 chord, a half-diminished seventh chord a major third higher than the 13 chord. (you could substitute Em11b9b5 for C13)

Recalling how the chromatic scale maps out on a fretboard in standard tuning ( see July19's lesson). We can map out the 13 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).

|-1|--|-9|--|-3|11|--|-5|--|13|b7|--|-1|
|-5|--|13|b7|--|-1|--|-9|--|-3|11|--|-5|
|--|-3|11|--|-5|--|13|b7|--|-1|--|-9|--|
|b7|--|-1|--|-9|--|-3|11|--|-5|--|13|--|
|11|--|-5|--|13|b7|--|-1|--|-9|--|-3|11|
|-1|--|-9|--|-3|11|--|-5|--|13|b7|--|-1|

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 F13. To change to to another 13 chord, we use the same process as for other moveable chords (barre chords, etc.).

F13 "E-shape"(root note on the 6th string)

--|-1-|---|-9-|---|---| 
--|-5-|---|13-|b7-|---|
-9|---|-3-|11-|---|---|
13|b7-|---|-1-|---|-9-|
--|11-|---|-5-|---|13-|
--|-1-|---|---|---|---|
0   1   2   3   4

|----3-1-1-3--|
|--3-3-3-3-3--|
|--2-2-2-0-2--|
|--1-1-1-1-1--|
|------1-1-1--|
|--1-1-1-1-1--|

F13 "D-shape" (root note on the 4th string)

|-9-|---|-3-|11-|
|13-|b7-|---|-1-|
|11-|---|-5-|---|
|-1-|---|-9-|---|
|-5-|---|13-|b7-|
|-9-|---|-3-|11-|
  3   4   5   6 

|--5-3--|
|--4-3--|
|--3-3--|
|--3-3--|
|-------|
|-------|

F13 "C-shape" (root note on the 5th string)

|-3-|11-|---|-5-|
|---|-1-|---|-9-|
|-5-|---|13-|b7-|
|-9-|---|-3-|11-|
|13-|b7-|---|-1-|
|-3-|11-|---|-5-|
  5   6   7   8

|--8-6--|
|--8-6--|
|--7-7--|
|--8-7--|
|--8-6--|
|-------|

F13 "A-shape" (root note on the 5th string)

|---|-5-|---|13-|b7-|---|
|---|-9-|---|-3-|11-|---|
|13-|b7-|---|-1-|---|-9-|
|-3-|11-|---|-5-|---|13-|
|-7-|-1-|---|-9-|---|---|
|---|-5-|---|13-|b7-|---|
  7   8   9  10  11  12

|--10-10-10-10-10--|
|--10-10-10-10-11--|
|---8--8--8--8--8--|
|---8--8----10--8--|
|---8--8--8--8--8--|
|---8--------------|

F13 "G-shape" (root note on the 6th string)

|13-|b7-|---|-1-|
|-3-|11-|---|-5-|
|-1-|---|-9-|---|
|-5-|---|13-|b7-|
|-9-|---|-3-|11-|
|13-|b7-|---|-1-|
 10  11   12  13

|-10-10--|
|-10-10--|
|--------|
|-13-13--|
|----13--|
|-13-13--|

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.

Arpeggios

Probably the most common way of hearing chords with notes not all played at once would be the playing of arpeggios.

Consider simple fingerpicking patterns such as P-I-M-A. (which would be using, in order, one at a time, the thumb,first,second, and third fingers of the picking hand) We could such a pattern with notes from a chord (here D7=XX0212) like this:

|--------2--|
|------1----|
|----2------|
|--0--------|
|-----------|
|-----------|

That would be one example of an arpeggio. 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 F13 (in E-shape, 1rst position) Compare shape with notes in TAB.

|-1-|---|-9-|---|  
|-5-|---|13-|b7-|
|---|-3-|11-|---|
|b7-|---|-1-|---|
|11-|---|-5-|---|
|-1-|---|---|---|
  1   2   3   4

|-----------------1-3-1-|
|-------------1-3-------|
|-----------3-----------|
|-------1-3-------------|
|---0-3-----------------|
|-1---------------------|

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

|-1-3-1---------------|
|-------3-1-----------|
|-----------3---------|
|-------------1-3-----|
|---------------------|
|---------------------|

Or how about we create a fingerpicking pattern such as:

|--------3------------|
|-----------3---------|
|-----3---------------|
|--1------------------|
|-----3---------------|
|--1------------------|

Ok so we can play 13 chords several ways, but what do we do with them? Are there any general rules? (yes. Can we break them? you bet.)

CHORDS in CONTEXT

We often see 13 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)

In ninth chords the major scale harmonized becomes:
Imaj9-ii9-iii7b9-IVmaj9-V9-vi9-vii7b9b5

In eleventh chords the major scale harmonized becomes:
Imaj11-ii11-iii11b9-IVmaj9#11-V11-vi11-vii11b9b5

In thirteenth chords the major scale harmonized becomes:
Imaj13-ii13-iii11b13b9-IVmaj13#11-V13-vi11b13-vii11b13b9b5

We can see here that the only chord in the major scale with a dominant 13th chord is the 5. Recall that the 5th note is referred to as the dominant note in the Roman Numeral System (see july 19th's lesson).

Where else does the dom 13 chord turn up?
Without getting into the modes of these scale systems as well, we find dom13 chords in the natural minor, harmonic minor, and melodic minor scales (also in their modes).

In the natural minor (minor scale, or aeolian mode), the dom13 is the bVII13 (in the key of Am: bVII11= (G13= G,B,D,F,A,C,E), Am= (A,C,E)). All note movements are within a whole-step. The progression bVII-i (or V-vi) is called a "deceptive cadence."

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 13 chord does not naturally occur.

In fact the 13 chord is synonymous with the mixolydian mode. There are no other 7 note or smaller scales with the 13 chord in them (as the root chord). In order to find another scale outside of the modes of the major scale with a 13 chord in it, we will need to find an 8-note or higher scale to find one.

See dom7 lesson for notes on progressions with dom chords, substitute the dom13 for dom7.
http://simianmoon.com/snglstringtheory/chords/dom7.html

INVERSIONS and CHORD SYNONYMS

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:

G13= G,B,D,F,A,C,E (root position, 1 is in the bass)

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

Speaking of substitutions, the dominant note (5) of the major scale as a functional position probably sees more substitutions of extended and altered chords on that spot than any other note (functionally). Some extensions and alterations often found on the dom9 chord are listed below for the intermediate/advanced student to work through and explore:

13 = 1,3,5,b7,9,11,13
13#5 = 1,3,#5,b7,9,11,13
13b5 = 1,3,b5,b7,9,11,13
13#11#5 = 1,3,#5,b7,9,#11,13
13#11b5 = 1,3,b5,b7,9,#11,13

And the list goes on...
we could omit notes, etc. we often see these things in jazz heads. If you don't know how to play one of these chords, there's a good chance you could get away with substituting a 9 or 7 for it (of course, you'll lose part of the flavor, but in a jam...). it might be helpful to learn some 11 shapes without 5's in them (so it doesn't clash when substituted for a dominant chord with an altered 5).

Here are some in F (F13(no5))
F13 = 1X123X (E-shape, root on 6th string)
F13 = XX3333 (D-shape, root on 4th string)
F13 = X8X8 10 10 (A-shape, root on 5th string)
F13 = 13 x 13 x 10 10(G-shape, root omited)

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. 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 13 chord I would suggest learning voicings that contain the root,3rd,7th,13th.
1,3,b7,13 = 7/6 (no5)
and also the root,9th,11th,13th.
1,9,11,13 = I13 (no3,no5,no7) = ii7

Next lesson on Minor Thirteenth Chord.

Peace,
Christopher Roberts
snglstringtheory@aol.com


How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

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Last updated February 13, 2004.
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