Chord Formation: “What Are Ninths, Elevenths, And Thirteenths?”

Terms like ninths, elevenths, and thirteenths are associated with chord formation.

If you’ve come across the term ninths, elevenths, and thirteenths and are interested in learning what they are, then this lesson is for you.

Let’s get started by learning what ninths, elevenths, and thirteenths are.

“What Are Ninths, Elevenths, And Thirteenths?”

Following traditional principles, chords are formed in third intervals. Consequently, there are seven chord tones:

The first

The third

The fifth

The seventh

The ninth

The eleventh

The thirteenth

Chord tones that are beyond the compass of an octave are referred to as extensions and this is because their significant role in extending the width of a chord.

The ninth, eleventh, and thirteenth tones are extensions; unlike the first, third, fifth, and seventh tones that are within the compass of an octave.

“Let’s Use The C Major Seventh Chord As A Reference…”

The tones of the C major seventh chord (its first, third, fifth, and seventh tones):

…are within the compass of the C octave:

…while other chord tones that extend the width of the C major seventh chord beyond the compass of an octave are called extensions.

Let’s take a closer look at these extensions.

Attention: To learn more about this, I recommend our 500+ page course: The “Official Guide To Piano Playing.” Click here for more information.

Quick Insights On Chord Extensions

The ninth, eleventh, and thirteenth extensions are basically chord tones that are a ninth, eleventh, and a thirteenth above the first tone.

In the key of C major:

C is the first:

D is the second:

E is the third:

F is the fourth:

G is the fifth:

A is the sixth:

B is the seventh:

C is the eighth:

D is the ninth:

E is the tenth:

F is the eleventh:

G is the twelfth:

A is the thirteenth:

So, after the first, third, fifth, and seventh tones (which are C, E, G, and B):

…are the ninth, eleventh, and thirteenth (which are D, F, and A):

Using C as the first tone:

The ninth (which is D):

…can be associated with the second tone of the major scale (which is also D):

The eleventh (which is F):

…can be associated with the fourth tone of the major scale (which is also F):

The thirteenth (which is A):

…can be associated with the sixth tone of the major scale (which is also A):

Attention: To learn more about this, I recommend our 500+ page course: The “Official Guide To Piano Playing.” Click here for more information.

The Association Of Extensions With Intervals

So, the three extensions — the ninth, the eleventh, and thirteenth — are related to the major second, perfect fourth, and major sixth intervals.

The major second interval is a product of the relationship between the first and second tones of the major scale. In the case of the C major scale:

…the first and second tones are C and D:

…which is a major second interval. The octave transposition of D:

…to D:

…produces the ninth interval (C-D):

…and the extension (which is D):

The perfect fourth interval is a product of the relationship between the first and fourth tones of the major scale. In the case of the C major scale:

…the first and fourth tones are C and F:

…which is a perfect fourth interval. The octave transposition of F:

…to F:

…produces the eleventh interval (C-F):

…and the extension (which is F):

The major sixth interval is a product of the relationship between the first and sixth tones of the major scale. In the case of the C major scale:

…the first and sixth tones are C and A:

…which is a major sixth interval. The octave transposition of A:

…to A:

…produces the thirteenth interval (C-A):

…and the extension (which is A):

Using the C major scale as a reference, we derived the following extensions: the ninth (which is D), the eleventh (which is F), and the thirteenth (which is A).

Here’s How To Determine Chord Extensions

Let’s end this lesson by determining chord extensions in a few keys.

Using the D major scale (as a reference):

…extensions can be derived from the following intervals:

The major second (D-E):

…produces the ninth (D-E):

The perfect fourth (D-G):

…produces the eleventh (D-G):

The major sixth (D-B):

…produces the thirteenth (D-B):

Using the Ab major scale (as a reference):

…extensions can be derived from the following intervals:

The major second (Ab-Bb):

…produces the ninth (Ab-Bb):

The perfect fourth (Ab-Db):

…produces the eleventh (Ab-Db):

The major sixth (Ab-F):

…produces the thirteenth (Ab-F):

Using the F major scale (as a reference):

…extensions can be derived from the following intervals

The major second (F-G):

…produces the ninth (F-G):

The perfect fourth (F-Bb):

…produces the eleventh (F-Bb):

The major sixth (F-D):

…produces the thirteenth (F-D):

Following the same procedure, the ninth, eleventh, and thirteenth chord extensions can be determined.

Final Words

In a subsequent lesson, we’ll be learning how these chord extensions can be used in the formation of extended chords.

See you then!

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Chuku Onyemachi

Head of Education at HearandPlay Music Group

Onyemachi "Onye" Chuku is a Nigerian musicologist, pianist, and author. Inspired by his role model (Jermaine Griggs) who has become his mentor, what he started off as teaching musicians in his Aba-Nigeria neighborhood in April 2005 eventually morphed into an international career that has helped hundreds of thousands of musicians all around the world. Onye lives in Dubai and is currently the Head of Education at HearandPlay Music Group and the music consultant of the Gospel Music Training Center, all in California, USA.

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