2.3 Harmonic Extensions

9th, 11th and 13th: the colour of modern jazz

Key Concepts

What are Extensions?

Notes added after the seventh (9, 11, 13) which continue the pattern of overlapping thirds. They correspond to the 2nd, 4th and 6th scale degrees, raised by an octave.

Why are they used?

They create harmonic colour and sophistication without altering the chord’s tonal function. They are fundamental to the sound of modern jazz and contemporary music.

The Nones (9)

The most common and natural extension. It can be major (9), minor (♭9) or augmented (#9). It works with all types of chords.

The Eleventh (11)

Note: natural (11) on minor chords, augmented (#11) on major chords to avoid dissonance with the third.

Thirteenth-Month Bonuses (13)

The richest chords: theoretically 7 notes (the entire scale). In practice, the fifth and 11th are omitted to avoid sonic confusion.

Practical Voicing

Always retain: the root (on the bass), the third and the seventh (which define the quality). Add the characteristic extensions. Omit the fifth and the natural ninth if necessary.

What are harmonic extensions?

Harmonic extensions are notes added beyond the seventh, continuing the pattern of overlapping thirds. They are fundamental to the sophisticated sound of modern jazz.

Concept: The extensions are the 9th, 11th and 13th notes, which correspond to the 2nd, 4th and 6th notes of the scale played an octave higher. For example, the 9th is the 2nd an octave higher.

From the Triad to the Extended Agreement

Triad

C-E-G

Seventh

Cmaj7

C-E-G-B

Ninth

Cmaj9

C-E-G-B-D

Thirteenth

Cmaj13

C-E-G-B-D-F#-A

Correspondence with the Scale degrees

Scale degrees:

1 - 2 - 3 - 4 - 5 - 6 - 7

Extensions:

1 - 9 - 3 - 11 - 5 - 13 - 7

The 9th = 2nd + an octave, the 11th = 4th + an octave, the 13th = 6th + an octave

The None (9ths)

The ninth is the most common and natural interval. It can be a major, minor or augmented ninth.

Nona Maggiore (Major 9)

Major 7th + major 9th chord. A rich, bright sound.

C (1)

E (3)

G (5)

B (7)

D (9)

Cmaj9 = C–E–G–B–D

Formula: 1 3 5 7 9

Usage: Imaj9, IVmaj9 – tonic and subdominant chords

Dominant 9

Dominant 7th + major 9th chord. Blues/jazz sound.

G (1)

B (3)

D (5)

F (♭7)

A (9)

G9 = G-B-D-F-A

Chord: 1 3 5 ♭7 9

Usage: V9 – very common in turnaround progressions and blues

Minor 9

Minor 7th + major 9th chord. A sophisticated, modern sound.

D (1)

F (♭3)

A (5)

C (♭7)

E (9)

Dm9 = D–F–A–C–E

Chord progression: 1 ♭3 5 ♭7 9

Usage: IIm9, IIIm9, VIm9 – widely used in jazz

Unaltered (♭9 and #9)

Minor ninth (♭9) or augmented ninth (#9) on dominant chords to create tension.

G7♭9: G-B-D-F-A♭

G7#9: G-B-D-F-A#

"Hendrix Chord": The 7#9 is known as the "Hendrix chord". It has a very intense blues-rock sound.

Practical Examples with the None

An analysis of how ninths are used in harmonic construction.

"Autumn Leaves" – Turnaround

Voicing: Dm9 – G9 – Cmaj9

Analysis: II–V–I with ninths on all chords. The ninths add colour without altering the progression.

Listen

"Purple Haze" – Hendrix Chord

Voicing: E7#9 (E–G#–D–G)

Analysis: The raised ninth creates the characteristic G#-G cluster. An unmistakable blues-rock sound.

Listen

"All Blues"

Voicing: G9, C9, D7♭9

Analysis: Modal blues built on ninth chords. The D7♭9 creates the characteristic tension.

Listen

"Don't Know Why"

Voicing: Cmaj9, Dm9, Fmaj9

Analysis: Major 9th and minor 9th chords create an intimate atmosphere. Jazz-pop with elements of mainstream music.

Listen

Comparison Table of the None

Agreement	Formula	9th interval	Sound Character	Typical Use
maj9	1-3-5-7-9	9th major	Bright, rich, stable	Imaj9, IVmaj9 (tonic/subdominant)
9 (Sun 9)	1-3-5-♭7-9	9th major	Blues, funk, it all works	V9 (dominant), blues progressions
m9	1-♭3-5-♭7-9	9th major	Sophisticated, modern, sweet	IIm9, IIIm9, VIm9 (jazz standards)
7♭9	1-3-5-♭7-♭9	Minor 9th	Tension, chromaticism, altered	V7♭9 (strong resolution), diminished scale
7#9	1-3-5-♭7-#9	Augmented 9th	Raw, blues-rock, intense	"Hendrix chord", altered blues

The 11ths

The eleventh (the fourth raised by an octave) requires care, as it can create dissonance with the third of the chord.

Minor 11

The natural eleventh works well with minor chords.

D (1)

F (♭3)

A (5)

C (♭7)

E (9)

G (11)

Dm11 = D–F–A–C–E–G

Note: The fifth (A) is often omitted to avoid confusion in the sound.

Lydian #11 (Major 7#11)

In major scales, the #11 is used to avoid conflicts with the third. Sound of the Lydian mode.

C (1)

E (3)

G (5)

B (7)

D (9)

F# (#11)

Cmaj7#11 = C–E–G–B–D–F#

Why #11?: A natural 11 (F) would form a minor second with the third (E), which is too dissonant.

Dominant 11 (sus)

In dominant chords, the 11th can replace the third (suspended chord).

G11: G-C-D-F-A

(Class 3B omitted)

Suspended: Similar to G7sus4. Creates a harmonic suspension.

Dominant 7#11

7#11 over the dominant for a Lydian-dominant sound (whole-tone scales).

G7#11: G-B-D-F-A-C#

Use: A modern sound, typical of bebop and post-bop.

Comparison Table of the Elevenths

Agreement	Formula	Type 11a	Why this choice?	Sound Character
m11	1-♭3-5-♭7-9-11	11th natural	No conflict with ♭3	Suspended, modal, fluctuating
maj7#11	1-3-5-7-9-#11	#11 (Lydian)	Avoid the 2nd minor with the 3rd	Sparkling, luminous, ethereal
7#11	1-3-5-♭7-9-#11	#11 (Lydian-Dom)	Whole-tone sound, modern	Suspended, altered, bebop
11 (up)	1-11-5-♭7-9	11th natural (instead of the 3rd)	Replaces the third	Pending, unresolved, open

Basic rule: The natural 11th clashes with the major third (a minor second interval). On major chords, always use #11 or omit the third.

Practical Examples Using Elevenths

An analysis of how elevenths create harmonic colour and a suspended sound.

"Maiden Voyage"

Voicing: Dm11, Em11 (suspended 11th chords)

Analysis: Suspended chords with the 11th create an oceanic, floating atmosphere. A modal jazz piece based on harmonic colours.

Listen

"The Simpsons Theme"

Voicing: Cmaj7#11 (final chord)

Analysis: #11 (F#) in the Lydian mode gives the theme its characteristic bright, suspended sound.

Listen

Thirteenth-Month Bonuses (13ths)

The thirteenth is the sixth transposed up an octave. Thirteenth chords contain all the notes of the scale (theoretically 7 notes).

Major 13

The richest chord: it contains all the notes of the major scale.

Cmaj13 (full):

C-E-G-B-D-F#-A

(1-3-5-7-9-#11-13)

Cmaj13 (practical voicing):

C-E-B-D-A

(5th and 11th omitted)

Practical note: It is impossible to play all 7 notes. The fifth and/or eleventh are omitted.

Dominant 13

The most common chord progression in jazz. Rich and colourful.

G13 (full):

G-B-D-F-A-C-E

(1-3-5-♭7-9-11-13)

G13 (practical voicing):

G-B-F-A-E

(5th and 11th omitted)

Essential: The third (B) and seventh (F) must always be present to maintain the dominant function.

Minor 13

Rare but very sophisticated. Used in modal jazz.

Dm13:

D-F-A-C-E-G-B

(1-♭3-5-♭7-9-11-13)

Usage: More common in modal jazz than in tonal progressions.

Dominant 7♭13

Minor thirteenth (♭13 = ♭6) on altered dominants.

G7♭13:

G-B-D-F-E♭

(1-3-5-♭7-♭13)

Accidental: Creates chromatic tension. Often combined with ♭9 or #9.

Practical Examples Involving Thirteenth-Month Bonuses

An analysis of how thirteenths create rich and full harmonies.

"Superstition"

Voicing: E♭m9 with an implied 13th in the groove

Analysis: Funk with sophisticated harmonies. Variations on simple grooves create harmonic richness.

Listen

"So What" – Voicing

Voicing: Dm11/13, E♭m11/13

Analysis: Bill Evans’ voicings with multiple extensions (9, 11, 13). Suspended modal sound.

Listen

"Isn't She Lovely"

Voicing: Cmaj13 – F13 (intro)

Analysis: Progression featuring a dominant 13th and a major 13th. A rich, joyful sound typical of the R&B/soul style.

Listen

"Reelin' in the Years"

Voicing: Dominant 13 chords

Analysis: The use of 13th chords in the arrangements creates the characteristic sophisticated sound. Jazz-rock fusion.

Listen

Practical Voicing of Thirteenths

It is impossible to play all 7 notes of a 13th chord. Here are some practical examples of usable voicings:

Piano - G13

Left hand: G

Right hand: F – A – B – E

(♭7 - 9 - 3 - 13)

Omitted: 5th (D), 11th (C)

Guitar – Cmaj13

From the 6th to the 1st string:

x - 3 - 2 - 2 - 0 - 0

C - B - E - A

(1 - 7 - 3 - 13)

Jazz Progressions with Extensions

Let’s see how extensions are applied to standard jazz progressions, transforming a simple II-V-I into a sophisticated, modern sound.

No Extensions (Basic)

II–V–I in C major:

Dm7 → G7 → Cmaj7

A classic yet simple sound. It works, but it lacks character and sophistication.

With Extensions (Modern)

II–V–I in C major:

Dm9 → G13 → Cmaj9

A rich and sophisticated sound. The extensions add colour without altering the harmonic function. This is the modern jazz standard.

With Altered Extensions (Bebop)

II–V–I in C major:

Dm11 → G7♭9♭13 → Cmaj7#11

IIm11: The suspended 11th builds tension

V7♭9♭13: Maximum tension with accidents, resolves strongly

Imaj7#11: Bright resolution with #11 Lydian

Rhythm Changes with Extensions

"I Got Rhythm" forms the basis of hundreds of jazz standards. Here’s how to apply the extensions:

Measurements	Basic	With Extensions	Function
1-2	B♭maj7 – Gm7	B♭maj9 – Gm9	I – VIm (Tonic)
3-4	Cm7 – F7	11 cm – 13 F	IIm – V (Rhythm)
5-6	Dm7 – G7	Dm9 – G7♭9#11	IIIm – VI (Secondary dominant)
7-8	Cm7 – F7	Cm9 – F7♭9	IIm – V (Turnaround)

Tip: You can add ♭9, #9, #11 or 13 to any V7 chord, depending on the mood. Have a go!

Practical Guidelines for Extensions

Available Extensions

On Major 7:

9, #11, 13

About Dominant 7:

9, ♭9, #9, #11, 13, ♭13

On Minor 7:

9, 11, 13

On m7♭5:

11, ♭13

Notes to Avoid

Some extensions create problematic dissonances:

11 natural over a major 7th (use #11)
13 major over minor chords with ♭6
9 major over ♭9 chords

Golden rule: Avoid minor seconds between the extensions and the root notes of the chord.

Practical Voicing

In practice, it is impossible to play all the notes in an extended chord. Here are the priorities:

Essential (always): Root (lowest note), Third, Seventh
Features: The extensions that provide the colour (#11, ♭9, etc.)
Optional (often omitted): Fifth, natural 9th

Example: For G13♭9, play: G (bass) – B – F – A♭ – E (third–seventh–♭9–13)

Upper Structure Triads

A simple way to visualise extensions is to think of them as triads superimposed on the root chord.

Example: G7 with Upper Structures

G7 + D major triad

= G13

D-F#-A over G-B-F

(9-#11-13)

G7 + A♭ major triad

= G7♭9♭13

A♭–C–E♭ above G–B–F

(♭9-11-♭13)

G7 + E♭ major triad

= G7#9#5

E♭–G–B♭ above G–B–F

(♭13-#9-#5)

Study Tips

1. Start with the Nones

The ninth is the most natural and reliable extension. Add 9 to all the chords you already know (Cmaj7 → Cmaj9, Dm7 → Dm9). Get used to the sound before moving on to the other extensions.

2. Practise voicings on the piano

Even if you’re not a pianist, the piano clearly illustrates the extensions. Practise rootless voicings (without the root note) like Bill Evans: 3-7-9-13 for the 13th.

3. Analyse jazz standards

Pick up a Real Book and systematically replace: all maj7s with maj9s, all m7s with m9s, and all 7s with 9s or 13s. Listen to the difference. “Autumn Leaves” is the perfect place to start.

4. Study #11 Lydian

The #11 over major chords is magical. Learn to recognise the Lydian sound (bright, suspended). Practise Imaj7#11 and IVmaj7#11 in all keys.

5. Accidents to the Dominants

The V7 chords are a playground for accidents. Try out all the combinations: 7♭9, 7#9, 7♭9#11, 7♭9♭13. Each accidental has a different colour. The diminished and whole-tone scales contain them all.

6. Listen to the Masters

Bill Evans (piano), Herbie Hancock (modern voicings), Steely Dan (sophisticated pop), Stevie Wonder (expanded R&B). Analyse their voicings note by note.

7. Use Upper Structures

Think of chords as overlapping triads. On G7, play a D major triad (D–F#–A = 9–#11–13). This makes it much easier to visualise.

8. Transcribe the voicing

Transcribe the voicings from your favourite tracks. Use software such as Transcribe! to slow the tempo down. Note WHICH extensions are used and WHERE. Recurring patterns will emerge.

Common Mistakes to Avoid

1. 11 Natural on Major Chords

Error: Cmaj7 + F (11 natural) = a muddy, dissonant sound

Solution: Use #11 (F#) on major chords, or omit the third altogether by playing a sus11

2. Too many simultaneous notes

Mistake: Trying to play all 7 notes of a 13th chord

Solution: Omit the 5th and the natural 9th. Retain only: 1 (low) – 3 – 7 – characteristic extensions

3. Ignoring the Harmonic Function

Mistake: Adding random extensions without understanding the harmonic context

Solution: The 3rd and 7th always define the quality. The extensions relate to colour, not structure

4. Accidents to Non-Dominant Chords

Error: Using ♭9 or #9 on maj7 or m7 chords

Solution: Accidents (♭9, #9, ♭13) ONLY work on dominant chords (V7). On other chords, they are too dissonant

5. Don’t Listen to the Bassist

Mistake: Playing the root note when there’s a bass player

Solution: When playing in a band, use rootless voicings. The bass covers the root note, so you can focus on 3–7 extensions.

6. Mixing ♭9 and Natural 9

Error: Voicings containing both the natural ninth and the altered ninth

Solution: Choose one or the other. Their overlap creates a colour cluster that is too narrow

7. Extensions in the Grave Register

Error: Playing intervals below middle C on the piano

Solution: The extensions sound best in the mid-to-high register. At lower pitches, they become muddy and indistinct

8. Forgetting the Melody

Error: Extensions that clash with the melody

Solution: If the melody contains a note that is out of your range, omit that part. The melody always takes precedence

Final Summary

Harmonic extensions are the key to a sophisticated, modern sound. Here are the key points to remember:

Basic Concept

The extensions (9, 11, 13) are the 2nd, 4th and 6th scale degrees raised by an octave. They continue the pattern of overlapping thirds beyond the seventh.

The Nones (9)

The most common and natural extension. It works with all types of chords. It can be major (9), minor (♭9) or augmented (#9) on dominant chords.

The Eleventh (11)

Please note: a natural 11th over minor chords, #11 (Lydian) over major chords. The natural 11th creates dissonance with the major third.

Thirteenth-Month Bonuses (13)

The richest chords (theoretically 7 notes). In practice, the 5th and 11th are omitted. Always retain the 1-3-7 + characteristic extensions.

Altered Dominants

V7 chords accept all accaccidents: ♭9, #9, #11, ♭13. They create tension that resolves strongly to the tonic. They are fundamental to bebop.

Practical Voicing

Priorities: 1) Fundamental (low), 2) Third and Seventh (quality), 3) Characteristic extensions. Omit the fifth and natural ninth if necessary.

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