Volume IV · Chapter 27
Extended Harmony
MUSIC 21B · C-ID MUS 150Chapter quiz →
In the musicianship bookChapter 30: Extended and Altered Chords
Introduction: Stacking Higher
Triads stack two thirds; seventh chords stack three. Keep going and you reach the ninth, eleventh, and thirteenth. A thirteenth chord stacks six thirds and contains all seven notes of a diatonic scale, so stacking further just brings back the root. These extended chords appear occasionally in Classical music, often in Romantic and Impressionist music, and constantly in jazz and popular music, where they're named with lead-sheet symbols.
The upper extensions are compound intervals: the 9th is a 2nd plus an octave, the 11th a 4th plus an octave, the 13th a 6th plus an octave. Their quality matters. A major ninth sounds bright; a minor ninth (♭9) is tense, especially above a major third.
The Dominant Ninth in Common-Practice Harmony
Eighteenth- and nineteenth-century composers mostly used the dominant ninth (V9). In four voices, omit the fifth. The ninth behaves like the seventh, as a dissonance that resolves down by step, and it's normally placed above the third (usually in the soprano) and at least a ninth above the bass.
- In major, V9 has a major ninth (6̂). In minor, it has a minor ninth (♭6̂), written V♭9.
- Remove the root from V♭9 and what's left is vii°7. That's why vii°7 sounds like a dominant: it's a rootless dominant ninth.
- The ninth often resolves within V itself (9–8) before the chord moves on, like a suspension.
Elevenths and Thirteenths
Elevenths and thirteenths are usually handled with care in common-practice music, where they often behave like suspensions or appoggiaturas over V that resolve before the harmony changes. Two shortcuts help you hear them:
- V11: the eleventh (1̂) clashes with the third (7̂), so the third is usually left out. The result often looks like IV over 5̂ in the bass (F/G in C). Lead sheets write it as G9sus or G11.
- V13: the thirteenth (3̂) sits in the soprano above the root, third, and seventh (the fifth, ninth, and eleventh are usually omitted). It either resolves down by third to 1̂ or is held into the tonic.
Lead-Sheet Chord Symbols
Jazz and popular musicians name chords with symbols: the root, then a suffix for quality and extensions. A chord symbol tells you which pitches to use, not how to voice them. Here are the most common symbols, all on C:
| Symbol | Name | Spelled on C | Formula |
|---|---|---|---|
| C6 | major sixth | C E G A | 1 3 5 6 |
| Cmaj7 (CΔ7) | major seventh | C E G B | 1 3 5 7 |
| C7 | dominant seventh | C E G B♭ | 1 3 5 ♭7 |
| Cm7 (C–7) | minor seventh | C E♭ G B♭ | 1 ♭3 5 ♭7 |
| Cø7 (Cm7♭5) | half-diminished seventh | C E♭ G♭ B♭ | 1 ♭3 ♭5 ♭7 |
| C°7 | diminished seventh | C E♭ G♭ B𝄫 | 1 ♭3 ♭5 𝄫7 |
| Cmaj9 | major ninth | C E G B D | 1 3 5 7 9 |
| C9 | dominant ninth | C E G B♭ D | 1 3 5 ♭7 9 |
| Cm9 | minor ninth | C E♭ G B♭ D | 1 ♭3 5 ♭7 9 |
| C7(♭9), C7(♯9) | altered ninths | C E G B♭ D♭ / D♯ | 1 3 5 ♭7 ♭9 / ♯9 |
| C7(♯11), Cmaj7(♯11) | raised eleventh (Lydian) | … F♯ | add ♯11 |
| C13 | dominant thirteenth | C E B♭ D A | 1 3 ♭7 9 13 (5 and 11 omitted) |
| Csus4, C7sus4 | suspended fourth | C F G (B♭) | 1 4 5 (♭7) |
| C6/9, Cadd9 | added-note chords | C E G A D / C E G D | no seventh |
Two spelling conventions to watch: a ♯11 is spelled as a raised fourth (F♯ above C), not G♭; and ♭9/♯9 are spelled as altered seconds (D♭, D♯), even though a ♯9 sounds like a minor third.
Voicing Extended Chords
With five, six, or seven notes available and only so many fingers (or players), extended chords are almost always voiced selectively:
- Omit the fifth first (unless it's altered); then the root, if a bass player has it.
- Keep the third and seventh: these guide tones define the chord's quality.
- Avoid the natural 11 over a major third: the minor ninth between 3 and 11 clashes. Use ♯11 instead, or a sus4 chord without the third.
- Shell voicings (root + 3 + 7, or root + 7 + 3) are the jazz guitarist's and pianist's left-hand basics.
- Rootless voicings (3–5–7–9 or 7–9–3–5, swapping 13 for 5 on dominants) let the bass take the root and move smoothly from chord to chord.
Guide Tones and the ii–V–I
The ii–V–I is the most important progression in jazz. Its guide tones (the thirds and sevenths) form two smooth lines: the seventh of each chord falls by half or whole step to the third of the next, while the other guide tone holds.
Tritone Substitution
Any dominant seventh chord shares its tritone with the dominant seventh a tritone away: G7 (B–F) and D♭7 (C♭–F) contain the same two guide tones. Replacing V7 with this tritone substitute (subV7, or ♭II7) keeps the essential voice leading but makes the bass slide down by half step to the tonic.
Slash Chords
A slash chord names a chord and a bass note: C/E is a C triad over E (first inversion). When the bass is not a chord tone, the symbol describes a richer sonority: F/G (F triad over G) is a G9sus or G11 without a third, a favorite soft dominant in gospel and pop. D/C is a Cmaj7(♯11) without its fifth.
Try It: Chord Symbol Builder
Chord Symbol Builder
Choose a root and a chord symbol. See its spelling and formula, and hear it in close position or as a rootless voicing over the bass.
Summary
- Ninth, eleventh, and thirteenth chords extend the stack of thirds; the thirteenth contains all seven diatonic notes.
- In common-practice music, V9 (V♭9 in minor) resolves its ninth down by step; vii°7 is a rootless V♭9. Elevenths and thirteenths act like suspensions and appoggiaturas over V.
- Lead-sheet symbols name root, quality, and extensions; ♯11 and ♭9/♯9 are spelled as altered fourths and seconds.
- Voice extended chords by omitting the fifth (then the root) and keeping the guide tones; avoid natural 11 over a major third.
- Guide tones move smoothly through ii–V–I. The tritone substitute (♭II7) shares V7's tritone and slides the bass down by half step.
- Slash chords name a bass note; non-chord-tone basses (F/G) create suspended and extended sonorities.