Extensions and Altered Tensions

When Unit 3 built chords, the stacking of thirds stopped at the seventh. There was no particular reason for it. Nothing prevents the stack from continuing.

Stacking thirds above C gives C – E – G – B♭ – D – F – A, all seven notes. The three above the seventh are extensions, also called tensions.

Why 9th, 11th, and 13th

D is also a second above the root C. So why call it a 9th?

Because the name records the order of the stack rather than the position folded into an octave.

The same D plays a different role depending on whether it is placed as a 2nd or a 9th.

• as a 2nd (in sus2, or low in an add9 voicing) — adjacent to the root, and it grinds against it
• as a 9th — above the seventh, where it is heard as the natural continuation of the stack

So C(add9) and C9 are different chords. The first is C E G D with no seventh; the second is C E G B♭ D.

Symbol	Notes	Seventh
Cadd9	C E G D	none
C9	C E G Bb D	yes (minor 7th)
Cmaj9	C E G B D	yes (major 7th)
Cm9	C Eb G Bb D	yes (minor 7th)

Thickening from triad to extension

▶Triad C▶C7▶C9▶C13

Check: Notes are added one at a time above the same C chord. The triad has a clear outline, the 7th makes it want to move on, the 9th adds color, and the 13th adds weight. Only the upper notes change; the bottom three are identical throughout. Decide for yourself where it stops being the same chord.

C E G

The third decides which extensions work

Extensions cannot all be added freely. The constraint follows from one principle.

Do not place a note a half step above whatever establishes the chord’s quality.

On a C chord that note is the third, E. A half step above it is F, the 11th. So stacking a plain 11th above a major triad or a dominant seventh blurs the chord’s outline. Notes like this are called avoid notes.

There are two escapes.

1. omit the third — this is what C11 (C G B♭ D F) does; the major/minor distinction disappears and the chord floats
2. raise the 11th — C7(♯11) gives F♯, opening the distance from E to a whole step

Minor chords change the situation. The third of Cm is E♭, a whole step from the 11th F, so m11 chords present no problem. The same 11th being available or not depending on chord quality comes from exactly this.

Check

Why is the 11th (F) avoided over Cmaj7?

F clashes with the seventh B by a half stepF sits a half step above the third EF is dissonant against the root Cmaj7 chords cannot take an 11th

Check answer

Altered tensions — the privilege of the dominant seventh

Above a dominant seventh, extensions can be shifted by a half step. Those are altered tensions.

Name	In C7	Derived from
♭9	Db	9th lowered a half step
♯9	D#	9th raised a half step
♯11	F#	11th raised a half step
♭13	Ab	13th lowered a half step

Why is this permitted only on a dominant seventh? Because a dominant seventh already demands resolution. The tritone between third and seventh is already saying it wants to move on. Adding altered notes does not change the destination; it only increases the quantity of tension.

Doing the same to a tonic chord, which is meant to be stable, destroys the function itself. Alteration is an operation that makes an unstable chord more unstable, so it means something only above a chord that was unstable to begin with.

Raising dominant tension in stages

▶G7 → C▶G7(b9) → C▶G7(#9) → C▶G7(#9,b13) → C

Check: Every one of these resolves to the same C tonic chord. The first is a plain dominant seventh, the second adds ♭9, the third ♯9, and the fourth both ♯9 and ♭13. The more tension, the greater the drop on arriving at the tonic. Confirm that adding tension does not change the destination — all four land in the same place.

plain dominant seventh

Spelling shows the structure

The enharmonic material from Unit 0 applies directly to notating extensions.

The ♯9 in C7(♯9) is spelled D♯. On the keyboard that is E♭, but writing E♭ duplicates the letter of the third, E, and reads as “a minor triad with a lowered third.” The 9th sits a ninth above the root, so its letter has to be D.

The guitar voicing commonly used for C7(♯9) sounds E (the third) and D♯ (the ♯9) simultaneously. That is why it sounds as though a major third and a minor third are coexisting, and that coexistence of bright and dark is the characteristic texture of a great deal of blues and funk.

Check

In principle C13 consists of C E G Bb D F A. Why is the 11th, F, omitted in practice?

F duplicates the role of the fifthThere are too many notes to playF sits a half step above the third E and clouds the chord qualityF is dissonant against the 13th, A

Check answer

▶ Check extension chords in the chord finder Enter C9, Cmaj9, Cm9, and Cadd9 in turn and compare. The name changes purely with the presence and quality of the seventh Chord Finder →

Extensions add notes within the framework of stacked thirds. The next lesson removes the framework itself, abandoning harmony driven by tension and resolution in favor of harmony that preserves the color of a single mode.