Extended Tertian Harmony: 9th, 11th, and 13th Chords

Concept: By adding additional thirds to triadic harmony, one can create 9^th, 11^th, and 13^th chords.

Note: It is common - and often necessary - to omit some notes of the chord, especially in four-part writing.

Examples:

Function: Most 9^th, 11^th, and 13^th chords are dominant chords (V⁹, V¹¹, V¹³), though in reality any triad can be extended. Other common non-dominant extended tertian chords are based on I and IV. Stacking extra thirds onto a triad does NOT change its original function! For instance, a V¹¹ chord still typically resolves to I (or i), and a ii⁹ chord still typically resolves to dominant harmony (V).

Position: Extended tertian chords are usually found in root position, as they tend to lose their identity when inverted. Secondary function: 9^th, 11^th, and 13^th chords can also occur as secondary dominants.

Analyze this progression:

Summary

Chord	Typical Members Present	Voice-Leading Guides
V⁹	R, 3, 7, 9	9^th and 7^th resolve downward to the 5th and 3rd of the tonic triad.
V¹¹	R, 3, 7, (9), 11	11^th is retained as a common tone with the tonic triad.
V¹³	R, 3, 7, (9), 13	13^th is usually in the highest voice and resolves downward to the tonic. If the tonic triad contains a chordal 9^th, the 13^th could resolve downward to the 9^th of I⁹.