Extended chords stack successive thirds above the seventh, and the thirteenth uses all seven scale degrees

Adding the note a seventh above the root turns a triad into a seventh chord; continuing to stack thirds extends it further. Another third above the seventh gives a ninth chord (5 notes), another gives an eleventh (6 notes), another gives a thirteenth (7 notes) — at which point the chord contains every degree of a seven-note scale, so the thirteenth is the last possible extension. Each extension adds colour and complexity beyond the triad. In practice you don’t play every note: the essential tones are the root, the third, the seventh, and the highest extension, and the fifth (and often the root, supplied by the bass) is omitted. Chromatic alterations — lowering the fifth or ninth, raising the eleventh — add further colour. The dominant seventh (major triad plus minor seventh) is the exception that stays common in many genres because of its strong pull to resolve toward I; the fuller extended chords are staples of jazz-derived harmony, which often moves through them by smooth voice leading rather than functional resolution.

Examples

Cmaj7: C–E–G–B. C7 (dominant): C–E–G–Bb. Cmaj9: C–E–G–B–D. Dm11: D–F–A–C–E–G. C13: C–E–G–Bb–D–F–A (all 7 notes). Rootless jazz voicing of Cmaj9: play only E–B–D (third, seventh, ninth), leaving the root to the bass.

Assessment

Build Am9 and G13 listing only the essential notes (root, 7th, and the extension), and say which notes you can safely omit while preserving the colour. Explain why the thirteenth is the final extension in a seven-note scale.