In music, extended chords are tertian chords (built from thirds) or triads with notes extended, or added, beyond the fifth, including all the thirds in between the fifth and the furthest extended note. Thus, seventh, ninth, eleventh and thirteenth chords are extended chords. The thirteenth is the furthest extension possible as, by that point, all seven tonal degrees are represented within the chord.
In practice however, extended chords do not typically use all the chord members; the fifth is often omitted, as are notes between the seventh and the highest note (i.e., the ninth is often omitted in an eleventh chord; the ninth and eleventh are usually omitted in a thirteenth chord).
Note that the use of compound interval equivalents to name the extensions beyond the seventh (e.g., 9th instead of 2nd) is not an indication that the chord contains compound, rather than simple, intervals (although they often do). It simply serves to indicate the proper position of the extended note in relation to the two-octave series of thirds from which all extended chords are derived, as follows:
1 - 3 - 5 - 7 - 9 ( = 2) - 11 ( = 4) - 13 ( = 6)
Chords extended beyond the seventh are rarely seen in the Baroque era, and are uncommon in the Classical era. When used in the Romantic era, they were almost always found on the dominant scale degree (as V9, V11, and V13).
When playing extended chords on instruments which are limited to four or fewer tones, it is important to select which notes to play so as to still give the sonority or effect as the intended extended chord. Always play the root, third, seventh, and the most extended note if possible. The root is the central note of the chord, the third defines the chord's quality as minor or major, the extended note is what makes the chord extended, and the seventh defines the chord as an extended chord and not an added note chord. Any notes which happen to be altered, such as a flatted ninth, would also need to be included. Thus in a thirteenth chord one would play the root, third, seventh, and thirteenth, and be able to leave out the fifth, ninth, and eleventh. (Courtesy of Wikipedia)