Dominant thirteenth chord in the context of "Sixth (chord)"

In music, extended chords are certain chords (built from thirds) or triads with notes extended, or added, beyond the seventh. Ninth, eleventh, and thirteenth chords are extended chords. The thirteenth is the farthest extension diatonically possible as, by that point, all seven tonal degrees are represented within the chord (the next extension, the fifteenth, is the same as the root of the chord). In practice however, extended chords do not typically use all the chord members; when it is not altered, 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), unless they are altered to give a special texture.

Chords extended beyond the seventh are rarely seen in the Baroque era, and are used more frequently in the Classical era. The Romantic era saw greatly increased use of extended harmony. Extended harmony prior to the 20th century usually has dominant function – as V, V, and V, or V/V, V/ii etc.

In music, a factor or chord factor is a member or component of a chord. These are named root, third, fifth, sixth, seventh, ninth (compound 2nd), eleventh (compound 4th), thirteenth (compound 6th), and so on, for their generic interval above the root.In harmony, the consonance and dissonance of a chord factor and a nonchord tone are distinguished, respectively.

Chord factors are taken into consideration in voicing and voice leading. A chord contains exactly as many factors as it contains unique pitch names (octaves don't matter), while a voicing can have any number of voices that draw from and represent some or all the factors of a chord in various octaves. Thus, a chord with three unique pitch names always has three factors, even if some of those pitches are doubled or omitted in a particular voicing. For example, the figure to the right shows a four-note voicing of a C Major triad, which has three chord factors. The "root" chord factor (pitch name "C"), is represented twice in the voicing by voices 1 and 4 in different octaves. The chord factor called the "fifth" (pitch name "G") is represented in voice 2 (shown in red).