The term sixth chord refers to two different kinds of chord, the first in classical music and the second in modern popular music.[1][2]
The original meaning of the term is a chord in first inversion, in other words with its third in the bass and its root a sixth above it. This is how the term is still used in classical music today, and in this sense it is called also a chord of the sixth.[3]
In modern popular music, a sixth chord is any triad with an added sixth above the root as a chord factor.[4] This was traditionally (and in classical music is still today) called an added sixth chord or triad with added sixth[5] since Jean-Philippe Rameau (sixte ajoutée) in the 18th century. It is not common to designate chord inversions in popular music, so there is no need for a term designating the first inversion of a chord, and so the term sixth chord in popular music is a short way of saying added sixth chord. There are three main types of added sixth chords: major sixth, minor sixth and minor flat sixth.