Generally speaking, a sixth chord is any chord which contains the interval of a sixth.

The simplest example is the first inversion of a triad, which consists of a third and a sixth above the root; when the term sixth chord is used without qualification, it usually refers to such a chord. In early music this was considered an autonomous harmonic entity with their root named by their bass, while after it is considered simply inversions of chords with the bass being the third (not the root) and the root being the sixth (not the bass).

There are also a number of non-standard sixth chords. The added sixth chord, as the name suggests, is a triad with an added sixth. It is generally built on the sub-dominant (fourth scale degree), although they can be built on any note. An added sixth chord built on C consists of the notes C, E, G, and the added sixth A. These are the same notes as those of an A minor seventh chord - whether such a chord should be regarded as an added sixth chord or a seventh depends on its context and harmonic function. To explain the analyses as added sixth chords, against common practice period theory, Cope (1997) provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (added sixth chords by popular terminology), or a first inversion seventh chord (possibly the dominant of the mediant V/iii). According to the interval strengths of the added sixth chord the root of the strongest interval of the chord in first inversion (CEGA), the perfect fifth (C-G), is the bottom (C), the tonic.

The Neapolitan sixth is the first inversion of a major triad built on the flattened supertonic (second degree of the scale) - a Neapolitan sixth in C major, therefore, consists of the notes D flat, F and A flat.

There are a number of augmented sixth chords. Each of them have a major third and augmented sixth above the bass. When these are the only three notes present, the chord is an Italian sixth; when an augmented fourth is added above the bass, the chord is a French sixth; while adding a perfect fifth above the bass of an Italian sixth makes it a German sixth (the etymology of all these names is unclear). All usually have the flattened sub-mediant (sixth degree of the scale, A flat in C major, for example) as the bass note -in this case, they tend to resolve to the dominant.

Source

• Cope, David (1997). Techniques of the Contemporary Composer, p.40-41. New York, New York: Schirmer Books. ISBN 0028647378.