In music theory, a Neapolitan chord (or simply a "Neapolitan") is a major chord built on the lowered second (supertonic) scale degree. It most commonly occurs in 1st inversion so that it is notated either as ♭II6 or N6 and normally referred to as a Neapolitan sixth chord. In C, a Neapolitan sixth chord in first inversion contains an interval of a sixth between F and D♭.
Ex: C Major
Ex: C Minor
In tonal harmony, the function of the Neapolitan chord is to prepare the dominant, substituting for the IV or ii (particularly ii6) chord. For example, it often precedes an authentic cadence, where it functions as a subdominant (IV). In such circumstances, the Neapolitan sixth is a chromatic alteration of the subdominant, and it has an immediately recognizable and poignant sound. For example, in C major, the IV (subdominant) triad in root position contains the notes - F-A-C. By lowering the A by a semitone to A♭ and raising the C by a semitone to D♭, the Neapolitan sixth chord F-A♭-D♭ is formed. In C minor, the resemblance between the subdominant (F-A♭-C) and the Neapolitan (F-A♭-D♭) is even stronger, since only one note differs by a half-step. (Note that the Neapolitan is also only a half-step away from the diminished supertonic triad in minor in first inversion, F-A♭-D, and thus lies chromatically between the two primary subdominant function chords.)
The Neapolitan sixth chord is particularly common in minor keys. As a simple alteration of the subdominant triad (iv) of the minor mode, it provides contrast as a major chord compared to the minor subdominant or the diminished supertonic triad. The most common variation on the Neapolitan chord is the Neapolitan major seventh, which adds a major seventh to the chord (this also happens to be the tonic).
Jazz players think of this as a tri-tone substitution for the V chord. For example in the Key of C the Neapolitan 6 chord is a D-flat major triad (in first inversion). A D-flat major triad (usually jazz players add the minor seventh making it a D-flat dominant chord) can serve as tritone substitution for the dominant. In this case a tri-tone substitution for the G dominant chord.