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This phrase most often refers to the Neapolitan 6th chord (also written as N6), although the term is derived from its main use in the Neapolitan School. This is a major triad in first inversion (or 6-3), whose root is a flatted supertonic. What this means is that the second note in the scale is lowered by a half step, and a major chord is built off of it. Then the chord is inverted, so that the root of the chord is now the highest pitch.

For example, in C major, the Neapolitan is based on the second degree/note (D) lowered a half step (Db), with the major chord built off of it. In this case, the major chord is that of a Db chord (Db, F, Ab). When inverted, the Db is now the highest pitch, so the chord is now spelled F - Ab - Db. That's the Neapolitan 6th Chord.

The reason it is called a "6th" chord is because the interval between the F and the Db is a minor sixth. One other main way to see the chord is as a N67, which is a Neapolitan 6th with a seventh. In the case of the Db major chord above, the full spelling would be Db, F, Ab, Cb, and then inverted would be F, Ab, Cb, Db.

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Music from the city of Naples.

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Yes. (More variants and substitutions of the N chord like n [Neapolitan minor chord], N-parallel etc. were also common in XIXth century music.) Although it does not occur in the Classical period, the Neapolitan major 7th chord (and its inversions) was widely used during the Romantic era. Two examples are Berlioz: Requiem/Kyrie (the 7th can still be regarded as a pedal point) and Hugo Wolf: Der verzweifelte Liebhaber (the chord can be considered as independent). In jazz, cadences like Dbmaj7-G7-C also occur fairly frequently. In this case, the Nmaj7 chord retains its subdominant function. The Neapolitan chord with a minor 7th is enharmonic to a leading-tone German sixth chord which loses its (secondary) subdominant function and, in C major, Db7(more precisely, its enharmonic counterpart)-C becomes a new dominant-tonic relationship (see Tritone substitution). Thereby, augmented sixth chords which are transposed up by a 4th and get resolved to the tonic are also called Neapolitan dominant chords (even if the augmented 6th is not a real 7th). Moreover, the presence of a _real_ Neapolitan dominant 7th chord (in which the 7th must be resolved downwards) involves flattening the tonic itself (the 7th will be Cb in C major/minor), greatly weakening the frames of tonality. Therefore, at least in classical music, such chords are mostly used for modulation (e.g. in the 3rd mvt. of Beethoven's Violin concert, where it occurs in its 3rd inversion), so, in this case, they also lose their original function. Therefore, most occurrences of Ndom7 should either be regarded as dominants (in cadences like Db7 C7 in jazz and popular music) and not subdominants, or its inversions should be "flipped" enharmonically if you do not want to get out of key. However, in popular music, there are also quite a few cadences used for modulation which can be interpreted by assuming that they include something like a Ndom7 (or even a n7 minor 7th chord). Example: C A79b D-7 Gb/Ab Db leads from C major to Db major. In this case, D-7 is the n7 in Db.


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