The Neapolitan 6th chord is my very favourite chord (closely followed by "chord iii", but I'll explain that one another time). I've loved it ever since I first heard it (long before I found what it was called). I even attended a fascinating lecture about it at an Open University summer school several years ago. (The lecture covered the various types of augmented sixth chords (French, German and Italian sixths) as well, but the Neapolitan is better than all of them!)
So, what is a Neapolitan 6th? I'll try to explain as clearly as possible, because once you know what they are, you'll spot them throughout the repertoire. They're most common in baroque music, although they aren't restricted to that period - there are several in Gerontius, for example. They occur more often when the music is in a minor key than major, but either is possible. Now, in any key, you can have a chord based on any note of the scale. (I presume that most of you know that a "normal" chord on any given note consists of the note itself plus the notes a third and a fifth higher within the scale - so that the chord of C major would be C, E and G, but the chord of C minor would be C, E flat and G, because in C minor every E is an E flat. ... If you didn't already know this bit, I realise it's a bit confusing, but at the moment my target audience is people who *do* already understand how chords are usually formed, so if this is totally new to you, I'm sorry!)
Now, in the key of E minor, the scale goes: E, F sharp, G, A, B, C, D sharp, E. That's the harmonic minor scale (as opposed to the melodic minor), and if you've ever wondered why it's called that, it's because these are the notes used in the harmony - as follows: chord 1 (the tonic chord) is the chord of E minor (E, G, B). Chord 2 is actually a diminished chord (F sharp, A, C). Chord 3 is G major (G, B, D). Chord 4 (the subdominant) is A minor (A, C, E). Chord 5 (the dominant) is B major (B, D sharp, F sharp). Et cetera. (The "dominant seventh" chord - very common, and I'm sure you've all heard of it - would be B, D sharp, F sharp and A... why 7th? Because the A is a seventh above the B.) (If you're wondering why some notes are sharp and others are natural, go back and look at the E minor scale - that's why.) (If you're wondering why there's a D in chord 3 but a D sharp everywhere else, that's a good question - a simplified answer is that if chord 3 had a D sharp in it, it would be an augmented chord, which isn't often used in traditional harmony. Or, put another way... the harmony works better if chord 3 is a major chord. Not a very satisfying answer but it's as good as you're going to get for the moment!)
Now, before I explain what the Neapolitan 6th chord is, let me explain what it ISN'T. It isn't a chord based on the 6th note of the scale - it's called "6th" for a different reason. (It's called Neapolitan because it was popular with a Neapolitan group of composers.) So what is it? Well, to make a Neapolitan 6th chord, here's what you do: find the 2nd note of the scale (so in E minor that would be F sharp). Flatten it by a semitone (so it becomes F natural). Form a major chord based on that note (in this case, F major (F, A, C)). This chord is sometimes called a Neapolitan chord. However, it is hardly ever used in that form - invariably it appears as a first inversion chord, which means that although it does consist of F, A and C, it doesn't have the F at the bottom of the bass (which is called "root position"), it has the A instead. (If the C was at the bottom it would be a second inversion.) And it's the fact that it's used as a first inversion that gives it the name "6th" - the 6th is the interval between the A and the F.
Have a look at the example above (from the end of the "Have lightnings and thunders" double chorus of the St Matthew Passion - I was quite startled to put "matthew passion" into YouTube and find that the exact one-minute clip I wanted was the top result!). This section is in E minor. Look at the fifth bar. All the notes are either F, A or C, but the basses have A. That makes it a Neapolitan 6th. (Why is this chord usually used as a first inversion? Because the harmonic progression works better that way. I could explain why, but I've already gone on longer than I intended to, and I imagine some people's brains are hurting already.) Listen to the last few bars until the sound of the Neapolitan 6th sticks in your head - it's very distinctive. (It's at 1:02 in the video clip.)
And finally, one of my favourite pop songs, and not just because it includes a Neapolitan 6th. It's REM's Everybody Hurts. This song is in a major key, but the middle section (starting at about 2:22) is in the relative minor, and the Neapolitan comes at about 2:46. (I think it's probably a root position one rather than a 6th, because of what the bass does, but the sound of the chord is almost identical.) A great moment in the history of pop (and one of the best-ever videos, too - do watch it rather than just listening).
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