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So I have just started reading about the Neapolitan 6th, & I'm new to this topic. I know that it is generally used in its first inversion, & is often followed by chord V. Thus it is used in the bII - V - i chord progression (with bII being in first inversion).

A website mentioned about writing this chord in a cadence. It said:

Double the third of the Neapolitan 6th chord. The lowered second scale degree always moves down to the leading tone.

Is this what is generally done while writing the Neapolitan chord? Do you need to double only the 3rd of the chord, or is it possible to double the root of the chord?

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Yes, you generally double the 3rd of the chord. It's the chord note that is easier to resolve. Let's take this example in C major, a simple I bii V I:

enter image description here

You can see that both the neapolitan chord and V use the note D (flat in the first chord, natural in the second one). This is usually considered a bad harmonic relationship (in two chords played next to each other), but with the neapolitan chord, it works. But if you were to double the root (Db), this would be trickier to resolve. Doubling the 3rd is the "safest" way to go.

The lowered second scale degree always moves down to the leading tone.

That is true. Look at the top voice of my example: C->Db->B->C. Db is indeed moving to the leading tone (B) and then to C at the end of my melody.

The progression you posted is one of the most common ones, but you can follow the chord with the I as well:

enter image description here

Or have the I in second inversion, which in turn is followed by the V

enter image description here

Also, it's quite common to find this chord after the iv (or IV in a major scale), because they have the same bass note:

enter image description here

Despite the fact that this is an out-of-scale chord, it sounds quite pleasant to the ears and is a widely accepted chord in the theory/harmony tests.

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