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While there are chord symbols & Roman numerals used to name a Neapolitan 6th chord, I haven't come across either of these for naming an Augmented 6th chord. The only names written were Italian 6th, French 6th and German 6th. The symbol for each was It.6, Fr.6 and Ger.6. Is this the only way to represent this chord?

Also, while using the Augmented 6th chord in a chord progression, I read that this chord is generally followed by chord V, or it goes to chord Ic and follows the cadential 6-4 progression i.e. ic - V - i. Are these the only possible ways of using the Augmented 6th chord, or there are others?

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The names It.6, Fr.6 and Ger.6 are pretty common ones. I've also seen some other names like:

  • IV 6# 5b for the German
  • IV 6# or #IV 6 for the Italian
  • II 6# 4 3 for the French

These are less common, but they are more "thorough" because they say on which chord they are built on and what notes are altered.

You are correct that in most cases these chords are followed by a V or I 64 chord. To be honest, I don't remember if this is a strict rule or if there are exceptions, but generally this is the case.

Here is an example of the German followed by a I 64:

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And an example of the italian followed by a V:

enter image description here

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German...

#iv6/5

French...

ii#6/4/3

In the case of the German I put the sharp in front of the Roman numeral to show the chord root is altered. Whereas in the French the chord root is not altered, but the 6th gets the sharp because it is raised chromatically from the diatonic sixth.

Of course the point here is to make clear none of the augmented sixth chord are rooted on bVI.

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