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I am studying modal shifting, borrowed chords and secondary dominants, and I am a little confused of their function, if they do not resolve their own tonic. Would their function then just be a borrowed chord? For example I have the following progression. I V7/vi IV IV I V7/vi V IV I V7/vi VI VI I V VI VI

Since the V7/vi, is not followed by the vi, what is its function. Is it still a secondary dominant? Is it classified as a modal shift, or a borrowed chord? This chorus section is in D. The verse is in Bm. Which I realize is the vi chord of D, which might change the whole analysis, itself. I’m a little lost. Any help would be much appreciated. Thanks!

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Secondary dominants often do resolve to their own tonic, but they can also resolve deceptively, an action sometimes hidden with traditional Roman-numeral analysis. This is what happens in your first instance.

We're in D major, as you said. The V7/vi is F♯7, which "should" resolve to Bm. But this chord actually resolves to IV, which is G.

But let's think more globally: in what contexts can an F♯7 resolve to G? Since that F♯7 was briefly in the context of B minor, let's imagine that G chord in the context of B minor, as well.

When we do so, we see that this motion to G is really a deceptive resolution of that F♯7 chord. In other words, the F♯7 to G is really V7–VI within the context of B minor. We can call this an extended tonicization, and we label it by bracketing both chords as "of vi," showing the V7–VI resolution above it.

I discuss a similar concept here.

This does not address the V7/vi to V, nor does it address the V7/vi to VI (it's unclear if that latter chord is B major or B♭ major).

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It is quite usual that V7/V resolves as V7->(ii)V7:

e.g. In G the secondary dominant is A7 of D: but between A7 and D we find am7-D7 (kind of a double suspension of the 4-3 and 9-8). But often the new root of the Dominant (D) is already there).

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Actually the secondary dominant can resolve back towards the first dominant, let me explain what I mean.

Let's use C major in our example.

If you have C: V/V, you basically have the dominant chord of the dominant note of C Major, which means in essence G: V. This gives you a D major chord with a f# that has to resolve to a G, now this G major chord can be a couple of things. It can be C:V or maybe even B:V I.

This would then be what is called a pivot chord, one which fits in two keys, something that is used to make modulations smooth.

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Does the tritone in the 'secondary dominant' resolve properly? Take your example of III7-IV. In C major that's E7 to F. Well, the tritone in E7, D and G♯, would be expected to resolve to C and A in the A minor chord. But those notes are also in the F major chord. So yes, I think we can usefully analyse this as a (deceptive) dominant function.

'Borrowed chord' isn't a function. It's just an excuse for something you can't fit into a nice neat diatonic or 'cycle of 5ths' pattern.

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