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I am composing this Adagio piece in E Minor and there’s one chord in the starting chord progression that I can’t seem to figure out the function of, that being D7. It seems on listening to be an applied dominant chord because it chromatically rises up in the bass(or it would if it was all in root position). But the note it rises to is the tonic. Here’s the entire chord progression:

E minor -> A minor -> D7 -> D# dim7 -> E minor

On listening, it seems to be V7 of III, that being G Major. But it doesn’t go to G Major at all, it just rises up to vii dim7 of E minor which then resolves to the tonic E minor. So then it can’t be an applied chord, right, as the supposed secondary tonic of G Major never appears in the progression and when G Major appears later in the piece, it is just the diminished seventh chord that shows up as a dominant function chord, no D7 in there at all. But, it can’t be a passing chord, because it doesn’t bridge 2 chords a third apart(I would need C Major or some other C or C# chord in my progression for it to be a passing chord as I understand it) and it can’t be an augmented sixth either because it doesn’t move outwards to a C# chord. The only thing that seems to fit is an applied chord, but even that doesn’t seem to fit well because of what comes after it.

That’s not to say that I haven’t seen applied chords that don’t resolve to their secondary tonic. I have, especially when the following chord is vii dim7 of the tonic, so something like this for example:

Cm -> Fm -> D7 -> B dim7 -> Cm

But notice that the applied chord in the C minor example is V7/V, not the V7/III that would be in my E minor Adagio progression if I went with the applied chord analysis. If it was just a triad, I would be bound to analyze it as VII, the subtonic. But because it’s a dominant seventh chord, that subtonic analysis makes less sense. So, how would you analyze this chord in the key of E minor, since each possibility I have described has something about it that isn’t in the actual progression. Here’s the progression again:

Em -> Am -> D7 -> D# dim7 -> Em

And my voicing of it if that helps at all:

enter image description here

So how is the D7 functioning here? Is it a V7/III that simply doesn't resolve to its secondary tonic of G major? Or would a different analysis fit better than a secondary dominant?

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I think it is still an applied dominant to G, but instead of resolving to that temporary tonic of G, it just resolves deceptively to vi of G, which is your original tonic of E minor!

This is relatively common, and something I label with some bracket notation:

    Em: i   iv   V   viio7/vi   vi
                \_________________/
                        III

Following a handful of textbooks, I consider this an extended tonicization because it lasts longer than a simple V/x to x yet also isn't a full modulation.

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Is it a V7/III that simply doesn't resolve to it's secondary tonic of G major?

Yes.

Imagine you're listening to this tune for the first time ever on your computer, and right at the end of the D7 chord, the computer crashes and you don't get to hear what would have come after it. But you did not know the playback was going to end. Does this change what happened in your mind during that D7 chord? Does the stopping of playback somehow un-do the chord? No.

It might help to think of the effect of a chord instead of its "function". The effect of a D7 chord in your example is (most probably) to put you in a state of mind where a G chord would feel like a resolution.

There are other aspects to modifying the sense of expectations, like voice leading. For example if you go Em - Am/E - D7/F# ... then the expectation of the bass moving up to G is even greater. Or what do you think? :)

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Other answers call this a deceptive cadence and I agree. I’d like to add one thing. D7 has a very similar type of resolution of the 3rd and 7th to Em as it does to G, the F# goes up to G and the C goes down to B. It only lacks the 5th movement of the chord roots which in turn makes it sound like a resolution but... deceptive. The D#o7 has a very similar resolution to Em and even has 3 of 4 notes in common with the D7, only the roots are different.

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If you analyze this passage in G major, this is known a deceptive cadence, which is a dominant chord resolving to the vi. In this case, the D7 is resolving to Em, which is the relative minor of G.

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You state that the piece is in E minor. Well, OK. But this feels very like a deceptive cadence in G major. Further complicated by the addition of the dim7 acting as the dominant of E minor.

And that's all fine. Ambiguity rules! Is that D chord the ♭VII7 of E minor or V7 of its relative major? A (barely) chromatic chord or a brief modulation? We don't need to decide, just savour the ambiguity.

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  • So why the dvs?
    – Tim
    Dec 19 '20 at 10:47
  • Indeed. Perhaps orthodoxy demands a definitive answer! Even when there isn't one. Dec 19 '20 at 15:57
  • Maybe one day, it won't be called music theory any more, but 'well, here's a few educated guesses - take yer pick or make some of yer own'.
    – Tim
    Dec 19 '20 at 16:21
  • That's not a bad description of the Scientific Method. Beginners crave definitions and rules. Then they realise it's more a matter of exploration and working hypothesises. Maybe it first hits a music student with the realisation that a tritone can resolve two ways. Dec 19 '20 at 19:36
  • Yes, it's funny, but I used tts for years before I found out the 'theory' behind it...
    – Tim
    Dec 19 '20 at 19:59
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Applied chord = secondary dominant. I had to look that up!

Secondary dominants do not have to lead to the chord they're dominant to. The D7 seems like it's heading towards G - after all, we have the classic 2-5-1-prior, so when the G doesn't figure, but D♯o comes instead, it's working as an interruped - or deceptive - cadence.

The diminished chord, chromatically changed from D7, is very close to D7♭9,(dominant of G again) or B7♭9,(dominant of Em) which leads nicely to the Em, tonic chord.

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