# Harmonic puzzle, did I solve it?



## caters

So I came across an odd harmony in Mozart's K 545 Andante that I am arranging for a string quartet. I have reduced the Alberti bass to block chords and I included the G from the right hand in the first chord.









I know that it is a dissonant chord which resolves to G minor and then to Eb major. This suggests a chord with dominant function since the tonic of the passage with the harmony in question is G minor.

From what I can tell, it is a dim7 resolving to a minor chord. Then the minor chord itself resolves into a major chord. The G and Bb are suspended across the harmonic changes.

The C# and E natural both resolve to D. Now just what dim7 is this? No leading tone so it can't be vii dim7, otherwise there would be an F#. It can't be ii dim7 either because A is not in the chord. So it seems like a secondary dominant being used as a primary dominant. So let me see what dim7 chords are in D minor.

vii dim7 of D minor: C#, E, G, Bb
ii dim7 of D minor: E, G, Bb, C#

Since C# is in the bass, it must be vii dim7 of D minor. So the harmony is this:

vii dim7/v, i, VI

So, did I solve it? Did I get the correct harmony here? And if so, why is this secondary dominant being used like a primary dominant? Is it because of the symmetry of the diminished 7th?


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## EdwardBast

To understand the progression one can't just look at those three chords in isolation. Here is what is going on:









In broad terms it's really just vii°7/V, V in G minor. The G and Bb from the 2nd beat on are suspensions (6 and 4 resolving to 5 and 3 on the second beat of the next measure), the Ger+6 chord is really just neighbor tones within the V chord.

Or, if one wishes a less reductive interpretation, one might say:

vii°7/V, i6/4, Ger+6, V (with 64 susp.)


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## millionrainbows

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## EdwardBast

millionrainbows said:


> It would be much clearer what you are asking if you'd specify what measure of the original this is.


m43, if I counted correctly, but I've quoted mm. 43-44 in #2.


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## caters

EdwardBast said:


> To understand the progression one can't just look at those three chords in isolation. Here is what is going on:
> 
> View attachment 118215
> 
> 
> In broad terms it's really just vii°7/V, V in G minor. The G and Bb from the 2nd beat on are suspensions (6 and 4 resolving to 5 and 3 on the second beat of the next measure), the Ger+6 chord is really just neighbor tones within the V chord.
> 
> Or, if one wishes a less reductive interpretation, one might say:
> 
> vii°7/V, i6/4, Ger+6, V (with 64 susp.)


So I got the diminished 7th and minor chord correct but by ignoring the C# in the right hand, I was mislead to Eb major being the harmony there. I didn't think the C# in the right hand there was so important because it was going by so fast, at the rate of 16th notes, and faster notes in general don't contribute as much to the harmony as longer notes. But evidently the fact that it is alternating with Bb and not resolving right away overrides the fast speed of the notes and makes that C# important in the harmonic analysis, whereas the C# in the next measure resolves without delay to a D and so is simply an accented non-chord tone and you can get the harmony just from the Alberti bass alone in that measure.


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## EdwardBast

caters said:


> So I got the diminished 7th and minor chord correct but by ignoring the C# in the right hand, I was mislead to Eb major being the harmony there. I didn't think the C# in the right hand there was so important because it was going by so fast, at the rate of 16th notes, and faster notes in general don't contribute as much to the harmony as longer notes. But evidently the fact that it is alternating with Bb and not resolving right away overrides the fast speed of the notes and makes that C# important in the harmonic analysis, whereas the C# in the next measure resolves without delay to a D and so is simply an accented non-chord tone and you can get the harmony just from the Alberti bass alone in that measure.


You misnamed two chords. You called the vii°7 chord the vii°7 of D minor when it is in fact the vii°7 of V in G minor, and you called the Ger+6 chord "VI." But the principal issue isn't misnaming the chords. It's that you aren't grasping the function of any of the three chords in the progression. The fact that you picked those three isolated chords in itself is a clue that you aren't hearing their functions because they don't really make sense without including what follows.

Note that when a vii°7/V looks like it's resolving to a i64 chord, it's really (usually and in this case) resolving to V but only the root (D) has yet moved into place. The G and Bb above are suspended from the diminished 7th chord.


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## millionrainbows

Edward, what determines whether you call the Ger+6 chord a "chord," or consider these to be neighbor tones within the V chord?

One seems harmonic, the other contrapuntal or melodic. Should you base it on what Mozart might have thought? Is the answer self-evident from the actual notes themselves?

The answer might reinforce my notion that "diminished" chords can be considered either way; as chords and/or frozen results of voice movement.


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## EdwardBast

millionrainbows said:


> Edward, what determines whether you call the Ger+6 chord a "chord," or consider these to be neighbor tones within the V chord?
> 
> One seems harmonic, the other contrapuntal or melodic. Should you base it on what Mozart might have thought? Is the answer self-evident from the actual notes themselves?
> 
> The answer might reinforce my notion that "diminished" chords can be considered either way; as chords and/or frozen results of voice movement.


You've framed the issue well. The answer isn't self-evident, if one believes there even is _a_ right answer. Both linear and harmonic considerations are at work. That's why I gave two interpretations. If one stresses the linear aspects, as I did in the first reading, then the Ger+6 chord and the i6/4 configuration can be understood not as independent harmonic entities but as neighbor motions and suspensions respectively within a sustained dominant. In this case one would need only two Roman numerals and lots of little numbers and abbreviations for non-harmonic tones. Alternatively, if one wishes to stress harmony, one could place a Roman numeral on every beat, as I did in the second reading, and forego some of the nit picky marking of linear phenomena. For this passage I prefer the more linear understanding, but I can imagine situations where the same motions might be better analyzed as separate harmonies - like if each "change" lasted a whole measure maybe.

Mozart had the vocabulary and concepts to hear it both ways. I have no idea how he might have described the passage. I think it's best to be able to see and hear the passage from both perspectives.

But, speaking cynically: if a Schenkerian asks you about it, go linear, if your undergraduate harmony instructor is asking, better stick more to the Roman numerals.


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