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I'm working on an analysis of Variation XVIII of Rachmaninoff's Rhapsody on a Theme of Paganini.

This famous variation is in D♭-major. I'm trying to analyze that first chord in measure 660. This chord (enharmonic to F♯ø7) is followed by an A♭7(sub6) chord (V7sub6) which leads to the tonic D♭-major chord at rehearsal number 51.

How would that first chord in measure 660 be analyzed?

Would it be considered a substitute for a iv7 chord (borrowed from the parallel minor, D♭/C♯ minor), but with a lowered fifth? (G♭m7b5)

Please let me know if you have any ideas on how to best approach analyzing this chord. Thanks in advance - much appreciated!

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    I'm personally wondering why the F sharps in your second measure are immediately followed by G flats. The D flats in that measure also look strange, especially since they don't fit in the F# half-diminished 7th chord. Makes me wonder if that second measure is misprinted and whether we can trust your sheet music.... – Dekkadeci Dec 9 '20 at 12:49
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    Thanks for the comment. That image wasn't the best representation. The one I added now should be a better representation of the excerpt. – Lennon_Ashton Dec 9 '20 at 13:12
  • The D flats problem I mentioned in my first comment still exists in Bar 660. – Dekkadeci Dec 10 '20 at 11:17

It's an enharmonic nightmare plus a subtle harmonic detail. Change the a-natural to b-double-flat and the e-natural to f-flat and you have a g-flat-minor-7 chord (chord iv7) plus a stray c-natural in the right hand (don't overlook the d-flat in the bass). That c-natural is a dissonance that would resolve up to the d-flat except that this resolution is elided with the cadential c-natural to d-flat resolution in the V13-I movement (it also carries on the idea of c-as-dissonance to d-flat from the bar before). It sounds like a regular pre-dominant and it is - with a bit of grit from the c-natural. Transpose the bar to d-major if it helps.

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    +1! I just let drop this Db of the left hand in my answer. I think we can ignore it to make it easier to understand what happens. – Albrecht Hügli Dec 9 '20 at 16:57

This piece is in Db.

Look at the bass-line 657 - 661:

Ebm6 -> Fm -> Gb/Bb -> Am/Gb -> Ab6 -> Db - whereby Am/Gb can be considered as harmonic equivalent to Gbm7b5!

Lets transpose it to C: Dm6 -> Em -> G/B -> Abm/F -> G6 -> C (Abm/F => Fm7b5)

as we can see the Am-chord over Gb is enharmonic Bbb-minor/Gb (in C this is obviously Abm/F=Fm7b5!)

We would have a simple iv-V-I cadence (iv borrowed from the parallel key) if there wasn't the dim 5 that we know of a ii7 in a minor scale: ti-re-fa-la. It is hard to say from where it is borrowed. Let's stay in C to make it easier. Fm is the iv subdom. of the relative key Cm. Fm7b5 is the ii7b5 of Ebm, parallel key of Eb, which is mediant key of C.

This means the chord Gb,Bbb,Dbb,Fb is a borrowed ii7b5 substitution of iv (Gbm), borrowed from Fbm, the parallel key of Fb, which is mediant key of Db.

Another approach to understand this chord is to read the piece in C#:

Then we have in measure 660 the cadence: Am/F# -> G# -> C# resp. F#m7b5 -> G# -> C#. F#m would be the minor subdominant, but it is substituted by a ii7b5 borrowed from E-minor.

in classical analysis this is: vii56 - iii - V6 - (ii7:mediant/parallel) - V 7 13 - I

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