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I'm trying to understand this simple progression in the middle of Paganini's 4th caprice.

This seems like I-?-I-V7-I in Eb major, but I am unable to figure out what the function of the second chord is. I know it is Ebdim7 (or Adim7 or Gbdim7 or Cdim7).

My attempts:

  • There is some nice voice leading from the A-nat to the B-flat in the third chord, which suggested it is a secondary leading chord of some sort, but the third chord is Eb, which doesn't make sense: io7 - I??
  • Perhaps the second chord could be viio7/V7, but this doesn't seem to make sense if there is a I chord between the viio7/V7 and the V7.
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  • Yes, this is - like you assume - a secondary viio7, you can say it resolves to I 46. Nov 24 '20 at 8:26
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    You offered some interesting reflections on this progression in your points under "My Attempts". Hidden in your attempts lies the real music theory: an open-ended investigation of the question you posted. All too often our "answers" on these forums miss the real truth under the guise that short and common understandings equate to truth. Thank you for that.
    – Ootagu
    Nov 24 '20 at 21:02
  • @Ootagu Yes, it is nice to see that my two attempts were not too far off: my first attempt is heading toward the "common-tone diminished" idea in Aaron's answer, and my second attempt is related to the "secondary leading chord to the dominant" idea in Albercht Hügli and Dekkadeci's answers.
    – angryavian
    Nov 25 '20 at 20:56
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This is basically a better-phrased version of Albrecht Hügli's answer, but I'd treat the chord progression as this, with the diminished chord in bold:

Isus4 - I - vii°7/V - I6/4 - V7 - I

Yes, I'd treat the diminished 7th chord as a secondary dominant, especially since it resolves its root by step to I6/4, then V7. The I6/4 chord is so strongly associated with the V chord and resolves into a version of it so often that some textbooks (including one I learned from) call it V6/4 instead.

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  • It‘s an endless and fruitless discussion whether this is V64 (dominant with suspension) or the 2nd inversion of the tonic. I wrote I 46 as in German it is called a fourth-sixth chord. The dim 7 can be considered as #IVdim7 or vii dim7/V. Nov 24 '20 at 13:42
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This is a "common-tone diminished seventh chord". It's used, in this case, as an elaboration of the I chord. You can read more about it and see examples in a few SE questions:

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A,C,Eb,Gb (=vii o7) -> Bb,Eb,G (=I46) (resp. V46

The secondary VIIdim to the dominant (also interpreted as #IVdim) usually in a I46 chord - like in your example.

e.g.: Very common in Bach‘s recitatives!

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  • What is the functional purpose of a secondary dominant that doesn't resolve?
    – Aaron
    Nov 24 '20 at 8:28
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    It does resolve - to V. The ‘I64’ shouldn’t be thought of as chord I but as chord V with dissonant 4 which resolves to 3, dragging 6 to 5 in the process
    – user71850
    Nov 24 '20 at 12:27
  • This is a good example of the opinion based side of music theory. I can live with both interpretations while others make a dogmatic arguing. The theory is derived of historical evolution and development of harmony and counterpoint. Nov 24 '20 at 13:55
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    I think keeping the distinction between I64 based on ‘morphology’ and V64 as ‘function’ is worthwhile in thinking about much 19C Western Classical music (and earlier). In Paganini’s time it was unquestioned that a perfect fourth above the bass was always dissonant and needed to resolve to a consonance. In the OP’s example the E-flat in the third chord is a perfect fourth above the bass, hence dissonant, hence not part of ‘the chord’. Opinion yes, but the opinion of Paganini’s contemporaries, so relevant to theory, if only in historical context.
    – user71850
    Nov 24 '20 at 22:48

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