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In the opening bar of Emil von Sauer's Etude de Concert no. 1, he starts on G flat major, then transitions to an F major 7 that resolves back to G flat major (VII7 to I).

I know this is late romantic harmony, but it sounds fully tonal and functional. Is there a functional explanation for this transition?

[VII7 to I]1

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This style is not exactly my wheelhouse but what I see and hear is that even though the second half of the bar contains notes of an F7 chord (dominant not major 7, note the Eb), the low Gb is the harmonic base. A few versions I heard make use of the sustain pedal which keeps the Gb as the lowest note throughout the bar.

This makes it a Gb diminished chord more than an F7. You have Gb, A, C, Eb on the page which in enharmonically correct terms for analysis would be Gb, Bbb, Dbb. The F natural (maj7 of Gb) is a commonly used non-chord tone on diminished chords.

That basically gives you Gb 2 beats, Gbdim 2 beats then Gb in the next bar, which is similar to the first bar two octaves higher.

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Ok I've been playing with this on the piano for a while and here's my best functional explanation. Let me know what you think.

The second Gb chord is not the same as the first, functionally. It's not really a I. The F7 would have resolved to a Bb, in this case a Bb minor. But instead it resolves deceptively to the VIb from the melodic Bb minor scale (which is the Gb chord).

So the second Gb comes from mode mixture.

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    The second measure is almost identical to the first two octaves higher, what makes it different? Commented Mar 15 at 19:33

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