I'm trying to do a roman numeral analysis of this piece, but i could not figure out the first two bars. Especially the third beat of the second bar.
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Ok this one is a little Tricky because you have Pedal point on the tonic (Ab) in the start. Which means other chords (that does not consist the Tonic) may appear.
In the example I'll write 3:2 to indicate measure 3, beat 2.
Here's what I think should be there:
you are on Ab-Major so the first one is obviously "I" (in the pickup measure)
1:1 It's obviously "I" too.
1:2 it's "V7" (Eb7) BUT the Prima (Eb) is missing and instead you have still the Pedal point Ab. perups that's what made is so difficult to understand.
2:1 "I" (Obviously)
2:2 second beat of second measure is "V", I think. It's the same idea only now you're missing two notes which are replaced by the pedal point. (I really don't like the compositional decision here, I think it would work much better without the Pedal point).
Measure 3-4, it's IV (Db) but you have a "delayed G note, which is not part of the harmony but a part of the melody. Trying playing that and it will be obvious.
And I believe you can work up with that. Good luck!
I think the G, Bb, and Db in bar 2 are being used as passing notes for two reasons: