Can someone explain the resolutions in Rachmaninoff Prelude in C# Minor?

Question

I started to learn the Rachmaninoff Prelude in C# Minor (Op. 3 No. 2). Until recently I have had not much experience with music theory, except for the very basic things. In order to remember the piece better, I would like to understand some parts better from a theoretical point of view.

Take for example the last two triplets in bar 17. The last one is a c# minor, so the triplet before occurs to me to be a dominant seventh, that is g#, to resolve in the classic way of V-I.

Bar 21 starts with A and ends with A. The final resolution to the A seems to be a d diminished seventh chord. Why has this to be a d? What is the reason or explanation behind this?

Answer 1

The chord on the third beat of m. 21 is G#dim7 (over a pedal A). Rachmaninoff happens to have left out the B, because the note isn't necessary to his harmonic or melodic purposes and doesn't fit the voice leading. G#dim, of course, is the vii chord in A, and serves a standard dominant function.

The clue that it is not Ddim is the spelling. Ddim would be spelled with Ab rather than G#.

Answer 2

Bar 21 starts with A and ends with A. The final resolution to the A seems to be a d diminished seventh chord. Why has this to be a d? What is the reason or explanation behind this?

This passage (measure) is cadencing (I-ii-viidim7-I) in A - the sub-mediant key of c#-minor. Mind the pedal note.