So, I analyzed the harmony and structure of Grande Valse Brilliante op. 18, and most of the cadences make perfect sense to me, but there are 2 cadences that don't really, one on the tonic, which I can explain better and one on the subdominant, which is weird to me. Here are both of the cadences in question(second cadence is in Db major):
I can explain the tonic cadence better than the subdominant one. Okay, here goes. The typical definition of a half cadence is a cadence on the dominant which feels like an end, but incomplete, or as Seth Monahan says in his video on cadences "it leaves us waiting for the next one".
Tonic Half Cadence
Measure 90 of Grande Valse Brilliante has that tonic half cadence and so does measure 98. In both cases, a secondary diminished chord of V goes straight to the tonic, in this case Ab major. And in the answering subphrase, you have V7 going to that same I. And this combined with the dynamics means that the first cadence on tonic feels more like a cadence on V, a half cadence, than the IAC it would be if you went with the strict definition of half cadence.
Subdominant Half Cadence
Measure 122 has that subdominant half cadence that I am stumped on. Why do I say subdominant? Well, the key is Db major here and look at bar 121, you have these notes:
Gb, Db, Bb
That's the IV chord in Db major. Now look at bar 122, what do you see?
Gb, and Bb with a chromatically rising bass through D and Eb.
And it can't be V7, because the only notes typical of the V7 chord in there are Eb which is on the third beat, a weak beat and Gb which is in the preceding IV chord. If it were a third inversion V7, I would be expecting this instead:
Ab, C, Eb, Gb
But there is no Ab or C, so this can't be it. The easiest explanation is that you have non-chord tones in the bass and it's still a IV chord. That's the one I went with. But this shouldn't be possible. A IV chord with a dominant function? And yet, I can't say that it's a PAC on the subdominant because there is a V7/IV, but it doesn't feel like a tonicization of IV if you know what I mean, it feels too brief to be a tonicization. And I can't say that it's a plagal cadence either as it isn't moving back to tonic from the subdominant. And the phrase starts on the dominant of IV and the answering phrase on the dominant of I so again, not your typical half cadence on V. And yet, it somehow sounds like a half cadence.
So what is going on at the subdominant cadence if it isn't a tonicization of IV or a typical half cadence? Why does it feel like Chopin is doing the impossible here by making IV have a dominant function? And is the tonic cadence that I mention sounds like a half cadence really a half cadence? I mean it sure feels like one compared to the IAC in bar 94.