Reply to a 20 year old thread.
I think the best way to understand the progression is not to try to pigeon whole it into a "correct harmonic progression" but to find the progression which makes most sense to you. I think it is wrong to try to analyze this "harmonically" because it is not a typical cpp style harmonic piece and because of the way it is played. The point of harmonic analysis for performance is not to understand some innate harmonic structure but to make it easier to remember and perform. Usually these concepts do coincide because typically most music is conceptualized in typical harmonic idioms.
The point of performing a piece is to perform it, not to "understand it". Again, sometimes these coincide and many times one wants them to coincide because one has trained their mind on the "common idioms". But it would be wrong to analyze an atonal piece using ccp harmony not because it is technically wrong but because it would be counter productive. The music was not composed with such ideas so forcing it into them is going to obscure rather than reveal.
Similarly with some of Chopins work(and other composers or parts of music). In some sense one has to broaden their understanding of harmony and analysis to include more abstract perspectives not because it is "right or wrong" but because it simplifies(and maybe that makes it right in and of itself). In this vein each person will have different requirements because their perspectives and background is different.
I will demonstrate the way I am thinking about this piece "harmonically".
1. I completely ignore the bass line/left hand. It is irrelevant. First, it is extremely simple. Second, you will be spend most of the time with the right hand. Third, it typically is harmonically independent of the left hand(although it does color the chords in a meaningful way it is either not a chord tone in the right hand or a passing tone).
2. Hence the analysis proceeds only from the right hand.What is important in this etude is the execution of the arpeggios and it is that which pretty much defines this etude(and not the harmony as he could have done many different things). The etude is the arpeggio and how the arpeggios change throughout.
3. For the most part, the entire piece is just a repetition of a typically difficult 4 note arpeggio through octaves. The difficulty in the piece lies in the stretching, the speed, and the strange chords used.
Therefor, the analysis proceeds into clarify the arpeggios in terms of performing them.
For example. The first chord is clearly a Cmaj arpeggio. This likely is all one needs to understand it. One does not need to be more specific such as the shape of the arpeggio. One can make it more clear by thinking of it as C + GCE or C + Cmaj 2nd inversion. Very likely if one is attempting this piece they likely already can internalize such figures if they are common enough. This is a relatively common figure(e.g., something that might generally be played with both hands harmonically.
The next arpeggio is an F chord. One can think of this as C + ACF or C + Fmaj 1ist inv. It is as if Chopin is taking some simple basic child's chordal exercise that is suppose to be played in two hands and playing them all in the right. The descending progression is an Am. The F note in the previous arpeggio moves down to E. The 4 bar moves the E down to a D. how you think about this depends on what is easiest for you to understand(e.g., it can be seen as a melodic change or a chordal change)
Next we get a Gmaj arpeggio figured as B + Gmaj. Then descending it is a D7 or if one wants a C + Dmaj first inv.
All this is pretty basic and conforms to cpp type of stuff at this point.
Next we get basically the same arpeggio ascending as the D7 but the F and A are lowered a semitone. This, of course, turns a Dmaj into a Ddim chord and overall a D half dim. Then a G7 without the 3rd is played which turns into an augmented for the last beat. The C arp played in measure one is played again.
At this point things start to diverge.You can analyze these chords several ways depending on how you want to think about it.
Here we have C F C F. It's just a dyad/interval of a P4. One can notate this as C4. Overall it is clear that this is an Fmaj chord due to the A in the bass but we are ignoring the bass. Because I have C4 in my vocabulary use C4 (well, C4 could mean a 2nd inversion major chord if the 4 were a superscript but it wouldn't cause confusion). One could also see it as a F5 inverted or a C + F58. For me C4 is the simplest It doesn't matter if it's really is an F chord over all. I can essentially deduce that quickly because C4 + A = Fmaj. What matters for me is that it is the interval of a P4 off the C and it just repeats.
The next chord is C F# C E descending. what could we call this? Well, we can think of it as C E Gb which I notate as C-.
Then we have a C G C D. This is just a Csus2 chord. It then plays a G chord descending.
So all those chords can be seen as just a type of variation or prolongation of the Cmaj chord rather than trying to fit them harmonically in to some "logical progression". It's quite logical as just harmonic alterations of a C chord. What is important is not the "harmony" but the arpeggio. There is nothing wrong, say, with thinking of an Fmaj7 chord as an Am/F if the F only exists in the bass. You can hear it as an Am on top of an F note. The same idea applies anywhere. Ultimately you can learn to hear the notes in any chord simple you want(even if totally unrelated). It's like learning to see the old woman/young woman simultaneously rather than one or the other. The chord symbols are, in some sense, extraneous. They exist only to help is recall what we are to do as a performer. Usually it helps to try to fit things in common patterns we already know and this is why everyone will have somewhat of a different approach.
E.g., up to this point every arpeggio starts on a low C note except for the Gmaj chord. So if you wanted you could just try to remember the notes that change(just thinking in terms of the 3 upper notes and remembering you are always adding that "low C" before you play it except for that Gmaj chord).
In fact, for the most part, there is a limited number of possible "configurations" one can play in using these patterns in any meaningful way. You will constantly find the same patterns being used but just transposed(e.g., bars 4 and 5 are the same shape/configuration/sonority but starting on A or G).
So you can continue on like this and label the chords the best way you see fit. You are essentially created an ad-hoc system that works for you. You are finding what makes sense to you and using that as that will be the most reasonable for you to use(rather than trying to learn something new). It will be the quickest way to thinking about it. You might have to have several "exceptions". E.g., some chords may not make sense to you so you can try to fit them in to something that does but then make the exception. E.g.,
Take the arpeggio C F Ab G over a G bass. What does this chord look like to you? A G chord? Wheres the B? (or is it Bb?) It's "phrygian"? Is it a C chord? Csus4 with added Ab? For me I call this a G7b9sus4. This chord symbol makes sense to me. It's a little strange with the b9 but it's a phrygian dominant sus4 chord. G7sus4 chords are quite common so this is just the minor form.
But you might want to look at it as a Fmadd9 chord. It's exactly the same.
G7b9sus4 and Fmadd9/G are the same chord. Mentally they may involve different ideas but that is not because they are different but because our perceptions and background on how we learned such things are different.
For the most part the piece actually is not complicated harmonically. It uses some diminished chords, half diminished, majors, 7ths, etc. A few alterations here and there but nothing new.
Unfortunately Chopin didn't leave us any record of how he thought about it and even if he did likely it wouldn't be much use to us mortals. I think all of has experienced the effect of learning something and thinking it was very complicated only to realize that if one thought about it different it was easy.
My guess is that the optimal way to understand the changes is to understand how each arpeggio changes. Basically the differential changes. It's 4 notes, literally, that changes into 4 notes(not octave changes but for the next chord). Usually there is at least 1 common tone, sometimes two. Usually the changes are one step. You can think of it in terms of interval changes. E.g., "This interval expands outward a whole step each(e.g., C F G C -> C Eb A C)" or "We move the top note down a half step(such as from the first F to Am change).
Thinking in terms of these differential changes will spare one trying to fit chords to all the changes. A special notation could be devised where one simply tracks the changes. E.g.,
C -> F -> Am -> G
x x x x -> 0 2 0 1 -> 0 0 0 -1 ->-1 -2 -1 -1 (or 0 here depending on how we handled that change in D).
The main point I'm trying to make is that I think that one will not really benefit from a "standard harmonic analysis" that one typically does in most other music. Sure, in some ways there are a lot of changes such as the cycle of 5ths and some ii V i's. But just knowing that doesn't help one actually understand the "arpeggio changes" that makes this piece what it is. Chopin was on a different wavelength than those before him. He didn't think like Bach, Mozart, and Beethoven. I think trying to use their styles to understand him is wrong. It's like trying to understand Chinese by hearing it as if it were English. The more one studies Chopin's etudes the more one starts to understand his thinking.
-- I've added a pdf that shows the basic arps involved in the piece. If you practice then in various ways you will see how much easier it is than it looks. Of course you have to expand your mind a little about how things work but it shouldn't be too hard to comprehend what the pdf is saying. The PDF is about 95% of the RH in terms of technique and sound. Once you add the octaves it's about 99%. [excluding any errors in notation]
Topic: Analysis of Chopin's Etude Op. 10 #1 in C