Group 1

ALICE Good first effort! Great choice, because it's a simple piece, but also contains very clear examples of "tonicization" and "modulation." I can write this out more elaborately later if need be, but let me just comment on a few things first so you can try to make some modifications yourself.

First, about your way of labeling the harmonies: I know what you mean by "C major V7." And, actually, I see Angela below has already hinted at this: the harmony is an example of so-called "tonicization" (I mentioned above). That's the fancy name for when composers temporarily reinforce some chord other than the tonic (I chord) as if it were the tonic.
 

In this case, "C major V7" should actually be understood as V7 / IV (we say "five-seven of four"). The F major harmony in the second bar is the IV chord in C major. What is the dominant of F major (the "V7 of IV")? Well, it's the seventh chord built on scale degree 5 in F, which is C. And that chord contains a B-flat.

We call this C-dominant-7th chord a "secondary dominant," since we're supposed to be in C major, whose primary dominant is G.

This brings up an interesting question. Where exactly does the secondary dominant begin? You label make it seem like all of the first measure has a single harmonic function.

But actually, the B-flat comes on beat 4. Up until that point, it's all pure C major. The way I think you would hear the first 3 beats is actually as I chord in C, since the music could easily just stay put, or maybe move to the primary dominant of G.

So, I would label roman numeral I underneath the first beat of the first measure (we usually write roman numerals underneath the staff, since the bass is important in determining the harmony, and this is very important in measure 3 - see below). Then, under beat four, write "V7 / IV."

Then, you're in a narrow sense correct in measure 3 to label it "V7" (that's the primary dominant... no more B-flats, but - crucially - back to the B-natural, which is the leading tone to C). If you want to be super precise, it starts as a V chord and only becomes a V7 in the final beat when we hear the F.

BUT!!!!!! But look at your bass note. We have a C octave held all the way since the beginning, and it's still ringing. So, we've contaminated our G dominant 7th chord with a C, which is dissonant in relation to that harmony (it's the main note we're supposed to resolve the V7 to, after all, so it's clashing especially with the B-natural).

This is called a "pedal point," because on organs it's a great effect to hold a bass note with the foot pedal while the harmonies change above it. Bach was a champion of pedal point in all his music, not just organ music. In this case, it's a "tonic pedal," since we have scale degree 1 in the bass. But maybe even more common are "dominant pedals," where scale degree 5 is in the bass. Lots of tension can be created that way. I recommend you check out the C major prelude from Book 2 of the Well-Tempered Clavier. It starts with a long tonic pedal point not unlike this one!

So, how to label? I would at least write "C pedal point" (or just "C pedal") below the first bar with a line extending to the right through measure 3. Note that the C is a member of the harmonies in the first two measures, so we didn't have any dissonance there. So, the other way to do it is just write V7 over C with a horizontal line dividing them, like a fraction.

Alright, so then in measure 4 we're back to I. So, our first four bars see the following progression, deviating momentarily from our tonic before turning right back around and giving us a strong cadence (V7-I) in C major. So the first four bars can be labeled as follows:

C: [I     V7/IV] [IV        ] [V      V7] [I          ]
       C pedal point–––––––––

In measure 5 there begins a modulation. This is different from a tonicization in its duration and emphasis. Here, we're about to move to a new key and stay there for a bit.

I'd like you to try to make sense of this modulation. To what key has Bach modulated? What chords does he use to get us there, and - once we're in this new key - how do you think we should label the harmonies? (Hint: we are in a new key, so you'll need to consider a new set of roman numerals corresponding to that key.)

Try analyzing the next couple lines of music, keeping all this in mind, and show me. And, just to look ahead, you might notice that the piece ends back in C (as one should expect from a piece of 18th century tonal music!) So, the next question will be, how does Bach get back? But, let's focus on the modulation first. 

 ALICE It looks much better! A couple things on the analysis and then I'll address your question about m9

• Bar 5 is probably best analyzed as the beginning of the modulation to G. The argument is: bar 5 contains a D dominant 7th chord, which is V7 in G. So, we're either "tonicizing" G, the way we did to F in bar 1, or we're actually modulating – which is basically a bigger commitment to establishing our ear in a new tonic. Since we stay a while in G (with more D dominant 7th chords resolving to G), then calling it a modulation is pretty safe.
• That means you actually have to analyze in G beginning in bar 5. So, write G: and start applying roman numerals in G. Instead of V7/V, you can just write V7.
• To be super picky, the modulation really begins a beat before bar 5, on the fourth beat of bar 4. Do you see that C major chord with an E in the bass? Treat that as a "pivot chord," a chord that belongs both to the key you're coming from, and the one you're moving towards. C major is I in C and IV in G. So, underneath roman numeral I, you can indicate the new key and the corresponding label, G: IV. Angela you should pay attention to this too. I want you both to hear that fourth beat of bar 4 as (literally) the "pivotal" moment in the modulation.
• I should say ALICE (and Angela ), it's not wrong to analyze the whole thing in C, and consider the D dominant 7 chords as secondary dominants (V7/V). It's such a short piece, and Bach never really firmly cadences in G. So, theorists might be split on this. I'll have to see what Eric and Nicole think. 
• This brings up an interesting point: there's never one objectively correct analysis. Only tendencies that lead our ear to hear harmonies in one context or another. There might be ways to perform this so it sounds like G is your new key, and a different way of performing it that sounds like you never leave C, and just spend a while riding the dominant. For example, your tempo my determine how that is heard.
• I don't want to confuse you by saying that, but - I hope - liberate you a bit from the idea that there's some fixed truth you're trying to discover in these notes. Yes, there are parameters - you can't just call a harmony anything you want. But when it comes to talking about how harmonies function, things get a little stickier.

 ALICE As for the F-natural in bar 9. Let's assume we're in G. Your question is, if we're still in G in bar 9 and don't move back to C until 12, then what do you call that G dominant 7th chord? You could ask the same thing about the B-flat in measure 1. In fact, you'll analyze it exactly the same way, as a secondary dominant, V7/IV. This time, it's in G, so your IV chord is C! This is the cause of the confusion. So, Bach winks at measure 1 from his new tonic, and anticipates the true move back to C with the dominant 7th chord in bar 12.

ALICE Regarding the ornaments,the video Angela posted is good: they should be quick mordents (three notes: G-F#-G) played on the beat in a single impulse. Move forward a little into the key and rotate right-left-right when you play them, while keeping firm finger times, and they should sound nice and crisp.

But more importantly than that, I want you to start practicing this Prelude with your analysis in the front of your mind. Consider the tension between dissonant dominant chords and consonant tonic chords. Consider the difference between a temporary tonicization and a longer term modulation. Choose what chords you might emphasize, what arrival points you're aiming for, and how you might want to organize your dynamics in relation to the harmonies.

The real fun will come when we listen to each other play, and discover how the analysis influences our performance.

ALICE Yes, you should try analyzing the Burgmuller. And of course I don't expect you to understand everything I'm discussing in other threads, as some of it is getting pretty advanced. But I think it could be valuable to see what you do understand (you might be surprised), and then try to make sense of things that are a bit confusing. And it's okay if you're not sure.

I will invite participants to post their performances next week in these threads. There won't be a virtual recital, but I do want people to share their interpretation if they're comfortable, and maybe tell us a thing or two that they're trying to do with it. Then, there can be a bit of a celebration of however far you've gotten in these two weeks, and also some final feedback about your videos to keep you practicing and refining your analytic understanding and musical interpretations after the Intensive.

 Angela  Great! As I mentioned above, it's a useful piece to analyze. Let me know which Chopin Prelude you're talking about.

First off, just to correct your chord scale in the top left, I want to make sure you know that the triad built on B in C major is the viiº, not viº (you just left off one of the little i's).

For the first four bars, I suggest you read what I wrote to ALICE above. (And Alice, maybe don't keep reading this, since I'll be sort of answering some of the questions I asked you and I'd like you to try to figure them out yourself!)

Your first four bars are solid (as I told Alice, it's more conventional to put roman numerals underneath the staff; yes, the treble is where all the action is happening, but the harmonies are always determined by the bass, so it's good to "live" down there when you're analyzing. This is important especially in measure 3, as I told Alice. There's a C down there that we call a "pedal point," which has been ringing since the first bar. Now, the V7 chord above it still functions as a dominant resolving back to the tonic in measure 4. The C doesn't interfere with that, especially since it's so far away in register. But it's still important to account for it.

To answer your question above measure 5, yes - Bach modulates to G! The big give away is the F-sharp, but you also have to look ahead to make sure this isn't just a temporary tonicization, in which case we'd call this "V7 of V." In fact, we enter G major, and we need to use G major's chord scale to identify roman numerals. Bach modulates rather abruptly, although notice how he steps up to that F-sharp from E in the fourth beat of measure 4 (maybe emphasize that E to F# in your left hand when you play it).

So, under measures 5 and 6, you should write a "G:" before your new roman numerals so we know they apply to that new key, and then label V7 and I.

The remainder of your analysis is quite good. Rather than correct the inaccuracies and oversights, I'll give you these clues so you can try to go find them yourself:

• Bar 6 has another harmony besides G major
• Bar 7 contains a single note that doesn't belong to the ii chord (which you accurately labeled)
• Bar 8 has a C in it on beat 4. So how should you label it?
• Bars 9-12 has repeating Gs all the way through. How should you label this? (Hint, see measures 1-3)
• Bar 9 is technically not "I" anymore on beat 4. There's an F-natural, but that's not part of G major. How would you analyze this harmony, considering that we appear to remain in G through measure 12.
• What you write above Bar 12 is correct: you're moving back to C major with that G dominant 7th chord. So, you land on I in G, then add the F-natural and it functions as V7 moving back to I in Bar 13.
• But then he throws us another B-flat in Bar 13!! Bach is elegantly calling back his move in Bars 1-2. So how should you label it?
• What to make of Bar 14? What a wonderful moment, unlike any other in the piece, with the introduction of a 16th note scale. This helps to signal the final cadence is ahead, but so do the harmonies implied by the scale. There's actually two of them, one on the scale down and one on the scale up. Hint: look at what notes the descending and ascending scales begin on.
• Bar 15 changes harmonies on every beat. Try to get all of them.

Okay, you have your work cut out for you! Take your time and try to nail the rest of the analysis. I'm already getting ideas for how all of these events in the music could inform your interpretation. But see for yourself, and maybe by the end of this week you could play it?

Angela yes, chord symbols appear above the staff sometimes, for example in lead sheet notation. And sometimes you see figured bass symbols inside the staff, between bass and treble! But for this kind of analysis, it’s good to stay low.

Looking forward to seeing your follow up! And both Chopins would be fun to analyze.

Angela Most of what I said to ALICE is relevant to you. Look for that V7/IV in bar 9. Also, you can write Pedal point under bar 9 and draw a line all the way to bar 12.

I wonder Angela if you could actually help ALICE analyze the final few bars, once you return to C. Yours is correct, so see if you can explain your reasoning to ALICE .

Angela Good analysis and thanks for helping ALICE . One thing to note: the 3rd beat of bar 15 has a G and C held over from beat 2, and you can fill in E with your ear. It's a C major sonority, but you're right to call it V. This is an example of a "cadential 6/4." Eric Wen will discuss it more in the release this Friday. You should just write V with 6/4 above it, resolving to 5/3.