Group 1

Hi Lukas , looking forward to hearing what you're working on!

Maggie this is excellent. Very thorough. I would say you're ready for the E minor sonata. Could be a good challenge!

But let's focus on this Menuet/Trio movement first. Just a few comments and suggestions that can strengthen your analysis.

• First, I appreciate how you use horizontal lines to show the prolongation of harmonies. This helps reveal the harmonic rhythm.
• Most of your roman numerals are correct – there are a few I'd change, and others that are interpretable. The one thing you don't include is inversion, and I think this is important, since inversions track bass motion (and, in a way, they're our link to the past: we express them with figured bass symbols, which would have been how musicians of the time would have understood this score).
• Can you go back through and add inversion symbols? Should be pretty easy, since you're clearly already aware of them, otherwise you wouldn't have gotten the roman numerals right. You may already know them, but the symbols are: 6 and 6/4 (stacked vertically) for 1st- and 2nd-inversion triads, respectively, and 6/5, 4/3, and 4/2 for 1st-, 2nd-, and 3rd-inversion seventh chords. So, the viiº chord in bar 2 is in 1st inversion, so you'd write viiº6.
• Pretty good work labeling suspensions and non-chord tones! You could be more specific with your labels. The way I learned to write them is similar to writing inversions - you use interval figured, but connected horizontally instead of stacked vertically, and placed over the roman numeral. So over that viiº6 chord in bar 2, you'd write 7-6 over it (and it's called a "7-6 suspension"). This makes the 6 of the inversion a bit redundant, but it's okay.
• Since you have a good grasp of harmony, I suggest starting to think about cadences, phrases, and form. Notice, for example, that that the first 8 bars feature two 4-bar phrases, the first pausing on a so-called "deceptive cadence" (where V moves to vi instead of I). Then the 8 bars end in a "half cadence" (coming to rest on V, labeled "HC"). The other main cadence to look for is the "perfect authentic cadence" (PAC), which is when V resolves to I, both in root position, with the soprano voice resolving by step to scale degree 1.
• So, your next assignment! Go back through, maybe in a different color ink, labeling cadences and making note of phrase lengths and also the repetition of material. The Menuet is in binary form, so you can label the first 8 bars "A" and the phrase after the double bar "B." But I want you to look at how Haydn handles the B section. Does material come back? Is there new material? If so, where? Make note of anything surprising, asymmetrical, that might defy expectations. These are aspects of the music that might be helpful to articulate, to reveal the distinctiveness of the music. The next step will be to start trying to make them audible: help our ears hear the form, shape, and color of this music!

Finally, just a few corrections. I wrote a lot, but they're all small things to polish up the good work you've done.

• I would actually re-write I at the beginning of measure 8. The reason has to do with metrical position and emphasis: even though there are two I chords in a row, the one on the downbeat of 8 is on a strong beat, and is coupled with its resolution on V. It's not a prolongation like in the first bar.
• In bar 12, I wouldn't call the A an accented passing tone. I think it's a chord tone, and the harmony is actually V7 (V6/5). The reason is, it is the resolution of the G-sharp in the previous bar (viiº chords can function as dominants, and have leading tones that like to resolve to scale degree 1). This would make that B a non-chord-tone, and (if I'm not mistaken) it's called an "escape tone" – approached by step, but then leapt away from.
• In bar 21 we have what's called a "cadential 6/4." Essentially, it's a I chord in second inversion that functions as a dominant (it has scale degree 5 in the bass, and the 6/4 above it resolve to root position V chord. Some theorists actually label both chords "V", and show the 6/4 resolving to 5/3, which is more in keeping with figured bass notation.
• I'm not sure what you mean in bar 24 when you write "I/IV." It's just plain old IV with a 4-3 suspension. Beat 3 could probably just be thought of as I, with another suspension, or you could just call both notes passing tones on the way to the downbeat of 25.
• Bar 25, there's an A in there, so you should call it V7 (in inversions). You have other viiºs that are actually V7s. Look for them.
• You could argue that bar 26 is just more tonic. Roman numerals sort of fail in moments like these. Haydn is just using parallel motion to continue the line, but if you exclude the passing tones on beat 2, you have all the notes of a D major triad.
• In bar 27, it's not right to say "IV/V" (there are only secondary dominants: Vs and viiºs, no secondary tonics or pre-dominants). Just call it I, which can at the same time be labeled as IV as the first chord of your modulation. We'd consider this a "pivot" chord, since it belongs both to the key we came from and the one we're moving to.
• Your analysis of bar 28 shows the perils of roman numeral analysis! You could argue that the whole bar is V6/5, with beat 2 as passing tones and the last F-sharp an anticipation tone that resolves in the next bar. It's definitely not right to assign a unique harmony to beat 3. Play it and you'll notice that it doesn't sound like a ii chord, but just an extension of the dominant sonority traced through the measure.
• I'd say bar 31 still begins in A. Our ears don't know we're in D yet, certainly. You could say that it's a pivot chord, and label it both I in A and V in D. Then beat 3 consummates the modulation.
• Bar 32 is a classic example of "voice exchange." And you're right to call it all I.
• The neighbor tones in cars 37, 39, and 40 could be considered chord tones.
• Bar 41: good! You call the cadential 6/4 all "V," rather than I6/4 - V (which would also be accurate).
• Bar 42 is has a deceptive feel to it, since scale degree 5 steps up to 6. Not the easiest bar for roman numerals to capture, but technically you could call it vi7, viiº and I.

Maggie Very very very good. Very detailed, your formal analysis is sound, and thank you for the colors. One tiny thing: you don't need to write I6/V in bar 38. You can just write V6. But I knew what you mean, and it's technically not wrong, but just letting you know the convention.

Maggie said:
1. Should we expect a different key in the Trio section?

 No, not necessarily. But you'll see trios in the dominant.

Maggie said:
2. In b.26 and b.32, which labelling is more preferred? Simply I for the whole bar or a more particular labelling I 6/4 on the first beat and I on the third beat?

 I for the whole bar is fine. But if you want, you could call the first on I6/4 and the second one I6. But those inversions aren't so important in this case - they're not functioning in any special way. What matters is that I is outlined.

Maggie said:
3. Is it necessary to show the pivot chord each time when there’s a modulation or just label the chord in the new key?

 If there's a clear pivot chord, it's worth labeling it. There's no "right answers" to this kind of thing. Only more or less useful ways to express what you're hearing. Showing a pivot chord is a way of showing a moment of ambiguity in the music, where one key area overlaps with another one that it's modulating to.

Maggie said:
4. The last F-sharp in b.28 is an anticipation tone? I’m a bit confused.

 Yeah that's a little misleading. I take that back. Just call it a non chord tone. Eric or Nicole might have a better name for it. You could also, I guess, think of it as an extension of the E dominant harmony - a 9th above the root.

Maggie said:
5. For the cadential 6/4 in b.21, 29, 41, is it more preferable to label as V 6/4 - 5/3 than I 6/4 - V?

 Eric Wen will talk about this. The most accurate way to describe the function of what's going on is V 6/4-5/3. But this is not often taught in schools. I didn't learn it that way, and it wasn't until grad school that I met theorists who argued that it is better.

Maggie said:
A section — two 4-bar phrases, the first ends with an imperfect authentic cadence, the second ends with a perfect authentic cadence.

 I don't hear that as an IAC. Not every V-I is a cadence.

Nicole Great points! Early Haydn is pretty strange - in a good way. You think it's simple and formulaic and then you realize has was always up to something. I need to spend more time with it.

Christo Your analysis is quite good! Nice job. A few things. The first it pretty fundamental: you have lowercase and uppercase roman numerals switched around. The minor chord scale is labeled like this:

i   iiº   III   iv  V (when there's a raised 7th scale degree, in this case G-sharp )  VI   VII

Another thing: it's better to place roman numerals under the staff you're analyzing, since harmony grows from the bottom up.

Otherwise, all your numerals were correct! I wonder if the bars with E-D#-E-D#, etc, actually need a roman numeral, but I like your idea that it's all just i.

Next, you might go back through and ask yourself: where does Beethoven use "non chord tones" – notes that don't belong to the chords that get labels. For example, what to make of the C in bar 7, since that note isn't part of an E major triad? Maybe go through and circle the ones you find. Play them slowly with the surrounding harmony. Can you hear their dissonance. These are very expressive moments, especially because they are leapt up to. You'll see that Beethoven repeats this same kind of leap, but in different places over different harmonies. It's part of what makes bars 10-13 so beautiful.

I have a challenge for you. Can you play the harmonic progression you've labeled, but with block chords that stay close together? Don't spread out all over the keyboard like Beethoven asks. Just see if you can play the harmonies by themselves, and try to make it sound musical. Then, if you're feeling bold, try playing it in a different key!

Have you continued learning the rest of the piece? Are there other pieces you'd like to analyze? There's more we could do with this first page, but I'd like to know what you want to do.

Christo I like your revisions! I think it's fine where you labeled notes "passing tones." Those are tricky, because they're approached by a leap, but I think they having a passing function.

I don't quite agree with these: 

Those just look like passing tones to me, not extensions (add 9 / add 4). And the F isn't a sus, technically. It wasn't suspended from any harmony before that contained that note. Rather, I also think it's passing: imagine that lower G were a higher G... instead of leaping up, you'd step right down and pass through the F.

Same here. These are chromatic neighbor tones, not raised-7ths above E: 

Do you see why? They're not functioning harmonically. They're just decorating the E.

IMPORTANT! This is the beginning of a modulation to a new key.

What key do you think we're moving to? Hint: what key has C dominant 7th as its dominant chord (the chord built on the 5th scale degree)?

The other big hint is harmony in bar 25. This is the new tonic:

So, instead of VI, this is I. Label what key you're in now, and re-analyze 25-36 with that new tonic!

Christo Nice effort! Let me help you with the second page:

• First, on the 2nd repeat before page 2, you can start analyzing in F. We get the dominant of F major there (C-dom7). Write "F:" under those final thre chords and call them: V7 - I - V7, and that will bring you to the start of the second section on I in F on page 2.
• Bar 26: The non-chord-tones are fooling you hear. Focus on the chord outlines in the left hand, which in root position would be Bb-D-F. That's a B-flat major chord. What roman numeral is that in F?
• Bar 27: now, you need to see that Beethoven is using what's called a "pedal tone" here. The tonic note, F, is present in the bass throughout this line. I would write "tonic pedal" and analyze the chords you see above it. Sometimes F is in the chord, like in 25-26. But in 27, It's not. Ignoring the scale (which must contain passing tones), what harmony is an E-G-Bb chord? And what would its roman numeral be in F?
• You wrote ii for those bars, but a ii chord in F is a G minor triad (G-Bb-D), and I don't see those three notes together here.
• Bar 30: A new modulation begins here. Play or listen to the music from here. Where is the next strong-sounding cadence? (Last one we had was in bar 25 when we cadenced in F) Hint: the music speeds up when you land in the new key. Identify that key, and then re-analyze from bar 30 using the roman numerals from that chord scale.
• In general, you're missing seventh chords and labeling them as incorrect triads. Take your chord scale in a minor, or in F major, and add a fourth note to every triad, another skip above the top note. Those are your diatonic 7th chords (7th chords made using notes in a given key). The most important one is V7 (which requires raising the 7th scale degree in minor), and that's the one that you find here, in both A minor and C major.
• Check out my last two lessons in my Music Theory Basics course, where I go in depth on triads, 7th chords, and how they function in different keys.
• Bar 36: Correct! We're modulating back to A minor! And Beethoven uses and E major chord to get there. What roman numeral is E major in A minor? (Hint: use the harmonic minor scale to identify it - raising the 7th scale degree, G, to G-sharp).
• Bar 61: I like how you analyze this! Showing that chords are changing over an A pedal. You could just write "tonic pedal" and a horizontal bar.
• Bar 62: First, use lowercase for diminished triads, like you do for minor triads. Second, it's not actually viiº/i in a minor. It's a "secondary" chord taken from the chord scale of D minor, the iv chord, which you correctly label in bar 63. Look at the D minor chord scale, using the raised seventh, and you'll find that C#-E-G-Bb is viiº7. So, the proper way to analyze this bar is viiº7/iv.
• Bar 64: Yes, it's diminished. What is G#-B-D-F in a minor? (using the harmonic minor scale)
• Bar 66-67: I like that you take note of the bass line walking up chromatically! Now, how do we account for the D#? Again, it's a "secondary" chord that pretends momentarily like some harmony besides A minor is our tonic. In this case, it pretends that E (V) is our tonic, and borrows viiº7 from the E chord scale, making this viiº7/V.
• Bar 68: This is a "cadential 6/4" in a minor. It uses an inverted tonic chord, but it functions as (and sounds like) a decorated V chord.
• Bar 73: This is a great surprise. He lifts us to bII (flat major II), which is nicknamed the "Neapolitan." Usually neapolitans are in first inversion, but this one is unusual. Really, he's just walking up chromatically through the neapolitan on the way to viiº7 (in first inversion, so 6/5 are the figures) moving back to the tonic (i6). Then, finally, V-i, a prolongation of i with the chromatic scale over top, and a return to opening material.

This is some advanced stuff! If any of it made sense, that's great. See what you can understand, and let me know what questions you have.