Motivic Use in Beethoven’s Piano Sonata 20, Op. 49 No. 2
This article is an academic paper I wrote nearly a decade ago. I am still fascinated by the complete control that Beethoven has over his motivic materials, and the way that these motives affect the harmony, which is why I am adding it here. If you are taking advanced piano lessons, I hope this analysis will help you make better choices about interpretation. You may also read Taro’s post on Foreign Bodies for his thoughts on how strange and interesting moments arise in music when motivic function, and harmonic progression come into conflict. Before reading, you should download the pdf version of the Score and the Motive Guide and listen to the music. I’ve also embedded the pdf in the bottom of the article in case you prefer to view them here.
There are no major surprises save one when one listens to this piece or does a harmonic analysis. There is, however, a great amount of harmonic and motivic activity in this piece, derived mainly from several recurring motives. I will run through the interesting parts of this piece as they appear chronologically. Because of the many variants of each motive, I have not designated different labels for each variant.
Measure 1 exposes our first motive, an ascending triplet eighth-note arpeggio on the tonic chord G. Immediately following is our first variant, a triplet, but this time descending and compressed (a step then a skip) which arpeggiates a 7th chord. The motives are very closely related in this piece. Motive a gives rise to motive b in the second measure. The b motive is an entirely descending stepwise 3-note group. This first playing of b has the first variant of motive a dovetailed to its end. Motives c and e are heard at the same time as motive b. Motive c is a 3-quarter-note group whose first and last note are the same (g) separated by a lower neighbor (f#). Motive e is a truncated form of c, comprised of only the initial half-step. But the most interesting is motive d. It is labeled in the score as a minor third. What is important about this motive is not that it is a third, but that the first note is expected to resolve to a particular tone, and the second note is one tone higher than the expected resolution. Motive d is first seen across the barline separating m. 3 and m. 4. It is the b4 to d5 jump. The b note is contained in a G dominant 7 chord. In this instance b functions as the third of the chord and the leading tone to c. If it is to follow its tendency it must resolve upwards to c5. It doesn’t, however, and instead jumps up to d5. The move to the d can be considered an appoggiatura; it could also be explained as the correct place for the b to go if the leap is considered part of a lager motive (a4-b4-d5). This would be the inversion of motive a’s first variant. The d5 eventually does go to the expected c5 but by then the bass has moved and we really don’t tonicize C. This is important, as we will see later.
It is interesting to note that in the first four measures we hear all of the major motives, and that every element in those measures is somehow comprised of those motives. The first really interesting use of motives (besides how they are all derived from each other) is the combination of motives a and b, by dovetailing them together. The last note of motive b is the same as the first note of motive a1. This can be considered a motive in itself, but I must consider it two, seeing how the compression and elongation of a yielded b. This b+a1 motive begins in the bass in m. 2. It begins again in the soprano on the third beat, but this time in inversion. See example 1. This is why the b4 must jump to d5 and how motive d is formed.
Measure 6 is the same as m. 2 but just an octave higher with some ornamentation. We find the same things just discussed in the lowest voice of the arpeggio pattern and the melody. But what comes next shows the complete unity of this piece and the intricate overlapping and recombining of the motives. The arpeggios in mm. 6-7 can be explained by a two-voice analysis, a sustained tone in the higher voice, and the b+a1 motive. But this isn’t nearly as interesting as the arpeggio in m. 8. This arpeggio can be picked apart in three different ways. See example 2. The lowest voice can be considered motive b inverted. The upper tones, depending on which you consider, can be seen as either c or the inversion of c. I propose that it is both. Just as the b+a1 motive was played against its inversion, here c is played against its inversion in the arpeggio. Simultaneously, b is played in the soprano against its inversion in the low voice of the arpeggio. Beethoven seems to have a thing for playing these motives against their own inversions. This excerpt is seemingly so simple, but comprises two motives simultaneously played against their inversions. And it is so subtle!
Motive e gives rise to the chromatic run in m. 8, part of the reduction process here. Measures 9-11 yield a trick that Beethoven will do often. The lowest two notes in m. 9 are c and e, the lowest in m. 10 are b and d, but there is only one lowest note in m. 11. [This is because Beethoven is able to take any two voices and make them one or any one voice and make it two by using a combination of motives b and c. See example 3.] Beethoven combines motives b and c, which in m. 11 converge on the c note.
Measures 9-10 are parallel to mm. 13-14. If we look at the melody of mm. 13-14 in light of mm. 9-10 we notice that d#-e in m. 14 is expected to be a c#-d like m. 10. We also expect the ii6 chord in m. 13 to resolve to a I6 or even a V. Neither of these happens. Our b motive strikes again! The d#-e movement begins a tone higher than is expected. This allows Beethoven to stay on the same chord, though he changes it slightly. The ii6 becomes a II or V/V allowing us to eventually itonicize the dominant, D, by virtue of motive e, which turns c into c# and thus ii into V/V.
Measures 15-20 are basically liquidation leading to the second theme. They are nonetheless full of motivic fun. The arpeggios are obviously variants of motive a. What is interesting is the harmony and the quarter notes in the upper voice. We will begin with the harmony. In the constant changing between V and I6 4, the movement of the f# and a of V to the g and b of I and back to V produces two sets of motive c. See example 4. While that is going on, if we exclude the triplets in the high voice, the quarter notes produce a version of a1 overlapping with its own retrograde inversion. See example 5.
The second theme occurs next. It is entirely derived from the motives of the firsttheme. I will start with the melody. See the score for this. It begins at m. 21 with motive c based on the tonic (as was the first instance of c). This is then followed by an inversion of motive c ornamented. The ornamentation of c actually shows us motives b and d again. Instead of e-f#-e, the e goes to g (motive b, a tone one higher than expected) then resolves down to the f# and then the e, which produces motive b. At the same time, in the bass, an inversion of c is played against the first c in the melody (we have seen this before) and then another inversion of c against the ornamented version. But another c, however picky it may seem, also exists in m. 21. The a-g-a movement in the arpeggio could be considered another c, constituting three simultaneous c motives.
Measures 23-24 expand on the previous two. In the melody Beethoven uses the combination b+c trick to give us two voices. We then follow with the ornamented c that has a third below it, another unornamented inverted c. The b motive is played in the bass against the b added in the melody in m. 23 as the c motive is played against the two inverted c motives of m. 24.
The melody evens out a bit rhythmically and it is no surprise now that every three pitches can be considered a b motive. See the score mm. 24-27 and beyond. The accompaniment in mm. 25-26 is derived from two c motives as marked in the score. The accompaniment then moves to a single g in mm. 27. This is the b+c trick again. The low voice then moves by half steps upward (motive e) to bring us to the dominant just as it did in mm. 13-14. Beethoven then re-employs a lot of these tricks in a restatement. Then come the linear passages.
These lines (mm. 36-52) are mainly liquidations of motive a, but also motives c, d and e. The entire body is comprised of the triplet motive which is obviously motive a whether it occurs in the melody or bass, stepwise or skipwise. What is interesting (as marked in the score) is that when the runs are separated by quarter notes, the last note of the first run, the repeated quarter notes, and the first note of the second run usually forms the c motive or occasionally the b motive. They are marked in the score. Beethoven uses the same b+c trick to move between two and one voices here. He also combines two b motives together to get a longer 4-note motive. Further, in mm. 49-52, instead of playing on the a motive as done earlier, he uses the e motive as a basis for movement of the quarter notes which is the difference between scale degrees 3 and 4 in m.15 and scale degrees 7 and 8 in m.49.
After the repeat there is a harmonic shock. After cadencing on D major, we get d minor in m. 53. We initially think that we have gone to the parallel minor by virtue of the e motive, but not so. It is actually the iv of a minor. In this section we don’t get too many new tricks, but a few. The motivic use is labeled in the score. There are some notable events though. In m. 58 we have a g-f#-g in the melody, the c motive —but wait— there are 16th notes, the only 16th notes in the piece. What is he saying? Beethoven is trying to emphasize what is coming next, the augmented sixth chord. This chord is not random, but another combination of a motive and its inversion, in this case motive e. This takes us to the V of e minor solidifying the move from a minor to e minor.The melodic bits in mm. 59-63 are just recombinations of motive c (and or e depending on your reference point). Measures 64-65 get to expand a little bit on the e motive, which expands into b motives. This is part of the retransition.
There are no new tricks until m. 73. Well there is really not a trick here, but the absence of one. This is the first time we don’t have our d motive and we actually temporarily itonicize C. We even modulate there for a short time. By giving us the proper resolution of the V/IV chord in G (namely to C) Beethoven tells us that it is time to go back home. This is an important section because it addresses the tonal problem raised by the f natural. And this problem is finally resolved in mm. 108-109 when we are finally solidly back to our tonic key in m. 110.
The movement ends by cycling through some old ideas as it did in the exposition. The harmony changes every 2-4 beats throughout the piece except in cadential spots where the harmonic rhythm speeds up. When you review the score note that I have taken the liberty of not marking every instance of the motives, and have only really marked their first couple of uses of each type in each section. Beethoven has produced in this subtle movement a work in which all elements were derived from careful use of the motive.