Beethoven's masterpieces consist of Concerto's, Sonata's, Bagatelles, Rondo's, Symphonies, and Orchestral pieces. Now I'd got to say that's a lot of music for someone who lived almost twice as long as Chopin. However, Concerto's should rarely be played without accompaniment. Furthermore, Symphonies and Orchestral pieces should be taken out of the picture since we are discussing the strictly the piano. As a result, do a little elimination and most (if not all) of what he wrote were Sonata's, bagtelles, and Rondo's.
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Chopin and various others on the other hand (Mendelson, Listz), elaborate more fully on the Piano's potential (waltz's, sonata's, ballades, scherzo's, etudes, mazurkas, polaniases, and preludes), and not as a instrument that is used to accompany others. Listz perhaps of all people illustrate the virtuosic potential of the Piano. Even Mozart, although not as successfully as Liszt tried to show the Piano's capability. But Beethoven, great with his symphonies, did not focus on making the Piano a MASTER INSTRUMENT, but as a mere accompaniment to the rest of the orchestra.
Oh, come on, now. The piano was Beethoven's instrument. He took it from a fragile thing and forced its development to nowadays piano.
And that was surely his preferred instrument, the one he played best. Remember, he was a virtuoso pianist before becoming a composer. He wrote his pieces firstly to perform and when he grew mature, and deaf, he began composing for himself for the sake of music. But piano was always his preferred means of expression, for he could play the piano like few in his time. Take on the other hand violin, which when he was deaf was a nightmare for those that would accompany him.
Besides, as someone said here long ago, he really used the full keyboard and knew very well how to take it all from the grave sounds, some thing that Mozart didn't do best.
As for classification, Mozart and Haydn are classical, no doubt, but Beethoven is no longer on the EARLY-classic. He makes the transition for the romantic, although his early works are classical. But compare his 5th concerto with his 1st and note the evolution in style and density.
As for masterpieces, it's not only about Sonatas. Take his variations, Rondo a Capricio, Andante Favori, Fantasia Op.77. Frankly, I never heard his bagatelles played (I'm not including Fur Elise in the bagatelles because that's an albumblatt, if I'm not mistaken, and there are sets of bagatelles named as such).
He might not have etudes (at least I've never heard of one) but he has done some other things than just Sonatas and Rondo's. He did dances too, waltzes, ecossaises even Polonaises, and what is a Mazurka and a Waltz if not a dance? Chopin made ones inspired on the folklore of his own country... so did Beethoven. Surely, you're not expecting all non-polish composer to go writing a Mazurka, are you? Why would he?
I know I may be sounding narrow-minded, but the point is that the transformation of folk music to classical takes time and usually a composer uses as material what he knows best. So in European courts in the time of Beethoven, there was a different kind of dances which he used. Chopin used what he knew best than others: the music of his country, and made it popular. True he made Polonsaises, but perhaps that was already popular and serious outside Poland. There was a long tradition of doing dances "à la...." (Italians, Scottish, German, Polish, perhaps even Spanish), but may be Mazurkas at the time were still not considered serious.
Now, as for Beethoven's sonatas and masterpieces. I was surprised to see so many people in this forum (not just this thread) mention the 3rd movement of Moonlight. I've always liked it, but I don't consider it by far his best work. First all, I find the 1st movement much more seductive, and in a style similar to the 3rd, I think any movement of Appassionata is much more demanding, complex and satsifying.
Then we have his sonatas.
I've been always a fan of Beethoven. For me, Beethoven is the best composer of music. But I've always been divided regarding piano music specifically since I knew Chopin. And then I heard a recital of Chopin music, by a pianist that recorded the integral of his piano solo works. And in that recital, featuring perhaps one CD from the whole series, there were few moments that carried me away. I love Chopin's well-know pieces, but I understood then and there that he's also got minor things that made me think: Truly, Chopin is great, but he can be so boring at times. I'll stick to Beethoven who has never disappointed me.
Because Beethoven has this thing (in his music for all instruments, not only piano) that I very seldom find in others: his music carries me, makes me want to dance, clap hands, sing it as a I hear it. It takes me in its arms and makes me travel somewhere else. It is singable, it is danceable it does not leave you indiferent. It's impossible for me to listen to a Beethoven piece and stay sitting on the chair as if I was watching TV. On the contrary, most of the other composers get just that reaction from me, including Chopin with his 1st Piano Concerto and Liszt. Schubert is a different thing altogether, another one that makes me feel fantastically. But I found that the majority may make very interesting music from the technical point of view but it doesn't make me feel much, or at least it requires that I hear it so many times that at last I know it. But Beethoven is more immediate. And yet, it is no less complex or difficult.
I should say though that I do not want to be unfair towarsd Chopin. He has one thing that not even Beethoven does with me: it's that feeling of naturalness, of improptuness. I hear his music, and for me the paradigm is Ballade no1, and it seems like a river flowing, music that flows surprisingly, that looks like it takes turns you are not expecting but flows, flows like it escaped spontaneously from the composer's heart. True, but he's not always like this, and then I go back to the German master.
It is for this that after so many years listening to music I still find Beethoven to be the composer that works best for me, either on piano or on anything else. But I give it to you, that for me Chopin is 2nd (and was 1st for a long time) and I can play more Chopin than Beethoven. And besides these two, Schubert is next for the sheer lovability of his pieces. Even going a bit outside the piano, the 2nd movement of the Trout quintet is lyrical to the extreme, in a sense reminding me of moments of Beethoven's Kreutzer; and his Impromptus op 90 no1 and no3 fill me with an undescribable joy.
Perhaps I don't know enough piano music to talk about the rest yet, and that's why my views on this are always temporary. But for the moment, it is Beethoven - Chopin - Schubert - Liszt and the others.
Well, I'm no expert. I'm indeed not more than an amateur, but I'm expressing my point of views of the feeling not of the technical merits of a music.
Yours,
Alex