Although the best of Mozart's music is irresistibly likeable --- such as the Sinfonia Concertante for violin and viola, or the clarinet quintet --- I find a lot of the rest quite resistible, thank you. The same goes in spades for Haydn, amd doubled in spades for that host of tedious 18th Century musical drones from Cannabich to Von Dittersdorf. Beethoven, by contrast, seems to belong to another planet. Why is this?
At first thought, the technical differences don't seem to be so large. There are some key changes in Beethoven which were unconventional in his time, but these are in fact fairly rare. Here and there he employed dissonance for dramatic effect, like the famous climax of the development section of the first movement of the Third Symphony ("The Eroica,") but these instances are even rarer. Overall, the harmony in Beethoven's music (excepting the astonishingly prophetic Grosse Fugue) isn't all that different from that of his immediate predecessors.
Three other differences are more telling. First, Beethoven used the minor mode much more frequently than his immediate predecessors. I'm not referring only to movements in the minor --- like the great slow movements of the Third and Seventh Symphonies, the Seventh and Ninth Quartets, and so on. Beethoven also wove minor key into the music of major key movements much more intimately than was conventional in the Classical period. In the Second Symphony, for example, much of the first movement's development section is in the minor. In the "Eroica," the dissonant climax is followed by a haunting little theme in the minor. In many works, Beethoven does the trick of stating a major key tune and then immediately repeating it in the minor. And the last movement of Eighth Quartet has a main theme in which you can't decide whether it is in major or minor key. The effect of this major/minor mixing is to greatly increase the music's emotional scope and dramatic impact.
Second, the rhythms Beethoven employed were far more varied than those in conventional Classical period music. Think of the jagged, irregular rhythms of the last two movements of the Second Symphony, which a critic in 1804 compared to a "hideously writhing wounded dragon." (!) Syncopation and shifts in emphasis occur frequently in Beethoven, as for example in the second movement of the Seventh Quartet. This kind of fluidity, very different from the four-square or three-square regularity of the classical style, marked an innovation in rhythm almost as great as Stravinsky's from a century later (although less imitated).
Finally, Beethoven's writing is far more contrapuntal. Quite aside from explicit fugues like those of Ninth and Fourteenth Quartets, Beethoven's music is crammed with fugato passages, and with independent flows of multiple lines. A contemporary comment on one of the late quartets was:
The parts are interwoven to such an extent that everyone has all they can do just to follow one instrument, so that everyone wants to hear the quartet four times.
In short, Beethoven did not shrink from presenting the listener (and the performers) with complexity.
The music of his immediate predecessors is much simpler, in all but a very few cases. Mozart composed a great fugue for the last movement of his Symphony Number Forty-One, but otherwise used counterpoint very rarely, and Haydn even less. Conventional music of the period almost always followed the monophonic structure of a melody line over a chord-based, oompah sort of accompaniment. This, like the plodding, regular rhythms, illustrates the defining feature of the pre-Beethoven classical style: it is Easy Listening. That is precisely why commercial classical music stations program so much of it. It is as if Haydn & Co. anticipated exactly what the broadcast industry, and the purveyors of background music for elevators and telephone waiting, would require two centuries later.
Since Mozart demonstrably knew how to write a fugue, and perhaps Haydn did too, the avoidance of counterpoint must have been a matter of policy. So, I believe, was their avoidance (with very rare exceptions) of the minor key. Haydn & Co. must have calculated that patronage would be more forthcoming for works filled with forced gladsomeness. The result is a sensibility resembling a cross between highschool cheer-leading and "socialist realism" in the old USSR; it conveys to me a powerful sense of calculated pandering. Haydn & Co. pander to their audience, while Beethoven, in contrast, tries to engage it.This brings up the vexed question of the proper relationship between creative artist and audience. Beethoven wrote his share of fawning letters to patrons and prospective patrons, whiny complaints to patrons and publishers, tried to sell some pieces of music twice, and did write a few panderish commissioned pieces for special occasions. But in his major works, Beethoven obsessively maintained artistic integrity, the insistence on communicating on his own terms. That was nowhere clearer than in the visionary final quartets he wrote in the last few years of his life. By then, Beethoven's code of artistic autonomy was coming into its own; it would soon become quite conventional, and would be called the Romantic movement.
But despite his claim of artistic autonomy, Beethoven was in fact supported by aristocratic patrons for most of his life. Music and history owe a debt of gratitude to these patrons, who were an unusually discerning bunch: they were able to put up with Beethoven's difficult personality, terrible manners, and his (purely theoretical) anti-aristocratic politics, in the interest of his musical genius. They themselves were not only music enthusiasts, but in many cases musicians of some ability.
Beethoven's chief patron was the Archduke Rudolf, youngest son of one Austrian emperor and brother of the next. Rudolf was a pianist, and a longtime piano pupil of Beethoven's. Amazingly, he also received instruction from Beethoven in composition! [If any compositions by Archduke Rudolf survive, it would be interesting to hear them; I'll bet they are not much, but who knows?] Count Andrei Razumofsky, a patron who was a Ukrainian nobleman and a diplomat of the Russian empire stationed in Vienna, was an accomplished violinist and also played the Ukrainian bass lute. The Count's brother-in-law, Joseph Frantisek Maximilian, the seventh Prince Lobkowicz, was also a violinist and a major supporter of Beethoven. Another important Beethoven patron was Prince Lichnowsky, who was a pianist and a composer.
Some of Beethoven's patrons were outsiders in the sense of suffering physical disability. Archduke Rudolf was epileptic; his lifelong devotion to music was perhaps related to exclusion, because of his physical condition, from imperial military and political machinations. Prince Lobkowicz, born with a hip defect, had to walk with a crutch, and was reportedly in pain much of the time all his life. The families of Lobkowicz and Lichnowsky, like that of another Beethoven patron Prince Kinsky, were Bohemian rather than Austrian. This may have made them outsiders, in subtle ways, in the social order of the imperial capitol. [An ironic side-note: the forbears of these Catholic Bohemian noble families, supporters of the Austrian Empire, had been on the conservative side in the Thirty Years War of the 17th Century, which abolished both independence and Protestantism in Bohemia; and here were their descendents, in turn-of-the-19th Century Vienna, financing that raging radical Ludwig van Beethoven.]
Whatever the reasons, these aristocratic patrons lavished plenty of money on their beneficiary over the years, and worshipped him to a remarkable degree. According to one story, even after Beethoven had broken with Prince Lichnowsky in one of his temper tantrums, the Prince would sneak up to Beethoven's flat in Vienna to stand outside the door just to listen to the great composer improvise on the piano. (Since Beethoven was deaf as a post by then, his improvisations may have been on the unusual side, which speaks all the more in Prince Lichnowsky's favor.)
The prince and other patrons seemed to understand and moreover to accept the insult which Beethoven, in his temper tantrum, had famously hurled at Prince Lichnowsky earlier: "There are thousands of princes," Beethoven is supposed to have shouted, "but there is only one Beethoven."