We've all heard of Mozart, Beethoven, Bach, etc. because their fame has lasted through the centuries. More modern composers like Mahler and Stravinsky were recorded and became famous while they were alive because it was fairly easy to be able to listen to them. My question is how come composers like Mozart were such superstars during their times without any ways of hearing them other than in live performances? Surely there couldn't be that many people who could listen to their work live.
Edit: I left out a word.
Bach wasn't very famous in his lifetime, actually, his reputation grew over time, partly because his music was used to teach theory (as it still is today), and partly because he was rediscovered and people appreciated him more the second time around. That's part of a different discussion though. As far as fame goes, there are three main ways composers became famous in the 17th and 18th century. The first is through successful live performance, don't downplay this.
Composers like Mozart and Beethoven had their works played by the top ensembles in the largest cities in Europe at a time when symphonies and opera companies were as famous and discussed as modern film and music stars. Beethoven and Mozart were comparable in star power to the biggest stars of today, and a debut of a new composition by them was greeted with the sort of anticipation moderns reserve for a new Steven Spielberg movie or album by Kanye or Jay Z.
The second way composers of that era became famous was through famous patronage. There was a pecking order in the aristocracy, with Dukes trumping Counts and Barons, and Royals trumping lesser Dukes, and Royals of richer and more powerful nations trumping royals of smaller nations. Gaining a major benefactor was in itself cause for notice. These old composers were like modern auto racing teams when it came to sponsorships. Getting a job as court composer for a Holy Roman or Austrian Emperor was the equivalent to being hired to race for the Red Bull or Mercedes Racing team, when a new guy got the job his work was under the magnifying glass. This was one of Bach's failings, he repeatedly auditioned for and failed to get important sponsors. Some of his most famous works are failed audition pieces, like the Brandenburg Concerto's, Bach's try for the position of Court Composer for the Elector of Brandenburg.
The third way, and one moderns never really think of, was through sheet music sales. Before people owned televisions, radios and computers most of them owned a musical instrument and the family band was a way to pass an hour or two in the evening. This is why so many famous composers who are known today mainly for a handful of symphonies wrote dozens or even hundreds of works for solo piano and other instruments: these were the most popular sheet music sellers and once a composer had a decent reputation music shops would stock and recommend their new works to customers.
A top flight patron meant you would have new works debuted in major palaces and concert halls in front of large audiences. You would be talked about in the press and by word of mouth afterward. And once your music started showing up in shops as sheet music people could take home and play themselves (the same as we now do with albums purchased in stores or online) you were pretty much a star.