There were many great composers of a classical tune like Mozart, Bach, and Beethoven. I don't know present great composers of a classical tune like them. Could you teach me?
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Classical music composers from previous eras were the "popular" music of their day. Some of them were publicly appreciated in their own day, but some of them weren't, specially in the 19th century, as their music was considered too farfecthed or just plain ugly. The lady who actually fainted with great commotion at the first presentation of Ravel's Bolero is just an anedoctal extreme example, but negative reactions from critics and/or public to pieces that we now consider masterpieces were not uncommon.
These composeres and their music have reached our present day's ears after centuries of study and appreciation. Our ears have (generally speaking) grown accustomed to their music and that's one of the reasons why they are generally appreciated.
On the contrary, the work of contemporary "classical" (i.e."erudite" or "non-vernacular") composers is far from being the popular music of today. On the one hand, actual contemporary popular music in its multitude of genres has taken most of the attention of the public. On the other, erudite composers, in their effort to explore and find new ways, have become estranged from the general public. A few have reached mediatic attention (John Cage), and some have reached even a certain level of commercial success (Phillip Glass), but none (that I can think of) has gotten the universal recognition and acceptance that the big classical composers now have. This is not related to the intrinsic quality of their work, but to the fact that hey are not limiting themselfes to just repeat the styles of the familiar classical composers.
One realm where perhaps a middle ground has been reached is that of music for film soundtracks. Many composers with theory and classical training exist (John Williams certainly the most well known) that apply the erudite approach to music composition for film and try to please the contemporary taste in a creative and (some times) inovative way.
So, to wrap up, if you're looking for current day "immortal melodies" like those of Shubert, contemplative addagios like Mahler's, or Beethoven type explosive bursts of emotion, I suggest you try orchestral film scores.
Your question calls for a lot of opinion and speculation, so I'm not sure if it can be answered very authoritatively.
That said I'll try to answer as objectively as possible. Joseem mentioned some things that are important to keep in mind. when Beethoven and Mozart were around there was no rock or jazz music. Classical music was it for the upper classes. Lower classes had folk music, and many of the melodies are still very familiar today, but the identities of the composers have not come with them. There were no radio or phonograph players, so when people entertained themselves st home they had to play it themselves (unless they were REALLY rich and could hire someone). Sheet music was often a good source of income for composers.
This makes their time hard to compare with ours, where classical music has become somewhat of a niche. To a great extent it will be what future musicians and historians choose to keep alive. Will an orchestra 200 years from now decide to play or record John Cage or Esa-Pekka Salonen (his Violin Concerto is one of my favorites, btw) or Philip Glass? That's almost impossible to say.
I can look at some of the current trends in the way historians are writing about recent music and the way orchestragoers react to them (they are, after all, what pays for the orchestra). Unfortunately it seems there is a trend in music historical analysis to write off a great deal of experimental music as a tangent and in the end, fairly inconsequential.1 2 I don't agree with that assessment. For example, I have loved Krzysztof Penderecki for years. I have always thought him to be a composer worthy of greatness. But he is, at least for now, most known for his earliest and most experimental work, which writers don't appear to have much respect for. Unless musicians - players and conductors - decide to carry his work into the future it seems some writers are fine with tossing him, and other modern music aside as an aberration.
Many conductors, in addition to the Mozart and Beethoven repertoire, often put into their concerts a piece of modern music that they believe is important and should be heard, if not enjoyed. Unfortunately audiences, even after over 100 years of modernity, still have a bad reaction to modern pieces. 3
One thing that is certain to put a composer on the path to future recognition is having melodies that stick in your head. Mozart's melodies are impossible to forget. Who can deny the catchiness of Beethoven's Fur Elise or the Ode To Joy from his 9th? A current composer who excels in this regard is John Williams. As far as I know he's never written a symphony. His work is done for movies, but it transcends that role. The melodies become recognizable outside of the movie theater. In addition to this, he is well respected among musicians.4 His list of awards is endless, not only in the film industry 5 but in the music industry also.6 Orchestras have not shied away from playing his scores in a serious setting. These things combined give me a confidence in saying that his work will still be alive and well in the future.