There is always a limited amount of something, amount of fingers on your hand, amount of leaves on a tree, but what about music? Will we ever be in a situation where all the music possibly thought up will end?
Bounded rationality is a theory by Herbert Simon that says that out ideas are bounded to our thinking capacity. In other words, people are limited to what they already know. Now link this to music, yes there may have been hundreds of thousands of songs that have been made yet there is one thing you may have noticed. Have you ever listened to a song you are sure you haven't heard of before and think you recognize that song somewhere? No, you are not going crazy, it's either the artist got lazy and stole from Paul McCartney or bounded rationality has taken place. For example, Avicii - SOS sounds exactly like Ed Sheeran - Shape Of You. Coincidence? Don't worry, the world isn't actually running out of music, we are simply using the same limited amount of chords we have had for centuries.
According to MediaMusicNow "If one hundred writers each created one new melody every second, this would exhaust every possible melody in 248 years." So, if you thought your next Taylor Swift song will the sound the same as The Beatles - Hey Jude, Don't worry, it won't.