The 'Beautiful' in music is actually a very poetic title. It is hard to describe and bring accross.

First, "the beauty in music" definitely sounds more natural than "the beautiful in music". Although the phrase "the beautiful things in music" could sound more natural, it wouldn't sound as fancy. You could also replace "things" with a more concrete word. There's apparently also a well known book in German called "On the Beautiful in Music" from 1854. The original title is "Vom Musikalisch-Schönen". To give a sense of German, I suppose in bad English it's "On the Musical[ly] Beautiful [thing]". So perhaps there was some influence here when translating the title into English. That's just my guess. It's hard to say what the difference in meaning is exactly, but you could argue "the beauty in music" sounds more abstract than "the beautiful in music". For example "the beauty in music is that it can make people feel happy" vs "[one of] the beautiful things in music is harmony". It's more natural in some other languages to say things like just "the beautiful". In English you often want to say something like "the beautiful people" or "the beautiful thing". The beautiful something. On the other hand, when you're talking about a class of people in general, then sometimes you could say things like "the bold and the beautiful", "the rich and famous". But they sound a little formulaic to me, like "the X and the Y". It can also sound a little dehumanizing. There's also "victory goes to the bold", but it's harder to think of phrases using only one adjective this way.

From a grammar standpoint, the reason the writer chose beautiful instead of beauty is the fact that beautiful is an adjective which is a word that helps to describe a noun, which in this case, is music. I hope this helps!