It is, but it is increasing the branching factor by much more than finding all the "good" melodies in 400 years.

Here's a good example of music that stands on it own right despite using the melody of despacito: https://www.youtube.com/watch?v=ydqReeTV_vk - I'm pretty sure that most people at HN will appreciate this one whether they like despacito or not :)

I think the relevant thing about the pigeon hole principle is that it deals with fundamentally discrete things. Sure, there is a finite number of scores using twelve notes in a finite period of time, but that's just not how we judge or compare music. I would say that there's so many branching factors in music that quantifying one piece is akin to measuring a coastline; the smaller your scale, the longer the coastline. Beyond timbre, there's other cultural factors like, who wrote the music. In a million years we might have umpteen songs with the same score, but they'll still occupy different pigeon holes in the collective consciousness.