Music is interesting to listen to because it isn't random. It has patterns, repetitions, missed predicted repetitions and regularities that the human brain can detect and - usually - enjoy. Here is an interesting question - what would be the worlds ugliest music?
If you think the answer is random, then you need to think more carefully about what randomness implies. If you generate truly random numbers, or even very good pseudo random numbers, you do get patterns. If you ask a human to generate random numbers they avoid patterns and with the result that some sequences don't occur and this isn't random. A random sequence of coin tosses is likely to come up H,H,H,H... as frequently as any other sequence. Often we need numbers that have a distribution that avoids obvious patterns and these aren't random sequences.
As this Ted Talk video explains it is difficult to create a sequence that has no repetitive structure. The need for such a sequence first occurred because sonar systems required a signal that could be transmitted and received after being shifted up or down such that the shift could be unambiguously detected. If the ping had any pattern, any regularity, then there is the chance that it might match its shifted self simply by accident.
The search for the perfect ping that has no structure takes us into the subject of Galios theory and some advanced discrete mathematics. Eventually the perfect ping was found and this is what has been converted into a piano work and played in this video. To make sure that the rhythm was structureless, a golomb ruler was used to set the note lengths.
Just listen and see if you think it is the most ugly music on the planet:
Personally I don't think it sounds as bad as it could! The reason is that, while lack of structure might make it less than interesting, there are structures in music that actually sound bad - dissonance for example. So the world's ugliest music probably has structure but not structure we find pleasing.