The music issue can be really confusing even for Muslims, but I’ll relate what I feel is probably the best chain of reason I’ve heard on the subject.
So, this is the verse in the Koran that is sometimes interpreted as being anti-music:
And of the people is he who buys the amusement of speech to mislead [others] from the way of Allah without knowledge and who takes it in ridicule. Those will have a humiliating punishment. ~ 36 : 6
Amusement of speech often being used to mean singing and by extension wind and string music due to the particular wording in Arabic. From the hadith:
that he heard the Prophet (ﷺ) saying, "From among my followers there will be some people who will consider illegal sexual intercourse, the wearing of silk, the drinking of alcoholic drinks and the use of musical instruments, as lawful.
However, there are two versions of this hadith - one that contains “musical instruments” and one that does not and there are various opinions about which source is more valid. Additionally, there is a prohibition of teaching female slaves to sing or selling them as entertainers due to the previously mentioned verse of the Koran.
So, typically in jurisprudence, if something is not explicitly forbidden or required by the Koran it is up to individual judgement. Since God did not explicitly forbid music, then there is an argument to be made that the purpose of 36 :6 does not pertain to music or at least not all music. The reference in the hadith is more about sexual purity since selling a woman as an entertainer has other obvious implications that might cause her and her male audience to sin through immodesty and lust.
Similarly, there is a hadith in which there was a holiday and two girls were singing a triumphant song in the vicinity of the Prophet (peace be upon him). Abu Bakr rebuked them, but the Prophet (peace be upon him) told him to leave them alone. If all singing or music were haram, then there would be no reason for him to allow it.
Taking all of that into context then, I feel like the prohibition extends to music which can cause an occasion of sin - so music that is profane, encourages lust or violence, or involves some sort of immorality. I’m careful about what I listen to and I try to avoid music that contains profanity and sexual content - so basically like the entire Katy Perry-esque brand of American pop music. I don’t feel like I’m missing much.