"What music do you listen to?"
There are different readings 乐 depending on its 汉字 compounds.
music 音乐，yin1yue4 is yue4
music fan，乐迷 yue4mi3
A lot of words dealing with music have the yue4 reading
le4 readings include :
Lots of le4 readings are for "happiness" words
I hope the formatting for this post is ok
2020.7.26 It is Mando. A few characters have more than one pronunciation. Sometimes it is a difference in tones, other times it's a completely different pronunciation. You have to think, these characters represent a meaning more than a sound. That's how Japanese and Chinese can share so many characters and retain some of the same meanings. Sometimes the meaning cover words that have inherently different pronunciations
Take another example, 行
「銀行； yin2hang2」 a bank
「旅行； lv3xing2」 a trip
「行李; xing2li」 luggage
「行不行?: xing2buxing2」 Is it OK? Is it allowed?
Sometimes in language learning, it's not as important to learn the "why", but to learn the "when it is used"
The way I understand it, it mostly works if you put the interrogative (shen me) where the answer would appear in the similar declarative statement answer. So
Q: "You listen to what music"
A: "I listen to American music" (or whatever)
The English grammar difference between this and your suggestion of putting it at the end is that the English word "what" is sometimes a determiner (goes before a noun) and sometimes it is a pronoun. In this example it is a determiner and goes before the noun "music" and it does the same in Mandarin. But in the sentence "what are you called?" it is a pronoun standing on its own, and the Mandarin does something similar but it goes at the end of the question not the beginning (ni jiao shen me).
Because 乐 has two different pronunciations, depending on context (i.e., what character it is combined with).
Sometimes things don't have an explanation, they just are. For example, why is "read" pronounced like "reed" in the present tense ("do you read much?"), but like "red" in past tense ("I read the article yesterday")?
Your question is like asking "why is 'read' pronounced 'reed', but 'read' is pronounced 'red'?"