In the given sentence, the word 'for' is associated with the nouns 'taste' and 'music' to denote that 'he has no taste for(towards, directed at) music.
The correct preposition to use in the sentence is "for."
"I go for a walk in the garden."
In this context, "for" is used to indicate the purpose or reason for going to the garden, which is to take a walk. Therefore, "for" is the appropriate preposition to use in this sentence.