This is not a useful way to think about antonyms. There is no useful linguistic or grammatical operation you can conduct by memorizing lists of antonyms. It is worthwhile learning the concept, and as your vocabulary increases, you may be able to sort some words into these categories. But it is no more use than that. In fact, it is largely useless.
Sorry if you have spent effort learning antonyms. This will not help you learn English.
Thank both of you for your answers.
It is a question extracted from my test. Although I am bored with such type of test because I know that it's pointless learning words by heart without understanding how to use them in certain contexts, I still try my best to do it in order to improve my academic performance at school.
"Unknown" is not suitable as an antonym because a composer may be great but not well-known. I'd have to choose "insignificant" since "great" is a measure of size or quality. If given free rein, I'd choose "minor".
Sorry. I'm not annoyed. I just took an opportunity to make a joke. As, frankly, I will always do.
If I had to be serious and select an antonym for 'great composer', it would be 'minor composer' or 'obscure composer'.