The most common and most likely answer to this crossword clue is the 4 plus 4 letter word TONE DEAF
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The straight part
We know that "unable to appreciate music" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unable to appreciate music = tone deaf.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does TONE DEAF mean?
TONE DEAF noun- Tone-deaf people, as a group.
- Unable to clearly distinguish the difference in pitch between different notes.
- Having little appreciation of music, whether or not as a result of tone deafness.
- Out of touch with the experience of ordinary people.
- Insensitive and offensive as a result of not noticing the current social context.