Cryptic crossword clue
Irrational and I hesitate to say outsize note providing musical direction 3,5

The most common and most likely answer to this crossword clue is the 3 plus 5 letter word PIU MOSSO

I've seen this crossword clue in The Times
P
I
U
M
O
S
S
O

Buddy explains!

The straight part
We know that "musical direction" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case musical direction = piu mosso.
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.

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