Bawdy record, what a jazz musician may produce (4,4)

I believe the answer is:

blue note

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'a jazz musician may produce' is the definition.
I can't tell whether this definition defines the answer.

'bawdy record' is the wordplay.
'bawdy' becomes 'blue' (synonyms).
'record' becomes 'note' (note can mean to record or notate).
'blue'+'note'='BLUE NOTE'

'what' is the link.

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I've seen this clue in The Guardian.

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