Crossword Genius

Brooding overture, perhaps including piano (13)

Ross

I believe the answer is:

introspection

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'brooding' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.

'overture perhaps including piano' is the wordplay.
'overture' becomes 'intro' (I've seen this before).
'perhaps' becomes 'section' (I can't explain this - if you can you should believe this answer much more).
'including' indicates putting letters inside.
'piano' becomes 'p' (musical abbreviation).
'section' placed around 'p' is 'spection'.
'intro'+'spection'='INTROSPECTION'

Can you help me to learn more?

(Other definitions for introspection that I've seen before include "Examination of one's own thoughts or feelings" , "Examination of one's inner feelings" , "Self-analysis" .)

I've seen this clue in The Times and The Sunday Times.
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