Crossword Genius

Coarseness in heartless song when following college rugby (7)

Ross

I believe the answer is:

crudity

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'following college rugby' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'coarseness in heartless song' is the wordplay.
'coarseness in' becomes 'cru' (I can't explain this - if you can you should believe this answer much more).
'heartless' suggests removing the centre.
'song' becomes 'ditty' (ditty is a kind of song).
'ditty' with its middle removed is 'dity'.
'cru'+'dity'='CRUDITY'

'when' acts as a link.

Can you help me to learn more?

(Another definition for crudity that I've seen is " Lack of refinement".)

I've seen this clue in The Independent.
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