Crossword Genius

One's played two blues oddly rejected by British university (7)

Ross

I believe the answer is:

ukulele

I'm a little stuck... Click here to teach me more about this clue!

'one's played' is the definition.
I can't judge whether this defines the answer.

'two blues oddly rejected by british university' is the wordplay.
'two' says to double the letters.
'oddly rejected' indicates alternate letters.
'by' is a charade indicator (letters next to each other).
'british' becomes 'uk' (I've seen this in other clues).
'university' becomes 'u' (abbreviation for university).
The alternate letters of 'blues' are 'le'.
'le' doubled is 'lele'.
'uk'+'u'='uku'
'lele' put after 'uku' is 'UKULELE'.

Can you help me to learn more?

(Other definitions for ukulele that I've seen before include "George Formby's little guitar" , "Instrument from Hawaii" , "Small guitar as played by George Formby" , "Small 4-stringed guitar" , "Small, four-stringed guitar" .)

I've seen this clue in The Guardian.
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