What does the cryptic crossword clue "Playing concertina not on without core piece (8)" mean?

This cryptic clue uses wordplay to arrive at the answer. Visit the page for progressive hints — definition, wordplay type, and a full step-by-step explanation.

Playing concertina not on without core piece (8)

Guardian Cryptic #26321 | 26 Across | 2014-07-25

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I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

CONCERTINA* less ON

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