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Centre gets sex change (6)

Ross

I believe the answer is:

fiddle

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This clue could be a double definition.

'centre' is the first definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Maybe there's a link between them I don't understand?

'sex change' is the second definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe you can see a link between them that I don't see?

'gets' is the link.

Can you help me to learn more?

(Other definitions for fiddle that I've seen before include "Toy - string instrument - cheat" , "Violin; falsify (figures)" , "Fix" , "Cheat on (e.g. expenses)" , "Sham" .)

I've seen this clue in the Sydney Morning Herald.
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