Not half hard-up, money's in cash one's blown (9)

I believe the answer is:

harmonica

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But I can't explain it at all! Could you help me understand?

(Other definitions for harmonica that I've seen before include "It's blown" , "Harp" , "An alternative mouth-organ" , "musical instrument" , "Mouth organ" .)

I've seen this clue in The Times.

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