Choose a deep sound? Not from this instrument! (7)

I believe the answer is:

piccolo

'this instrument' is the definition.
(piccolo is a kind of instrument)

I can't explain the rest of the clue.

(Other definitions for piccolo that I've seen before include "Small high-pitched flute" , "High flute" , "High wind instrument" , "Instrument of the flute family" , "Smallest of the flute family" .)

I've seen this clue in The Times.

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