Moved back and forth or sideways, in time to music perhaps (6)

I believe the answer is:

swayed

(Other definitions for swayed that I've seen before include "Being under the influence" , "Moved back and forth or sideways" , "Ruled; influenced" , "was unsteady on one's feet" , "Oscillated - influenced" .)

I've seen this clue in The Irish Times.

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