Riveted to music tempo (4)

I believe the answer is:

rapt

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'riveted' is the definition.
(I've seen this before)

'music tempo' is the wordplay.
'music' becomes 'rap' (I've seen this before).
'tempo' becomes 't' (this could be a standard abbreviation of which I'm unaware).
'rap'+'t'='RAPT'

'to' is the link.

Can you help me to learn more?

(Other definitions for rapt that I've seen before include "Spellbound, enthralled" , "Very attentive" , "'Transported, entranced (4)'" , "Ecstatic - engrossed" , "Engrossed, spellbound" .)

I've seen this clue in The Hindu.

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