Crossword Genius

Loud greeting uttered (4)

Ross

I believe the answer is:

high

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'loud' is the definition.
Both the definition and answer are adjectives. Maybe they are linked in a way I don't understand?

'greeting uttered' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'uttered' shows a homophone (sound like).
'hi' is a homophone of 'HIGH'.

Can you help me to learn more?

(Other definitions for high that I've seen before include "Relatively great or specific elevation" , "Great in rank" , "Outstanding feature" , "having senior ranking?" , "American school" .)

I've seen this clue in The Telegraph.
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