Crossword Genius

Casual greeting delivered louder (6)

Ross

I believe the answer is:

higher

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'louder' is the definition.
Both the answer and definition are comparative adjectives. Perhaps you can see a link between them that I don't see?

'casual greeting delivered' is the wordplay.
'casual greeting' becomes 'hiya' (I've seen this in another clue).
'delivered' shows a homophone (sound like) (delivered verbally).
'hiya' is a homophone of 'HIGHER'.

Can you help me to learn more?

(Other definitions for higher that I've seen before include "More lofty" , "More exalted" , "Superior or taller" , "Loftier" , "At greater altitude" .)

I've seen this clue in The Guardian.
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