A quiet ringing sound's attractive quality . . . (6)
I believe the answer is:
appeal
'attractive quality' is the definition.
(I've seen this before)
'a quiet ringing sound's' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'ringing sound' becomes 'peal' (sound of a bell).
'a'+'p'+'peal'='APPEAL'
(Other definitions for appeal that I've seen before include "Request made to umpire" , "Entreat, plead" , "fetching" , "Refer sentence to higher court for review" , "Charm in higher court?" .)