Harmonious, exclusive component of hymns and rhythms? (9)
I believe the answer is:
consonant
'harmonious' is the definition.
(similar in meaning)
I can't explain the rest of the clue.
(Other definitions for consonant that I've seen before include "Letter; harmonious chord" , "Something like G, B and D" , "B, C, D or F, perhaps?" , "not I, nor you, one hears" , "One of many letters" .)