Sing awful melody with no hint of musicality (5)
I believe the answer is:
yodel
'sing' is the definition.
(yodeling is a kind of singing)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for yodel that I've seen before include "Alpine warble" , "Sing in Tyrolean fashion" , "unusual singing" , "Falsetto singing" , "Sing falsetto like Swiss mountain people" .)