Transmitting a single short melody (2,3)
I believe the answer is:
on air
'transmitting' is the definition.
(eg transmitting on the radio)
'a single short melody' is the wordplay.
'a single' becomes 'one' (a single thing - only one).
'short' means to remove the last letter.
'melody' becomes 'air' (synonyms).
'one' with its last letter taken away is 'on'.
'on'+'air'='ON-AIR'
(Other definitions for on air that I've seen before include "with audience?" , "How one walks when elated" , "very happily?" , "Live broadcast" , "Transmitting now!" .)