Study a noted duet arrangement (5)

I believe the answer is:
etude
'arrangement' is the definition.
(thesaurus)
'study a noted duet' is the wordplay.
I cannot quite see how this works, but
an anagram of 'duet' is 'etud' which is within the answer.
A single letter 'e' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for etude that I've seen before include "Testing musical composition" , "Indian statesman" , "short musical piece" , "Noted composition" , "A short musical exercise" .)
