Crossword Genius

Assessor of accounts backed excellent performance spaces (9)

Ross

I believe the answer is:

auditoria

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'performance spaces' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'assessor of accounts backed excellent' is the wordplay.
'assessor of accounts' becomes 'auditor' (I am not sure about this - if you are sure you should believe this answer much more).
'backed' says the letters should be written backwards.
'excellent' becomes 'ai' (resembles 'Aa', old-fashioned term for excellent).
'ai' back-to-front is 'ia'.
'auditor'+'ia'='AUDITORIA'

Can you help me to learn more?

(Other definitions for auditoria that I've seen before include "Where concertgoers sit" , "Theatres, concert halls" , "Theatre areas for spectators or listeners" , "lecture theatres" , "music halls" .)

I've seen this clue in The Independent.
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