It was on a dead branch. It sang a couple of times with soft long notes. I took a photo (no.3) when it was singing but stopped before I could record it. It was a gentle and soft song.
Museum Victoria Field Guide to Victorian Fauna (also ACT) has recording of Aquila audax but not the "gentle and soft" one. We should copy their guide and add calls for all birds and frogs.
I tried to find a recording of their soft calls on the internet but I could not find any recordings close to the one I heard. If I am ever granted the same opportunity, I will try to record it. While I was searching recordings, I found information on their calls. Under 1.1 in the following website, it says 'Outside the breeding season, wedge-tailed eagles are usually silent, though they produce a range of specific, rather gentle calls'. http://www.environment.gov.au/resource/national-recovery-plan-wedge-tailed-eagle-1998-2003
That's so nice of you recording its call. I cannot recall the exact sound anymore as it's 6 months ago, but I think that it was a similar sort :) Thank you, Helen.