The program would wonder the same things as you: what are the filenames and where are they located. There is no way of simply looking up such information, so it would try a.mp3, aa.mp3, aaa.mps, b.mp3, et cetera indefinitely, eventually reaching www.ted.com/zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz.mp3 before moving on to www.ted.com/a/a.mp3 and repeating the process. In short, it is a search that could actually exceed your own lifetime.
However, if all of the MP3 are directly linked to somewhere on the site, and all of the pages are somehow traceable back to a single page, and countermeasures have not been enabled to deter/block web spiders, it would be possible to search every page on the site. Given the sudden bandwidth consumption, however, the operators would not be appreciative.
My suggestion: Just contact them and ask for a bulk download.
Is there a program that will search an entire domain for the .mp3 filetype and download all of them?
Im trying to do this at www.ted.com
they have links avaliable to download their videos in mp4 and some in mp3 format on each page. But the links arn't to actual files they are to pages that redirect to files so I'm not sure if that makes it harder to do.