I finally found a website that gave an example of the sound, I don't know why my first search didn't find it. The sound was Pactor. Although the sound I've heard is a variation of it, it still has the same base. I hear it on the ham band about once a week even though I thought it was prohibited on the ham bands.
Very odd that you would think that Pactor was banned on the ham bands and have never heard it before. It is the most popular TOR mode by far. There are 4 variations of it. You probably heard Pactor 2 or 3, and perhaps 4. P1 sounds like a chirp. P2 has 2 distinct tones but is more of a rushing sound. P3/P4 is still a rushing sound, but there are many more tones (the number of tones vary depending on signal conditions). The one thing in common is the "ack" chirp back as the IRS replies to the ISS. P2 and P3 are used heavily for message traffic in the US. P4 is not legal in the HF US HAM bands, but is used extensively in EU.
Pactor is highly effective in moving error free text or binary files. P2/P3 are also extremely robust and are great for keyboard QSO's as well.