> but 56k was fine over regular lines.

Sort of. The quality/length of your local loop made a difference.

And heck, 56k being able to do 56k in the first place was dependent on not having a "regular" line between the ISP and their central office (CO), but rather it being digital, whereas the line from the user to their CO was always analog. Removing a set of digital to analog and analog to digital conversions in the ISP -> user path was what allowed the download speed to reach 56k. Upload was limited to 33.6k because it included an additional set of conversions and introduced more errors, prohibiting the higher speed.

This shows getting up to 56k over normal phone lines was indeed tricky.

56k modems didn’t always negotiate to the full 56k. The handshaking allowed connections at much slower speeds. It depended on the quality of the line. This is the US - we didn’t have ISDN, at least no one I knew had it in 1996.

In order to get 56k, you needed to be on a reasonable quality line, and there needed to be an all digital (PRI) connection between the Telco end of your phone line and your ISP.

If your line was noisy good luck. If your line had loading coils in the path between the CO and you, that would help your voice calls but make 56k harder to achieve (and was definitely problematic for DSL). Most telephone lines had loading coils every wire mile between the CO and the customer. If you had any of the older wonky stuff telcos used to magic more pairs for customers out of thin air, chances are they wouldn't work at 56k.

56k modems is an application of Shannon’s Theorem.

You only got max speeds where the noise was low enough.

i think they're saying the actual speeds you'd get. i'd get faster speeds late at night (just me?)

sometimes you'd also reconnect because the handshake got messed up and you'd connect at 33.6 instead of 'real' 56k