I have never really noticed a problem with modems and the double beat ring tone however. There used to be loads of problems with the voicemail and call divertion tones here which originally were broken dial tones. They got around this by changing it to 2 different frequencies that just switch in and out so the modem still hears a continious tone but the caller hears the dial tone stepping up and down.
450Hz + 350Hz
call diversion is equal time with each tone
message waiting is the normal 450 hz tone rapidly interupted with the 350hz.
Also if you set modems to UK sometimes you had problems with recognising the ring tone here particularly in exchanges that still apply the progress tone (bebebebebebe) while they were waiting for a free modem at the ISP.
The progress tone's rarely heard on fixed line calls these days. I think it's actually being phased out under some ITU rules. I notice France Telecom seem to be using it less and less too.
Even though it's MUCH more rapid than a busy tone or a "reorder tone" ? the cheapo modems used to see it as busy.
I actually like the Irish tone system. It's extremely easy to understand compared to what i've heard elsewhere and that's not just because I'm used to it. It's just very self-explanatory.
Dialtone = continious 450Hz.
Busy = 450hz busy tone (similar to UK)
Congestion = same
The is no number unobainable tone it's always an announcement or the 3 tone dooo deee dooo.. thing.
Ring tone is same as the UK
I've found a lot of the European systems confusing and I don't like the non-warbling flat ring tones used in Europe. I prefer ours it's much more like what a phone sounds like ringing.
Even if they didn't change the actual ring pattern sent to the phones I think it would be nice if for once the rest of Europe adopted our system rather than the DIN / NF standard