The major obstacle with diagnosing an intermittent problem is knowing how long to wait for no more such incidents before declaring that the cause is known. The problem symptoms I only notice every month or so. If I do as you say, I would need to put up with having only one phone in the house out of the dozen I normally use. Plus I would need to do so for several months.
Oh, I agree with this as well. I said my best characterisation of the sound as either a fax service or the primary tone in a baud-rate negotiation is based only on personal (& fallable) recollection. I'm not sure if you saw it, but I did mention that I already have a shoebox-sized cassette recorder with patch cord to record the phone line. I intend to use this to analyze the tone for a definitive identification. If it is a modem, then I suppose I will need to set up a dial-up networking service as well.
In fact, over the years I have noticed that occaisionally people call me me and they say that my line was 'busy' earlier when I have been home AND not using the phone. I always concluded they must have dialed incorrectly.
It may very well be that whatever is happening is going on more often, and I only notice it when someone calls simultaneously.
Seriously, thanks. You have shown me the origin of the problem.