What country has this? Definitely not USA, Canada, Mexico, Australia, Spain, France, Italy, or Portugal.
EDIT: My mistake, thank you folks! Your experience traveling abroad is different than mine. For a proper train in especially Spain or Italy during off-peak hours, there were often only one per day for many routes.
Caltrain and BART are both still utter disgraces.
BART achieved 4 minute headways through the San Francisco subway portion. That also effectively limits headways on branch lines (absent additional trackage through SF) as when multiple 15m headway lines are combined the net headway is reduced.
For longer-haul commute service, 5--10 m headways aren't unreasonable, and a dedicated East-bayshore or Peninsula bayshore BART line might be able to accomplish this, with either a transfer or dedicated trackage in SF itself.
(Muni Metro runs on what was intended to be additional BART trackage.)
See:
Many metro lines in Paris run at less than 3 minute intervals during peak times (when there aren't any "incidents"). Even the aging line 6 has around 3 minute intervals during rush hour.
I'm not very familiar with the Bay Area, so I don't know how these would compare to the line described by OP distance-wise. Longer distance trains in Paris (RER and other suburban lines) don't run at 3 minute intervals either.
or a train every 1 minute 40 seconds
(2 track railway, all station stops)