Seeking help with a time calculation

Platform is Linux.

In an Expect script, I want to calculate the number of seconds until the
next "X minutes after the hour".  E.g., if X is 37 and the current time is
15:30:30, then the result I seek would be: 390.  If X is 37, and the
current time is 15:50, then the result would be: 2820.

It's the number of seconds I have to wait (sleep) until that time arrives.

I have a method in AWK, which I can (and do) call from my Expect script,
but I am curious if there is a (simple) native Tcl way to do it.
--
Men rarely (if ever) manage to dream up a God superior to themselves.
Most Gods have the manners and morals of a spoiled child.