Expressing hourly temporal recurrence

What is the most idiomatic way to put into words a situation where a recurring event happens every hour at a certain minute. For example, consider that some event takes place at the tenth minute of each hour: 0:10AM, 1:10AM, 2:10AM, ...

My first ideas were "every hour at the tenth minute" or "every hour at minute 10". Are these options idiomatic and if not, what would be an idiomatic way of expressing this matter?


Solution 1:

There are three special cases:

  1. “Every hour [on the hour]” — 12:00, 1:00, etc.
  2. “Every hour on the half-hour” — 12:30, 1:30, etc.
  3. “Every hour on the quarter-hour” — 12:15, 1:15, etc.

Any other offset, as @verbose succinctly pointed out, is “Every hour at x [minutes] past the hour.”

(Sometimes "at" is substituted for "on", as is "after" for "past". Anything is square brackets is optional.)

“Nietzsche, with his theory of eternal recurrence. He said that the life we lived we’re gonna live over again the exact same way for eternity. Great. That means I’ll have to sit through the Ice Capades again.”
― Woody Allen

Solution 2:

The standard form is Every hour at x [minutes] past the hour. Merriam-Webster's example is this:

Trains leave every hour at ten minutes past the hour.

The minutes is optional, and my personal preference is to leave it out.

Since AmE tends to use after rather than past to express time, the following might be preferable depending on your audience:

Trains leave every hour at ten after the hour.

In conversation, one could be quite succinct: Every hour at ten past/after, leaving out the subsequent "the hour", would be transparent to most native speakers.