on the half hour

prepositional phrase3

1. •
   Happening hourly, but at 30 minutes past each hour; ie, 08:30, 09:30 etc.

   • Trains leave here for New York every hour on the half hour.
2. •
   Happening on the hour and at 30 minutes after the hour.

   • In one corner is an old grandfather's clock; the chimes are on the half-hour. — 2011
3. •
   At thirty minutes into a half.