Lyle, your problem sounds as if the minute hand is mounded 30 minutes
opposite of where it belongs.  The minute hand needs to be removed,
moved 30 minutes, and then re-installed.  Not seeing the clock, I can't
tell you how to do this.

More recent clocks have a hand-nut that needs to be unscrewed.  Older
clocks usually have a tapered pin through a hole.  If this is the case,
using needle-nose pliers, remove the pin, carefully remove the cup
washer so you don't lose it, remove the hand, and move it 180 degrees,
and then replace the cup washer and pin.  If there is a hand-nut, it
may be too tight to loosen by fingers.  Again, using needle-nose pliers
(preferably curved ones, but regular ones will work), loosen the nut
and then unscrew it.  Remove the hand as above, move it 180 degrees (30
minutes), and replace the hand and nut.

This should solve the problem, if the clock is designed to play only on 
the hour.  If it is designed to play on both the hour and half hour,
then there is a bent or broken pin inside the clock.  The movement will
need to be sent to a capable clock repairman.

Vincent Morgan,
New York City