I'm sorry, the situation is a bit more complicated, than it looks like:
Bach indeed was born on March 21, 1685 in Eisenach, but not on 'our'
21st of March, due to the fact, that the protestant Germany left the
Julianic Calendar not earlier than in the year 1700. So Bach's
'original' birthdate is a Julianic one, while we use the Gregorianic
calendar system. The difference between both systems was computed at
Bach's lifetime to 10 days. Thus we have to celebrate JSB's historically
correct birthday on (our) March 31st....
Almost all protestant German countries changed their still Julianic
calendar in Febrauary/March 1700 to the Gregorianic system (March 1st -a
Monday- followed February 18th -Sunday Invocavit- as a regular
weekday), which confronted Bach not only with10 lost days of his life,
he died 1750 subsequently under a Gregorianic date and prepared around
the calendar break 1700 for his last days in Ohrdruf and for his
departure to Lüneburg, to initiate a probably extraordinarily important
phase in his career as a young, gifted musician.
Hans-Joachim