Welcome to Bach Monster!
BORN March 21, 1685 (Julian / Roman Calendar) AND March 31, 1685 (Gregorian calendar).
Protestant Germany adopted the (more precise) Gregorian calendar in 1700, with the legal stipulation that all dates prior to Dec. 31, 1699, remain valid.
Since JS Bach was a Protestant Lutheran born in that timeframe, he always considered his birthday to be unchanged, MARCH 21, even after his 14th birthday.
He might have had extra reasons for a preference to hang onto the original date:
In summary, I contend that it is fundamentally proper to celebrate the music and life of JSB from his personally perceived, legally recognized birthday date of MARCH 21, AND ALSO the somewhat astronomically correct positional date of MARCH 31, and all dates between, linked as an 11-day birthday decad+.
You may decide to drink some 'bock' beer, you may choose to look up this JSB character on your interwebs, or just "Rock out with your Bach out".
As for me, I'm playing my Bach arrangements every day with occasional unadvertised hit-n-run concerts in strategic Silicon Valley locations ... see you out there.