BORN March 21, 1685 (Julian / Roman Calendar) AND March 31, 1685 (Gregorian calendar).
When Johann Sebastian Bach was born in 1685 in Protestant Germany, and where the Julian (Roman) calendar (created in 45 BC) was still being observed, his family's calendar showed March 21.
However, it was long known that the calendar dates had been 'drifting' for centuries; a day every 128 years it turns out. The longest and shortest days of the year were now about 10 days off the original ancient calendar dates, and Bach's birth likewise was uncertain.
About 100 years before, the Catholic Pope Gregory and his Italian astronomer scientists established the more precise calendar in the year 1582.
However, England and other Protestant countries and regions were slow to acknowledge any Catholic wisdom. They did eventually adopt the more precise Gregorian calendar, with the Lutheran Protestants in Germany officially changing over in 1700, and here's an important detail, with the legal stipulation that all Julian / Roman calendar dates prior to Dec. 31, 1699 would remain valid.
Since JS Bach was a Protestant Lutheran born in that time frame, he always considered his birthday to be an unaltered March 21 date, and was legally allowed to claim that, even after his 15th birthday.
Johann was pleased to find that his March 21 date on the new calendar now shared the beginning of Spring, and this may have helped to shape his preference to hold onto the original date.
Since the calendar days jumped ahead, when you readjust to the correct location in Earth's path around the sun, the start of Spring (vernal equinox) landed (and still does) on any one of 3 dates any given year, March 19, 20, or 21, pretty much right on his birthday every year. At least so long as his birthday was still on March 21... Never mind that the actual solar position is really at Gregorian calendar's March 31.
If you take the numbers from his original DD-MM-YY birthday, and match the numbers to their corresponding letters of the alphabet:
Okay, ignore the E, pretty close. So, now you're asking yourself,
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 with my group, Monsters of Bach, every day with occasional unadvertised hit-n-run concerts in strategic Silicon Valley locations ... see you out there.