11 Days

11 Days in India  
Indian astronomers looked especially to the Moon (Soma). The actual period of lunation is 29.53 days, so that 12 lunar months are completed in 354.37 days; and the Utsarniyanayanam calendar accounted for this by allowing a year of 12 exact lunar months, with 11 days reserved for the Atiratra sacrifice. An intercalary period of 12 days was later instituted. http://www.geocities.com/sarabhanga/yuga.html
11 Days in Babylonia 

There is another viewpoint that the Stems and Branches were most probably influenced by Babylonian (circa 1800 – 500 BCE) astronomy. 

The Babylonians, too, calculated days according to Lunar and Solar time. They, too, found out about the waxing and waning of the Moon from its orbit around the Earth, averaging 29.5 (29.5306) days. In 12 months, the number of days in Lunar time would amount to only 354 days.

Solar time, which is the Earth’s orbit around the Sun, takes approximately 365 (365.2419) days. The difference between Solar time and Lunar time is roughly 11 days. Therefore, by a Royal Decree, the Babylonian court astronomers were instructed to add an Intercalary month (Leap Month) whenever necessary to balance the calendar.


11 Days in  Hebrew Tradition connected with Phi

See: 11 Day gap between Solar and Lunar Years

Early Western alphabets have 22 letters, notably, Babylonian, Phoenician, Hebrew and Greek. Here the obvious astronomical connection is with the number 11, which has a rich symbolism of its own. There was an 11 day annual difference between the lunar and the solar calendar. Given solar and lunar letters, then there would be 11 + 11 = 22 letters.