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Well, firstly the original tax year followed the ancient Roman tradition of beginning the year with Spring, actually on the first Quarter day or Lady Day on March 25th.
Secondly to get around people's legitimate objection in 1752 that they would have been taxed for the 11 days that the government wanted to arbitrarily remove from history, the tax year was moved 11 days forwards into the new year.
The easiest universal timepiece to quickly observe is the moon.
Because of the motion of the moon about the earth and sun it conveniently passes through four easy to identify phases: new, first quarter, full, last quarter and back to new again.
This is the Metonic Cycle, which is named after the ancient Athenian Meton who discovered it in the fifth century BC (although this knowledge could easily have made its way from China).
There is another way to adjust the years and months so that they remain in rough synchronization without using leap days and that is to every few years introduce a whole new 'leap' month.
To work out when a festival should occur in any year observations are made of the moon relative to the sun so that the two systems are synchronised for the year.
The Eastern Orthodox Church has yet to make the change.
Incidentally, have you ever wondered why the end of the UK tax year is April 5th rather than something sensible like December 31st?
In the Christian year some feasts stay put including Christmas; All Souls Day and saint's days while others change - they are the movable feasts (e.g.
Palm Sunday, Easter, Ascension Day, Whit Sunday) that are tied to the moon.