"Meshing with the 260-day count is a 'Vague Year' or Haab of 365 days, so called because the actual length of the solar year is about a quarter-day more, a circumstance that leads us to intercalate one day every four years to keep our calendar in march with the sun.

Although the Maya were perfectily aware that the Haab was shorter than the tropical year, they did not change the calendar accordingly.

Within the Haab, there were 18 named 'months' of 20 days each, with a much-dreaded interval of 5 unlucky days added at the end.

The Maya New Year started with 1 Pop, the next day being 2 Pop, etc. The final day of the month, however, carried not the coefficient 20, but a sign indicating the 'seating' of the month to follow, in line with the Maya philosophy that the influence of any particular span of time is felt before it actually begins and persists somewhat beyond its apparent termination."

(The Maya)

This is similar - but not the same as - my idea about 59 belonging to the end of a double-moon period, while 60 is the beginning of the new period. The Mayan sign for 20 (similar to our 10 and the Sumerians 60) was not written as 'twenty' but as 'seating', that is the similarity. However, while 60 is the start of a new double-moon period, the Mayan time of seating belonged to the old period, not the new one. I.e. not the same.