With the lunar calendars, a solar year was based upon a 19-year period Seven of these years had 13 months. The entire period contained 235 months. Still using the lunation value of 29 and a 1/2 days devised by lunatics, this made a total of 6,932 and 1/2 days, while 19 solar years added up to 6,939.7 days, a difference of just one week per period and about five weeks per century.
A year is defined as being the interval between two successive passages of the Sun through the vernal equinox. (In actuality, the earth is orbiting around the Sun.) The vernal equinox occurs the instant the Sun is above the earth’s equator while traveling from the south to the north. (We are assuming here that it knows which way it’s going. That is more than I can say for myself most of the time.) This is considered the beginning of Spring. The two passages of the Sun through the vernal equinox comprise a tropical year, whose length determines the repetition of the seasons. The exact length of a tropical year is 365.24219 days.