Lunar calendar average length of the synodic month is days. Thus it is convenient if months generally alternate between 29 and 30 days (sometimes termed respectively “"hollow"” and “"full"”). The distribution of "hollow" and "full" months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed: These fractions can be used to construct a lunar calendar, or in combination with a solar calendar
Lunar month The nodes of the Moon's orbit precesses 360° in about 6,798 days (18.6 years). A draconic month is shorter than a sidereal month because the nodes precess in the opposite direction to that in which the Moon is orbiting Earth, one rotation every 18.6 years. Therefore, the Moon returns to the same node slightly earlier than it returns to meet the same reference star. Regardless of the culture, all lunar months approximate the mean length of the synodic month, the average period the Moon takes to cycle through its phases (new, first quarter, full, last quarter) and back again: 29–30