Other calendars have one (or multiple) larger units of time.Calendars that contain one level of cycles: Very commonly a calendar includes more than one type of cycle, or has both cyclic and non-cyclic elements. For example, the vast majority of them track years, months, weeks and days. A day may consist of the period between sunrise and sunset, with a following period of night, or it may be a period between successive events such as two sunsets. A lunar calendar is one in which days are numbered within each lunar phase cycle.A full calendar system has a different calendar date for every day.Thus the week cycle is by itself not a full calendar system; neither is a system to name the days within a year without a system for identifying the years.This resulted in an observation-based lunar calendar that shifts relative to the seasons of the solar year.The first calendar reform of the early modern era was the Gregorian calendar, introduced in 1582 based on the observation of a long-term shift between the Julian calendar and the solar year.The course of the Sun and the Moon are the most evident forms of timekeeping, and the year and lunation were most commonly used in pre-modern societies worldwide as time units.
This was mostly based on observation, but there may have been early attempts to model the pattern of intercalation algorithmically, as evidenced in the fragmentary 2nd-century Coligny calendar.The simplest calendar system just counts time periods from a reference date. Virtually the only possible variation is using a different reference date, in particular, one less distant in the past to make the numbers smaller.Computations in these systems are just a matter of addition and subtraction.Consecutive days may be grouped into other periods such as the week.Because the number of days in the tropical year is not a whole number, a solar calendar must have a different number of days in different years.