In this chapter, we use formulas from Section 1.12 to cast a number of the calendars presented in Part I into a unified framework. Years must be determined by the occurrence of some “critical” mean annual event, like a mean equinox or mean solstice. Months must also follow a uniform pattern. In single-cycle calendars, new years begin on the day the critical annual event happens before (or possibly at) some critical time of day. In double-cycle calendars, months begin on the day of a critical mensual event, and years begin with the month associated with the critical annual event.

Single Cycle Calendars

There are four “single-cycle” paradigms for calendars, as we independently allow

1. the determining critical annual event to occur strictly before, or to occur at or before, some critical time of day, and

2. the pattern of months to follow a fixed yearly pattern, according to equations (1.78)–(1.81) or to follow a mean monthly pattern, in tune with the yearly pattern.