Editing Hebrew calendar (section)

===Leap year calculations===
{{See also|Golden number (time)}}
To determine whether a Jewish year is a leap year, one must find its position in the 19-year Metonic cycle. This position is calculated by dividing the Jewish year number by 19 and finding the [[remainder]]. (Since there is no year 0, a remainder of 0 indicates that the year is year 19 of the cycle.) For example, the Jewish year {{#time:xjY}} divided by 19 results in a remainder of {{#expr:{{#time:xjY}}mod 19}}, indicating that it is year {{#ifexpr:{{#time:xjY}}mod 19|{{#expr:{{#time:xjY}}mod 19}}|19}} of the Metonic cycle. The Jewish year used is the ''anno mundi'' year, in which the year of creation according to the Rabbinical Chronology (3761 BCE) is taken as year 1. Years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle are leap years. The Hebrew mnemonic GUCHADZaT {{lang|he|גוחאדז״ט}} refers to these years,{{efn|In which the letters refer to [[Hebrew numerals]] equivalent to 3, 6, 8, 1, 4, 7, 9.}} while another memory aid refers to musical notation.{{efn|Intervals of the [[major scale]] follow the same pattern as do Jewish leap years, with ''do'' corresponding to year 19 (or 0): a [[whole step]] in the scale corresponds to two common years between consecutive leap years, and a [[half step]] to one common year between two leap years. This connection with the major scale is more plain in the context of [[19 equal temperament]]: counting the tonic as 0, the notes of the major scale in 19 equal temperament are numbers 0 (or 19), 3, 6, 8, 11, 14, 17, the same numbers as the leap years in the Hebrew calendar.}}

Whether a year is a leap year can also be determined by a simple calculation (which also gives the fraction of a month by which the calendar is behind the seasons, useful for agricultural purposes). To determine whether year ''n'' of the calendar is a leap year, find the remainder on dividing [(7&nbsp;×&nbsp;''n'')&nbsp;+&nbsp;1] by 19. If the remainder is 6 or less it is a leap year; if it is 7 or more it is not. For example, the {{Hebrew calendar/c|{{#time:xjY}}}} The {{Hebrew calendar/c|{{#expr:{{#time:xjY}}+1}}}}<ref>{{cite book |last1=Dershowitz |first1=Nachum |last2=Reingold |first2=Edward M. |title=Calendrical Calculations |title-link= Calendrical Calculations |date=2007 |edition=3rd |publisher=Cambridge University Press |page=91}}</ref> This works because as there are seven leap years in nineteen years the difference between the solar and lunar years increases by {{frac|7|19}} month per year. When the difference goes above {{frac|18|19}} month this signifies a leap year, and the difference is reduced by one month.

The Hebrew calendar assumes that a month is uniformly of the length of an average [[synodic month]], taken as exactly {{frac|29|13753|25920}} days (about 29.530594 days, which is less than half a second from the modern scientific estimate); it also assumes that a [[tropical year]] is exactly {{frac|12|7|19}} times that, i.e., about 365.2468 days. Thus it overestimates the length of the [[tropical year]] (365.2422 days) by 0.0046 days (about 7 minutes) per year, or about one day in 216 years. This error is less than the [[Julian Calendar|Julian years]] (365.2500 days) make (0.0078 days/year, or one day in 128 years), but much more than what the [[Gregorian Calendar|Gregorian years]] (365.2425 days/year) make (0.0003 days/year, or one day in 3333 years).