Four Calendars

The new Hebrew calendar can be seen as the endpoint of four calendars, against the four worlds. In order to present them we change the scale of the parameter z, from days to Chalakim. That is, we change, in the Gauss algorithm, the line

m0 = T - (10. + n) * K + L + 14. - z/2.;

into

m0 = T - (10. + n) * K + L + 14. - (z/1080.)/24.;

and we simultaneously change in the algorithm of the new Hebrew calendar the function gauss into:

public static Gauss gauss(int year, int n) {
return new Gauss (year, n, ((int) ((10 + n - (10 + n) % 19)/19) - ((10 + n >=0)?0:1))*1080*12);
}

We call this the fourth Hebrew calendar.

The third Hebrew calendar is the calendar obtained from this by replacing the long expression that is the third argument, for the value 642:

public static Gauss gauss(int year, int n) {
return new Gauss (year, n, 642);
}

The second Hebrew calendar is obtained from the previous one by ignoring parameter n. This actually was the calendar proposed by Aharon Ben Meir:

public static Gauss gauss(int year, int n) {
return new Gauss (year, 0, 642);
}

Finally we have the first Hebrew calendar by replacing 642 by 0:

public static Gauss gauss(int year, int n) {
return new Gauss (year, 0, 0);
}

We refer to the first Hebrew calendar as the old Hebrew calendar, and to the second calendar as the calendar of Eretz Yisrael. This calendar is improved by the third Hebrew calendar, called the calendar of El Shadai, and finally we have the fourth Hebrew calendar, the new Hebrew calendar.