Two Integral-Week Solar Calendars

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Two Integral-Week Solar Calendars

Peter Meyer
Karl said: "The main reason I like months of 4 or 5 weeks for a leap
week calendar [is that] a leap week can be accommodated in such a month

Months in the Gregorian Calendar are a misnomer, since they have no
connection with Moon cycles.  Who needs months?  Only those (almost
everyone) who can't imagine anything different from our present system
of time periods.

I define an "integral-week calendar" as a calendar in which the (solar)
years always have an integral number of weeks, where 'weeks' consist of
a certain fixed number of days, not necessarily seven. In an
integral-week calendar all days are part of some week.

In 2001 I invented two such calendars (defined at ) one based on a week of
5 days and one based on a week of 6 days.

The Integral Five-Day Week Calendar is a leap week calendar in that a
'normal' year has 73 5-day weeks, and a 'long' year has 74 5-day weeks.
Thus the number of days in a calendar year is 365 for normal years and
370 for long years.

The Integral Six-Day Week Calendar, is not a leap week calendar, since
a 'normal' year has 61 6-day weeks, and a 'short' year has 60 6-day
weeks. Thus the number of days in a calendar year is 366 for normal
years and 360 for short years.

In both of these calendars (due to how 'long' and 'short' years are
defined) the average length of the calendar year is exactly equal to
the vernal equinox year, that is, 365.2424 mean solar days.

Each of these integral-week calendars can conveniently be divided into
quarters, in one case of 18 or 19 weeks, and in the other of 15 or 16

The Integral Six-Day Week Calendar is more versatile in that the normal
and short years may be divided into halves, thirds, quarters, fifths,
sixths, tenths, fiftheenths, twentieths and thirtieths.

Only complete mental lethargy and total lack of imagination on the part
of almost all humans on this planet prevents either of these calendars
from being considered seriously as a replacement for the archaic
Gregorian Calendar.  And, of course, the cost and inconvenience of such
a replacement.

Peter Meyer