The Symmetry454 calendar (Sym454) is a proposal for

calendar reform Calendar reform or calendrical reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design. Principles The prime objective of a calendar is to unambiguo ...

created by Irv Bromberg of the

University of Toronto The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...

Canada Canada is a country in North America. Its ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, covering over , making it the world's second-largest country by to ...

. It is a

perennial A perennial plant or simply perennial is a plant that lives more than two years. The term ('' per-'' + '' -ennial'', "through the years") is often used to differentiate a plant from shorter-lived annuals and biennials. The term is also widel ...

solar calendar A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a solar calendar. ...

that conserves the traditional month pattern and 7-day

week A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are of ...

, has symmetrical equal quarters in 82% of the years in its 293-year cycle, and starts every month on Monday.

Calendar year

The proposed calendar is laid out as follows: : The last 7 days of December, shown in grey, are

intercalary days Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months. ...

that are appended only to the end of leap years. The idea of months having 4 or 5 whole weeks is not new, having been proposed in the 1970s by Chris Carrier for the Bonavian Civil Calendar and by Joseph Shteinberg for his "Calendar Without Split Weeks". Whereas the former has 5 + 4 + 4 weeks per quarter, and the latter has 4 + 4 + 5 weeks per quarter, the Symmetry454 Calendar has a ''symmetrical'' 4 + 5 + 4 weeks per quarter, which is why it is named Symmetry454. Balanced quarters are desirable for businesses because they aid in fiscal planning and analysis. All months have a whole number of weeks, so no month ever has a partial week. Each day number within a month falls on the same weekday in all months and years; in particular,

Friday the 13th Friday the 13th is considered an unlucky day in Western superstition. It occurs when the 13th day of the month in the Gregorian calendar falls on a Friday, which happens at least once every year but can occur up to three times in the same year. ...

never occurs under this calendar. All holidays, birthdays, anniversaries, etc. are permanently fixed. All ordinal day and week numbers within the year are also permanently fixed.

Leap rule

Unlike the

World Calendar The World Calendar is a proposed reform of the Gregorian calendar created by Elisabeth Achelis of Brooklyn, New York in 1930. Features The World Calendar is a 12-month, perennial calendar with equal quarters. Each quarter begins on a Sunday ...

or the

International Fixed Calendar The International Fixed Calendar (also known as the IFC, Cotsworth plan, the Cotsworth calendar and the Eastman plan) is a proposed calendar reform designed by Moses B. Cotsworth, first presented in 1902. The solar calendar divides the year into ...

(also known as the 13-Month Calendar), there are no individually scheduled intercalary "null" days outside of the traditional 7-day week. Instead, alignment of the weekday cycle with New Year Day is accomplished by using a leap week, which is appended once every 5 or 6 years. In

leap year A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) added to keep the calendar year synchronized with the astronomical year or ...

s, December becomes a 5-week month. The leap week is shown in grey text in the above calendar year. The preferred Symmetry454 leap rule is based upon a symmetrical 293-year leap cycle having 52 leap years at intervals that are as uniformly spread as possible: This expression inherently causes leap year intervals to fall into sub-cycle patterns of (5+6+6) = 17 or (5+6) = 11 years, which symmetrically group to 17+11+17 = 45 or to 17+17+11+17+17 = 79 years. The full symmetrical grouping for each cycle is: 45+79+45+79+45 = 293 years. Outside of calendar theory, this arrangement is known as

maximal evenness In scale (music) theory, a maximally even set (scale) is one in which every generic interval has either one or two consecutive integers specific intervals-in other words a scale whose notes (pcs) are "spread out as much as possible." This prope ...

. The 52/293 leap cycle has a calendar mean year of 365+⁷¹/₂₉₃ days, or 365 days 5 hours 48 minutes and about 56.5 seconds, which is intentionally slightly shorter than the present era mean northward equinoctial year of 365 days 5 hours 49 minutes and 0 seconds (mean solar time).

Calendar arithmetic

The ''Kalendis'' calendar calculator demonstrates the Symmetry454 calendar and interconverts dates between Symmetry454 and a variety of other calendars. The Symmetry454 arithmetic is fully documented and placed in the public domain for royalty-free computer implementation. Officially, Symmetry454 has been running since January 1, 2005, which was the first New Year Day after it came into existence. Its proleptic epoch, however, was on the same day as the proleptic epoch of the Gregorian Calendar = January 1, 1 AD.

Easter on a fixed date

Tentatively, Sunday April 7 on the Symmetry454 Calendar is proposed as a fixed date for Easter, based on a frequency analysis of the distribution of the Gregorian or Astronomical Easter dates. There are only five dates that Easter can possibly land on within the Symmetry454 Calendar, because only day numbers divisible by 7 can be a Sunday. The three highest-frequency dates upon which Easter can land are March 28, April 7, and April 14. Selecting the middle date, April 7, would fix Easter at its median position within its distribution range.

References

* "Designs for a new year", in the "Innovators" section of the Toronto Star newspaper, Friday, December 24, 2004, page A3, by reporter Peter Gorrie. * "''Star Trek'' Math Inspires Calendar Reform", Discovery Channel, Thursday, December 30, 2004, by Jennifer Viegas, Discovery News. *
Time and Again, the Calendar Comes Up Short
Sticklers for Symmetry Lament Imperfections in the 400-Year-Old Gregorian System; Earth's Inconvenient Orbit", The Wall Street Journal, December 31, 2009, by Charles Forelle, ''The Numbers Guy''. *
New Year’s Revolution: A proposed new calendar would give February an extra week and start every month on a Monday
, University of Toronto Magazine, in Leading Edge, Winter 2011, by Scott Anderson.

External links