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The Symmetry454 calendar (Sym454) is a proposal for calendar reform created by Irv Bromberg of the University of Toronto, Canada.^[when?] It is a perennial solar calendar that conserves the traditional month pattern and 7-day week, 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:

Quarter

1st month

2nd month

3rd month

1st

2nd

3rd

4th

The last 7 days of December, shown in grey, are intercalary days 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 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 or the International Fixed Calendar (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 years, 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:

It is a leap year only if the remainder of (52 × Year + 146) / 293 is less than 52.

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.

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). It is intentionally slightly shorter because the shorter the difference the less often a leap week needs to be added. If it were slightly bigger a week would need to be removed from the calendar (in effect a negative leap), which is more undesirable and disruptive than adding one.

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 possible dates for Easter within the Symmetry454 Calendar, since 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

Gorrie, Peter (December 24, 2004). "Designs for a new year". Innovators. Toronto Star. p. A3.
Viegas, Jennifer (December 30, 2004). "Star Trek Math Inspires Calendar Reform". Discovery News. Discovery Channel.
Forelle, Charles (December 31, 2009). "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 Numbers Guy. The Wall Street Journal.
Anderson, Scott (Winter 2011). "New Year's Revolution: A proposed new calendar would give February an extra week and start every month on a Monday". Leading Edge. University of Toronto Magazine.

External links

The Symmetry454 Calendar (full specifications, FAQs, arithmetic)
The Kalendis Calendar Calculator (freeware)
The Lengths of the Seasons (numerical integration analysis)
Solar Calendar Leap Rule Studies (shows why the 52/293 leap rule is preferred)

@@ Line 1: / Line 1: @@
+{{short description|Proposal for calendar reform}}
 {{more footnotes|date=July 2015}}
-The '''Symmetry454 Calendar (Sym454)''' is a proposal for [[calendar reform]] created by Dr. Irv Bromberg of the [[University of Toronto]], Canada. It is a [[perennial calendar|perennial]] [[solar calendar]] that conserves the traditional 7-day [[week]], has symmetrical equal quarters, and starts every month on Monday.
+The '''Symmetry454 calendar''' ('''Sym454''') is a proposal for [[calendar reform]] created by Irv Bromberg of the [[University of Toronto]], [[Canada]].{{when|date=June 2024}} It is a [[perennial calendar|perennial]] [[solar calendar]] that conserves the traditional month pattern and 7-day [[week]], has symmetrical equal quarters in 82% of the years in its [[Symmetry454#Leap rule|293-year cycle]], and starts every month on Monday.
 == Calendar year ==
@@ Line 16: / Line 17: @@
 |+style="color:white;background:blue" title="01, 1-1"| January
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="01"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 26: / Line 27: @@
 | 22 || 23 || 24 || 25 || 26 || 27 || 28
 |-
-| 29 ||    ||    ||    ||    ||    ||    &nbsp;
+|    ||    ||    ||    ||    ||    ||    &nbsp;
 |}
 |
@@ Line 32: / Line 33: @@
 |+style="color:white;background:blue" title="02, 1-2"| February
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="05"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 48: / Line 49: @@
 |+style="color:white;background:blue" title="03, 1-3"| March
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="10"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 66: / Line 67: @@
 |+style="color:white;background:green" title="04, 2-1"| April
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="14"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 82: / Line 83: @@
 |+style="color:white;background:green" title="05, 2-2"| May
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="18"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 98: / Line 99: @@
 |+style="color:white;background:green" title="06, 2-3"| June
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="23"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 116: / Line 117: @@
 |+style="color:white;background:red" title="07, 3-1"| July
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="27"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 132: / Line 133: @@
 |+style="color:white;background:red" title="08, 3-2"| August
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="31"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 148: / Line 149: @@
 |+style="color:white;background:red" title="09, 3-3"| September
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="36"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 161: / Line 162: @@
 |}
 |-
-!style="color:black;background:Darkblue"| 6th
+!style="color:black;background:gold"| 4th
 |
 {| border="1" style="border-collapse:collapse"
-|+style="color:black;background:darkblue" title="16, 6-1"| Ceattomber
+|+style="color:black;background:gold" title="10, 4-1"| October
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="40"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 180: / Line 181: @@
 |
 {| border="1" style="border-collapse:collapse"
-|+style="color:black;background:darkblue" title="17, 6-2"| Wearmber
+|+style="color:black;background:gold" title="11, 4-2"| November
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="44"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 196: / Line 197: @@
 |
 {| border="1" style="border-collapse:collapse"
-|+style="color:black;background:darkblue" title="18, 6-3"| Jumpbeanmber
+|+style="color:black;background:gold" title="12, 4-3"| December
 |- style="font-family:monospace"
 ! Mo || Tu || We || Th || Fr || Sa || Su
 |- title="49"
 |  1 ||  2 ||  3 ||  4 ||  5 ||  6 ||  7
@@ Line 223: / Line 224: @@
 ==Leap rule==
-Unlike [[the World Calendar]] or the [[International Fixed Calendar]] (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]]s, December becomes a 5-week month. The leap week is shown in grey text in the above calendar year.
+Unlike the [[World Calendar]] or the [[International Fixed Calendar]] (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]]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:
-{{quote|It is a leap year only if the [[Modulo operation|''remainder'']] of ( 52 × ''Year'' + 146 ) / 293 is less than 52.}}
+{{quote|It is a leap year only if the [[Modulo operation|''remainder'']] of (52 × ''Year'' + 146) / 293 is less than 52.}}
-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.
+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]].
-The 52/293 leap cycle has a calendar mean year of 365+<sup>71</sup>/<sub>293</sub> 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).
+The 52/293 leap cycle has a calendar mean year of 365+<sup>71</sup>/<sub>293</sub> 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). It is intentionally slightly shorter because the shorter the difference the less often a leap week needs to be added. If it were slightly bigger a week would need to be removed from the calendar (in effect a negative leap), which is more undesirable and disruptive than adding one.
 ==Calendar arithmetic==
@@ Line 239: / Line 240: @@
 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.
+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 a few 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.
+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 possible dates for Easter within the Symmetry454 Calendar, since 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.
 == See also ==
+* [[4–4–5 calendar]]: Similar month structure.
+==References==
-* [[4-4-5 Calendar]] Similar month structure
+* {{cite news |title=Designs for a new year |department=Innovators |newspaper=Toronto Star |date=December 24, 2004 |page=A3 |first=Peter |last=Gorrie}}
+* {{cite episode |title=''Star Trek'' Math Inspires Calendar Reform |network=Discovery Channel |date=December 30, 2004 |first=Jennifer |last=Viegas |series=Discovery News}}
+* {{cite news |url=https://www.wsj.com/articles/SB126212850216209527 |title=Time and Again, the Calendar Comes Up Short: Sticklers for Symmetry Lament Imperfections in the 400-Year-Old Gregorian System; Earth's Inconvenient Orbit |newspaper=The Wall Street Journal |date=December 31, 2009 |first=Charles |last=Forelle |department=The Numbers Guy}}
+* {{cite magazine |url=http://www.magazine.utoronto.ca/leading-edge/irv-bromberg-symmetry454-new-calendar-idea/ |title=New Year's Revolution: A proposed new calendar would give February an extra week and start every month on a Monday |magazine=University of Toronto Magazine |department=Leading Edge |date=Winter 2011 |first=Scott |last=Anderson}}
 ==External links==
@@ Line 254: / Line 262: @@
 *[http://individual.utoronto.ca/kalendis/seasons.htm The Lengths of the Seasons] (numerical integration analysis)
 *[http://individual.utoronto.ca/kalendis/leap/index.htm Solar Calendar Leap Rule Studies] (shows why the 52/293 leap rule is preferred)
-==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.
-* "[https://www.wsj.com/articles/SB126212850216209527 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''.
-* "[http://www.magazine.utoronto.ca/leading-edge/irv-bromberg-symmetry454-new-calendar-idea/ 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.
 {{calendars}}
@@ Line 266: / Line 268: @@
 [[Category:Leap week calendars]]
 [[Category:Specific calendars]]
+[[Category:2005 introductions]]