Sexagesimal calendar

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The sexagesimal calendar is a new proposal for a civil calendar, with universal scope, which is presented as a complete replacement of the Gregorian calendar for this purpose. It is a solar calendar, which follows the northern hemisphere winter solstice unlike the Gregorian, or many other solar calendars [a] which follow the vernal point.

Contents

This calendar is presented as a continuation of the current time system from the day to the year itself. Indeed, since we do not change the subdivisions of the day (in hours, minutes and seconds) according to the day considered, this calendar proposes constant subdivisions of the year. [1]

It was designed and developed by Edouard Vitrant. [2]

Sexagesimal subdivisions of the year

Sixths

The main sexagesimal subdivision of the year is the "sixty days", called sixth. There are 6 sixths in the year, named according to a theme from a manifestation of the flora of the temperate regions of the northern hemisphere. [1]
The names of the 6 sixths are:

There is no "month" in this calendar, the sixths are a kind of "double month".

Adventitious days

The 6 sixths of 60 days make 360 days. Between 6 objects there are 5 spaces, the latter are occupied by the 5 adventitious days placed at the end of each previous respective sixth. The account is good: [1] that's a good 365 days for the typical year.

As this calendar is a solar calendar that follows the northern hemisphere winter solstice and not a vague calendar, it incorporates a 6th adventitious day placed at the end of the year, at the end of the 6th sixth, every 4 years; or within an interval of 5 years, three times every 128 years or so in our time; in order to remain constantly "stalled" on the day of the winter solstice.

These 6 (5+1) days are public holidays and named according to their theme:

Sweeks

Each sixth is divided into sweeks, a kind of "6-day weeks"; there are therefore 10 sweeks per sixth. And so, there are a total of 60 sweeks per year.
The days of each sweek are named from Monday to Saturday as the first six days of the traditional civil week.

Regular subdivisions

The subdivisions of the different periods of the year are now simple and precise:

Since the "sixths" which serves as a "double month".
With the "half-sixth" we find a duration of the order of a "month".
The "fortnight" is around a quarter of a sixth, as well as two and a half sweeks.
The "quarter" (a "trimester") is found in the duration of a sixth and a half.
The "quardrimester" is found in the duration of two sixths.
And the "semester" in that of three sixths.

Writing convention

By extrapolating the writing of the numerical time (hour; minute; second and divisions of seconds), the numerical sexagesimal date is expressed in year, sixth and day of the sixth. [1] This contrasts with the usual convention for numerical dates in the Gregorian calendar, which indicates the day of the month, the month and then the year.

The year is expressed in 3 digits, to remove the ambiguity on the effect of the possibility given by the maximum life expectancy of humans, of a little more than a century. [1]
The number of sixth is expressed on 1 digit.
The number of the day of sixth is expressed on 2 digits. [b]

Typical year

Here is the typical year, from this calendar, presented in the table that follows: [3]

Number
of sweek		FrigéeÉcloseFloréeGranéeRécoleCaduce
1Monday 01Monday 01Monday 01Monday 01Monday 01Monday 01
Tuesday 02Tuesday 02Tuesday 02Tuesday 02Tuesday 02Tuesday 02
Wednesday 03Wednesday 03Wednesday 03Wednesday 03Wednesday 03Wednesday 03
Thursday 04Thursday 04Thursday 04Thursday 04Thursday 04Thursday 04
Friday 05Friday 05Friday 05Friday 05Friday 05Friday 05
Saturday 06Saturday 06Saturday 06Saturday 06Saturday 06Saturday 06
2Monday 07Monday 07Monday 07Monday 07Monday 07Monday 07
Tuesday 08Tuesday 08Tuesday 08Tuesday 08Tuesday 08Tuesday 08
Wednesday 09Wednesday 09Wednesday 09Wednesday 09Wednesday 09Wednesday 09
Thursday 10Thursday 10Thursday 10Thursday 10Thursday 10Thursday 10
Friday 11Friday 11Friday 11Friday 11Friday 11Friday 11
Saturday 12Saturday 12Saturday 12Saturday 12Saturday 12Saturday 12
3Monday 13Monday 13Monday 13Monday 13Monday 13Monday 13
Tuesday 14Tuesday 14Tuesday 14Tuesday 14Tuesday 14Tuesday 14
Wednesday 15Wednesday 15Wednesday 15Wednesday 15Wednesday 15Wednesday 15
Thursday 16Thursday 16Thursday 16Thursday 16Thursday 16Thursday 16
Friday 17Friday 17Friday 17Friday 17Friday 17Friday 17
Saturday 18Saturday 18Saturday 18Saturday 18Saturday 18Saturday 18
4Monday 19Monday 19Monday 19Monday 19Monday 19Monday 19
Tuesday 20Tuesday 20Tuesday 20Tuesday 20Tuesday 20Tuesday 20
Wednesday 21Wednesday 21Wednesday 21Wednesday 21Wednesday 21Wednesday 21
Thursday 22Thursday 22Thursday 22Thursday 22Thursday 22Thursday 22
Friday 23Friday 23Friday 23Friday 23Friday 23Friday 23
Saturday 24Saturday 24Saturday 24Saturday 24Saturday 24Saturday 24
5Monday 25Monday 25Monday 25Monday 25Monday 25Monday 25
Tuesday 26Tuesday 26Tuesday 26Tuesday 26Tuesday 26Tuesday 26
Wednesday 27Wednesday 27Wednesday 27Wednesday 27Wednesday 27Wednesday 27
Thursday 28Thursday 28Thursday 28Thursday 28Thursday 28Thursday 28
Friday 29Friday 29Friday 29Friday 29Friday 29Friday 29
Saturday 30Saturday 30Saturday 30Saturday 30Saturday 30Saturday 30
6Monday 31Monday 31Monday 31Monday 31Monday 31Monday 31
Tuesday 32Tuesday 32Tuesday 32Tuesday 32Tuesday 32Tuesday 32
Wednesday 33Wednesday 33Wednesday 33Wednesday 33Wednesday 33Wednesday 33
Thursday 34Thursday 34Thursday 34Thursday 34Thursday 34Thursday 34
Friday 35Friday 35Friday 35Friday 35Friday 35Friday 35
Saturday 36Saturday 36Saturday 36Saturday 36Saturday 36Saturday 36
7Monday 37Monday 37Monday 37Monday 37Monday 37Monday 37
Tuesday 38Tuesday 38Tuesday 38Tuesday 38Tuesday 38Tuesday 38
Wednesday 39Wednesday 39Wednesday 39Wednesday 39Wednesday 39Wednesday 39
Thursday 40Thursday 40Thursday 40Thursday 40Thursday 40Thursday 40
Friday 41Friday 41Friday 41Friday 41Friday 41Friday 41
Saturday 42Saturday 42Saturday 42Saturday 42Saturday 42Saturday 42
8Monday 43Monday 43Monday 43Monday 43Monday 43Monday 43
Tuesday 44Tuesday 44Tuesday 44Tuesday 44Tuesday 44Tuesday 44
Wednesday 45Wednesday 45Wednesday 45Wednesday 45Wednesday 45Wednesday 45
Thursday 46Thursday 46Thursday 46Thursday 46Thursday 46Thursday 46
Friday 47Friday 47Friday 47Friday 47Friday 47Friday 47
Saturday 48Saturday 48Saturday 48Saturday 48Saturday 48Saturday 48
9Monday 49Monday 49Monday 49Monday 49Monday 49Monday 49
Tuesday 50Tuesday 50Tuesday 50Tuesday 50Tuesday 50Tuesday 50
Wednesday 51Wednesday 51Wednesday 51Wednesday 51Wednesday 51Wednesday 51
Thursday 52Thursday 52Thursday 52Thursday 52Thursday 52Thursday 52
Friday 53Friday 53Friday 53Friday 53Friday 53Friday 53
Saturday 54Saturday 54Saturday 54Saturday 54Saturday 54Saturday 54
10Monday 55Monday 55Monday 55Monday 55Monday 55Monday 55
Tuesday 56Tuesday 56Tuesday 56Tuesday 56Tuesday 56Tuesday 56
Wednesday 57Wednesday 57Wednesday 57Wednesday 57Wednesday 57Wednesday 57
Thursday 58Thursday 58Thursday 58Thursday 58Thursday 58Thursday 58 [c]
Friday 59Friday 59Friday 59Friday 59Friday 59Friday 59
Saturday 60Saturday 60Saturday 60Saturday 60Saturday 60Saturday 60
---- [d] BacchanalCérèsMusicaLiberMemento MoriSext [e]

NB: The days written in red (Frigée 1st, the 6 adventitious days, and Caduce 58th) are public holidays.

Era

The sexagesimal calendar starts its count of years at the day of corresponding winter solstice, just after the end of the 13 bʼakʼtuns of the Mayan calendar, on December 21, 2012. This day is Frigée 1st, 1. [f]

To preserve the traditional temporal markers prior to the introduction of this new calendar, it is not retropolated. The dates that preceded will be expressed in the original calendar. [1]

Sextile rule

As presented in the note of the previous table, the "sext" day appears in the sextile years of 366 days of this calendar so that the first day of each year is always the day of the winter solstice expressed in UTC. This constant correspondence forms the "stalling" of this calendar on the winter solstice. [g] This correspondence is anticipated by astronomical calculation of the precise instant of the phenomenon of this solstice on reliable tables. [4]

The sequence of sextile years resulting from this stalling is therefore imposed de facto by intervals of 4 years most frequently, and sometimes of 5 years in the case of three times every 128 years or so in our time [h] .
This sequence gives the following sextile years [i] : 3; 7; 11; 15; 19; 23; 27; 31; [j] 36; 40…

Here is the calculation of the duration of the sexagesimal years, from year 1 to year 15, presented in the table that follows:
Sextile years are highlighted in lightgrey.

Sexagesimal
year		Gregorian date
of winter solstice [4]
(Frigée 1st)		Gregorian date
of the following
winter solstice		Duration
of the year
(in days)
1December 21, 2012December 21, 2013365
2December 21, 2013December 21, 2014365
3December 21, 2014December 22, 2015366
4December 22, 2015December 21, 2016365
5December 21, 2016December 21, 2017365
6December 21, 2017December 21, 2018365
7December 21, 2018December 22, 2019366
8December 22, 2019December 21, 2020365
9December 21, 2020December 21, 2021365
10December 21, 2021December 21, 2022365
11December 21, 2022December 22, 2023366
12December 22, 2023December 21, 2024365
13December 21, 2024December 21, 2025365
14December 21, 2025December 21, 2026365
15December 21, 2026December 22, 2027366

Durability

Stalldown on the winter solstice in the long and exceedingly long term

This permanent stalling on the day of the winter solstice ensures that it is always the day of Frigée 1st, the sexagesimal New Year. This is ensured based on astronomical tables that are calculated from continuous observations.

This is different from most calendars currently in use, which are based on a constant algorithm resulting from a single projection. For example, the Gregorian calendar was fixed at its introduction at the end of the 16th century, and although it is supposed to follow the vernal equinox, March 21 is not at all systematically the day of the vernal point. Leap years are not distributed as they would do this monitoring. Moreover, in the long term, the Gregorian calendar will shift more and more; because its average value (of the number of average solar days per year) is already slightly too long and that in addition, this real average value will decrease due to the increase length of the day by 2 ms/century, that's to say 1 s every 50000 years approximately.
The length of the year remains relatively constant over the long term.
Thus, around the year 4000, the Gregorian calendar will be shifted by a whole day. [5]
And it is predicted that just after the year 10000, the shift will already be about ten days. [5]

The sexagesimal calendar will always follow the winter solstice as long as this stalling will be maintained. This is done by judiciously placing sextile days, the place of which is anticipated exceedingly long in advance by astronomical tables.
The precise time of the solstice becomes less certain when it is calculated millennia in advance (or retropolated) because of residual uncertainties of observations and calculation.
Theoretically, if this stalling is maintained, this problem can be circumvented by continuous observations and repeated calculations. From each era we will observe and anticipate the stalldown. In our time, there are 365.2422 days per year, which makes sextile intervals of 4 years and 5 years three times every 128 years or so.

In the far future, 5-year intervals will become more frequent at the expense of 4-year intervals.

Application issues

The winter solstice was chosen as the sexagesimal New Year due to its proximity to January 1st, of which the latter is in fact an arbitrary date. [6]
There is about an 11-days difference between these two dates. The transition would therefore be made by shortening the deadlines of a given month of December and starting the new sexagesimal year at Frigée 1st.

But the main problem would remain the application (or non-application) of the traditional week. Indeed, the week is actually independent of the Gregorian calendar, and it is the best-followed calendar standard worldwide. Going back on this sequence would be likely to cause more trouble than the simplification supposed to be brought about by the sexagesimal calendar. Let us not forget that it was for this reason that a project for a new, more regular calendar, such as the introduction of the World Calendar was rejected in the 1950s.
A solution would be to keep the traditional week with this new calendar, by not directly applying the sweek in the sixths. [k] In fact, there would again be 14 types (or subtypes) of years, but the regularity of the sexagesimal calendar would already be very noticeable.

Notes and references

Notes

  1. ↑ Like Persian, Baháʼí or Indian calendars which follow the vernal point.
  2. ↑ For example, Granée 24th, 147 will be noted: 147.4.24. An adventitious day is numbered as the 61st day of the previous sixth. For example, the Bacchanal of the year 22, more usually Bacchanal 22, will be noted: 022.1.61. [1]
  3. ↑ Thursday, Caduce 58th is Children’s Day. [1]
  4. ↑ These 61st days of the sixths are the adventitious days, they are public holidays like descripted above.
  5. ↑ The sixth adventitious day "Sext" is placed at the end of sextile years of 366 days, every 4 or 5 years in our time, so that the following Frigée 1st (the sexagesimal New Year) is always the day of the winter solstice.
  6. ↑ Frigée 1st of the year 1 is noted: 001.1.01 [1]
  7. ↑ The only other calendars which use (or has used) this type of stalling are French Republican calendar (itsef on September equinox), and Baháʼí calendar since its reform on 2015 (itself on March equinox). Other calendars are based on algorithms.
  8. ↑ In 128 years, it would have 32 sextile years with only intervals of 4 years between them. With three intervals of 5 years in the sequence, it makes the same number of sextile years, here 31 in this case, if the last sextile year would have been erased to a normal year. And so, the sequence could be repeated.
  9. ↑ Calculated by the help of the solstice table. [4]
  10. ↑ The interval between years 31 and 36 is the first 5-years interval of Sexagesimal calendar.
  11. ↑ For example, the day of Bachhanal 22 (already cited above) will be a Sunday. It will be February 19th, 2034; in fact Frigée 1st, 22 will be December 21st, 2033. [4] And 60 days later (the 61st day of the first sixth in the year 22) will be February 19th, 2034. And it will be a Sunday. [7]
    The sweeks just before and after that Sunday will be identical to the traditional weekdays, but Frigée 54th would be a Sunday in order to be a Saturday, and Eclose 7th would be a Sunday in order to be a Monday.

References

  1. 1 2 3 4 5 6 7 8 9 Proposal
  2. ↑ Biography: Edouard Vitrant Design
  3. ↑ Typical year
  4. 1 2 3 4 Solstice d’hiver "Dates des solstices d’hiver de 1583 à 2999": Dates of winter solstices from 1583 to 2999
  5. 1 2 Borkowski, K.M. (1991). "The Tropical Calendar and Solar Year". J. Royal Astronomical Soc. Of Canada. 85 (3): 121–130. Bibcode:1991JRASC..85..121B.
  6. ↑ Frequently Asked Questions; Chapter: Why challenge the Gregorian calendar?
  7. ↑ Le convertisseur de calendrier, in French.

Sexagesimal.org: Edouard Vitrant invites you to discover the sexagesimal calendar. Website presenting this calendar with seven language links: in German, English, Spanish, French, Italian, Dutch and Portuguese.

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