Sexagesimal calendar

Not to be confused with Sexagenary cycle.

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 which follow the vernal point.

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.

It was designed and developed by Edouard Vitrant.

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.
The names of the 6 sixths are:

• Frigée: cold period.
• Eclose: period of hatch of vegetation.
• Florée: period of flowering.
• Granée: period of grain formation, fruiting.
• Récole: harvests period.
• Caduce: period of the fallen deciduous.

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

Adventice 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: that's a good 365 days for the typical year.

These 5 weed days are public holidays and named according to their theme:

• Bacchanal: dedicated to lovers, carnival festival, drink, cooking; around February 19.
• Ceres: festival of renewal, of creation; around April 21.
• Musica: Music Day; around June 21.
• Liber: day of the books, of written expression; around August 21.
• Memento Mori: Ancestors' Day, commemorations; around October 21.

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.

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 "thirties" we find a duration of the order of a "month".
The "fortnight" is a quarter of a sixth, as well as two and a half sweeks.
The "quarter" is found in the duration of a sixth and a half.
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. 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.
The number of sixth is expressed on 1 digit.
The number of the day of sixth is expressed on 2 digits.

Typical year

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

Number of sweek	Frigée	Éclose	Florée	Granée	Récole	Caduce
1	Monday 01	Monday 01	Monday 01	Monday 01	Monday 01	Monday 01
1	Tuesday 02	Tuesday 02	Tuesday 02	Tuesday 02	Tuesday 02	Tuesday 02
1	Wednesday 03	Wednesday 03	Wednesday 03	Wednesday 03	Wednesday 03	Wednesday 03
1	Thursday 04	Thursday 04	Thursday 04	Thursday 04	Thursday 04	Thursday 04
1	Friday 05	Friday 05	Friday 05	Friday 05	Friday 05	Friday 05
1	Saturday 06	Saturday 06	Saturday 06	Saturday 06	Saturday 06	Saturday 06
2	Monday 07	Monday 07	Monday 07	Monday 07	Monday 07	Monday 07
2	Tuesday 08	Tuesday 08	Tuesday 08	Tuesday 08	Tuesday 08	Tuesday 08
2	Wednesday 09	Wednesday 09	Wednesday 09	Wednesday 09	Wednesday 09	Wednesday 09
2	Thursday 10	Thursday 10	Thursday 10	Thursday 10	Thursday 10	Thursday 10
2	Friday 11	Friday 11	Friday 11	Friday 11	Friday 11	Friday 11
2	Saturday 12	Saturday 12	Saturday 12	Saturday 12	Saturday 12	Saturday 12
3	Monday 13	Monday 13	Monday 13	Monday 13	Monday 13	Monday 13
3	Tuesday 14	Tuesday 14	Tuesday 14	Tuesday 14	Tuesday 14	Tuesday 14
3	Wednesday 15	Wednesday 15	Wednesday 15	Wednesday 15	Wednesday 15	Wednesday 15
3	Thursday 16	Thursday 16	Thursday 16	Thursday 16	Thursday 16	Thursday 16
3	Friday 17	Friday 17	Friday 17	Friday 17	Friday 17	Friday 17
3	Saturday 18	Saturday 18	Saturday 18	Saturday 18	Saturday 18	Saturday 18
4	Monday 19	Monday 19	Monday 19	Monday 19	Monday 19	Monday 19
4	Tuesday 20	Tuesday 20	Tuesday 20	Tuesday 20	Tuesday 20	Tuesday 20
4	Wednesday 21	Wednesday 21	Wednesday 21	Wednesday 21	Wednesday 21	Wednesday 21
4	Thursday 22	Thursday 22	Thursday 22	Thursday 22	Thursday 22	Thursday 22
4	Friday 23	Friday 23	Friday 23	Friday 23	Friday 23	Friday 23
4	Saturday 24	Saturday 24	Saturday 24	Saturday 24	Saturday 24	Saturday 24
5	Monday 25	Monday 25	Monday 25	Monday 25	Monday 25	Monday 25
5	Tuesday 26	Tuesday 26	Tuesday 26	Tuesday 26	Tuesday 26	Tuesday 26
5	Wednesday 27	Wednesday 27	Wednesday 27	Wednesday 27	Wednesday 27	Wednesday 27
5	Thursday 28	Thursday 28	Thursday 28	Thursday 28	Thursday 28	Thursday 28
5	Friday 29	Friday 29	Friday 29	Friday 29	Friday 29	Friday 29
5	Saturday 30	Saturday 30	Saturday 30	Saturday 30	Saturday 30	Saturday 30
6	Monday 31	Monday 31	Monday 31	Monday 31	Monday 31	Monday 31
6	Tuesday 32	Tuesday 32	Tuesday 32	Tuesday 32	Tuesday 32	Tuesday 32
6	Wednesday 33	Wednesday 33	Wednesday 33	Wednesday 33	Wednesday 33	Wednesday 33
6	Thursday 34	Thursday 34	Thursday 34	Thursday 34	Thursday 34	Thursday 34
6	Friday 35	Friday 35	Friday 35	Friday 35	Friday 35	Friday 35
6	Saturday 36	Saturday 36	Saturday 36	Saturday 36	Saturday 36	Saturday 36
7	Monday 37	Monday 37	Monday 37	Monday 37	Monday 37	Monday 37
7	Tuesday 38	Tuesday 38	Tuesday 38	Tuesday 38	Tuesday 38	Tuesday 38
7	Wednesday 39	Wednesday 39	Wednesday 39	Wednesday 39	Wednesday 39	Wednesday 39
7	Thursday 40	Thursday 40	Thursday 40	Thursday 40	Thursday 40	Thursday 40
7	Friday 41	Friday 41	Friday 41	Friday 41	Friday 41	Friday 41
7	Saturday 42	Saturday 42	Saturday 42	Saturday 42	Saturday 42	Saturday 42
8	Monday 43	Monday 43	Monday 43	Monday 43	Monday 43	Monday 43
8	Tuesday 44	Tuesday 44	Tuesday 44	Tuesday 44	Tuesday 44	Tuesday 44
8	Wednesday 45	Wednesday 45	Wednesday 45	Wednesday 45	Wednesday 45	Wednesday 45
8	Thursday 46	Thursday 46	Thursday 46	Thursday 46	Thursday 46	Thursday 46
8	Friday 47	Friday 47	Friday 47	Friday 47	Friday 47	Friday 47
8	Saturday 48	Saturday 48	Saturday 48	Saturday 48	Saturday 48	Saturday 48
9	Monday 49	Monday 49	Monday 49	Monday 49	Monday 49	Monday 49
9	Tuesday 50	Tuesday 50	Tuesday 50	Tuesday 50	Tuesday 50	Tuesday 50
9	Wednesday 51	Wednesday 51	Wednesday 51	Wednesday 51	Wednesday 51	Wednesday 51
9	Thursday 52	Thursday 52	Thursday 52	Thursday 52	Thursday 52	Thursday 52
9	Friday 53	Friday 53	Friday 53	Friday 53	Friday 53	Friday 53
9	Saturday 54	Saturday 54	Saturday 54	Saturday 54	Saturday 54	Saturday 54
10	Monday 55	Monday 55	Monday 55	Monday 55	Monday 55	Monday 55
10	Tuesday 56	Tuesday 56	Tuesday 56	Tuesday 56	Tuesday 56	Tuesday 56
10	Wednesday 57	Wednesday 57	Wednesday 57	Wednesday 57	Wednesday 57	Wednesday 57
10	Thursday 58	Thursday 58	Thursday 58	Thursday 58	Thursday 58	Thursday 58
10	Friday 59	Friday 59	Friday 59	Friday 59	Friday 59	Friday 59
10	Saturday 60	Saturday 60	Saturday 60	Saturday 60	Saturday 60	Saturday 60
----	Bacchanal	Cérès	Musica	Liber	Memento Mori	Sext

Era

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

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.

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. This correspondence is anticipated by astronomical calculation of the precise instant of the phenomenon of this solstice on reliable tables.

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.
This sequence gives the following sextile years: 3; 7; 11; 15; 19; 23; 27; 31 (– first interval of 5 years –) 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:

Sexagesimal year	Gregorian date of winter solstice (Frigée 1)	Gregorian date of the following winter solstice	Duration of the year in days
1	December 21, 2012	December 21, 2013	365
2	December 21, 2013	December 21, 2014	365
3	December 21, 2014	December 22, 2015	366
4	December 22, 2015	December 21, 2016	365
5	December 21, 2016	December 21, 2017	365
6	December 21, 2017	December 21, 2018	365
7	December 21, 2018	December 22, 2019	366
8	December 22, 2019	December 21, 2020	365
9	December 21, 2020	December 21, 2021	365
10	December 21, 2021	December 21, 2022	365
11	December 21, 2022	December 22, 2023	366
12	December 22, 2023	December 21, 2024	365
13	December 21, 2024	December 21, 2025	365
14	December 21, 2025	December 21, 2026	365
15	December 21, 2026	December 22, 2027	366

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 the 1st Frigée, 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.
And it is predicted that just after the year 10000, the shift will already be about ten days.

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.

• In approximately 235000 years, there will be 365.22222... days/year, there will be as many intervals of 4 years and 5 years; each about every other time.
• In approximately 500000 years, there will be 365.2 days/year, there will only be 5-year intervals.
• In approximately 2800000 years, there will be 365 days exactly, this will be the horizon of the use as such of this calendar. A very distant deadline...

Application issues

The winter solstice was chosen as the sexagesimal New Year due to its proximity to the 1 January, of which the latter is in fact an arbitrary date.
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 1st Frigée.

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. In fact, there would again be 14 types (or subtypes) of years, but the regularity of the sexagesimal calendar would already be very noticeable.

External links

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.