Saturnalia
By Sean E. Russell on on Permalink.
In the category of Mostly Useless Software, I’ve built something called Saturnalia. It’s a calendar system.
There are a bunch of replacement calendar systems which attempt to wrap some sort of normalization around the movement of the Earth around the sun. Most of these efforts attempt to recreate the wild success of the metric system. Personally, I think all attempts to restructure things around decimal are silly, as duodecimal is a categorically and provably better base, and a lot of what the metric system did was to replace a better numbering system with an inferior one. Not all, but many Imperial measures were already in dozenal or some multiple thereof: 12 inches in a foot, a dozen eggs, 360 degrees in a cirle – at least that last survived.
When I was playing with a new (to me) programming language called V, one of the toy programs I built was to implement someone else’s calendar revision, the International Fixed Calendar. As I did it, I got thinking (as one does) about how the IFC could be better, and came up with Saturnalia.
Now, the goal of these sorts of things isn’t to actually change anything; no group will ever adopt or use Saturnalia. The real purpose of toy programs is to excercise the art of computer programming, to experiment and learn, without having to invest too much into it. The risk of writing something that becomes popular is that you then feel an obligation to maintain it; sometimes this is fine, but if you’re learning a programming language, you may decide you don’t even like the language. Little toy programs like Saturnalia let you explore a space without risk.
Now, it turns out that I do like V, and I’m actually kind of fond of Saturnalia. I’ve left it and come back to it, and every time it feels smooth… elegant, even. What I’ve found I don’t do is look at it and say, “that’s a stupid idea,” or “why did I do that?” So, having written it, and having found it - if not useful, then at least comfortable - I decided it was worth a blog entry.
Here, I’m just going to pull from the README.
Saturnalia Calendar
Here’s the full Saturnalia calendar. It’s a perpetual calendar, because it’s the same calendar every year: the only thing that changes is the year number.
| Jan | Feb | Mar | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | |||||
| W01 | 01 | 02 | 03 | 04 | 05 | 06 | W06 | 01 | 02 | 03 | 04 | 05 | 06 | W11 | 01 | 02 | 03 | 04 | 05 | 06 | ||
| W02 | 07 | 08 | 09 | 10 | 11 | 12 | W07 | 07 | 08 | 09 | 10 | 11 | 12 | W12 | 07 | 08 | 09 | 10 | 11 | 12 | ||
| W03 | 13 | 14 | 15 | 16 | 17 | 18 | W08 | 13 | 14 | 15 | 16 | 17 | 18 | W13 | 13 | 14 | 15 | 16 | 17 | 18 | ||
| W04 | 19 | 20 | 21 | 22 | 23 | 24 | W09 | 19 | 20 | 21 | 22 | 23 | 24 | W14 | 19 | 20 | 21 | 22 | 23 | 24 | ||
| W05 | 25 | 26 | 27 | 28 | 29 | 30 | W10 | 25 | 26 | 27 | 28 | 29 | 30 | W15 | 25 | 26 | 27 | 28 | 29 | 30 | ||
| Apr | Mai | Jun | ||||||||||||||||||||
| Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | |||||
| W16 | 01 | 02 | 03 | 04 | 05 | 06 | W21 | 01 | 02 | 03 | 04 | 05 | 06 | W26 | 01 | 02 | 03 | 04 | 05 | 06 | ||
| W17 | 07 | 08 | 09 | 10 | 11 | 12 | W22 | 07 | 08 | 09 | 10 | 11 | 12 | W27 | 07 | 08 | 09 | 10 | 11 | 12 | ||
| W18 | 13 | 14 | 15 | 16 | 17 | 18 | W23 | 13 | 14 | 15 | 16 | 17 | 18 | W28 | 13 | 14 | 15 | 16 | 17 | 18 | ||
| W19 | 19 | 20 | 21 | 22 | 23 | 24 | W24 | 19 | 20 | 21 | 22 | 23 | 24 | W29 | 19 | 20 | 21 | 22 | 23 | 24 | ||
| W20 | 25 | 26 | 27 | 28 | 29 | 30 | W25 | 25 | 26 | 27 | 28 | 29 | 30 | W30 | 25 | 26 | 27 | 28 | 29 | 30 | ||
| Jul | Aug | Sep | ||||||||||||||||||||
| Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | |||||
| W31 | 01 | 02 | 03 | 04 | 05 | 06 | W36 | 01 | 02 | 03 | 04 | 05 | 06 | W41 | 01 | 02 | 03 | 04 | 05 | 06 | ||
| W32 | 07 | 08 | 09 | 10 | 11 | 12 | W37 | 07 | 08 | 09 | 10 | 11 | 12 | W42 | 07 | 08 | 09 | 10 | 11 | 12 | ||
| W33 | 13 | 14 | 15 | 16 | 17 | 18 | W38 | 13 | 14 | 15 | 16 | 17 | 18 | W43 | 13 | 14 | 15 | 16 | 17 | 18 | ||
| W34 | 19 | 20 | 21 | 22 | 23 | 24 | W39 | 19 | 20 | 21 | 22 | 23 | 24 | W44 | 19 | 20 | 21 | 22 | 23 | 24 | ||
| W35 | 25 | 26 | 27 | 28 | 29 | 30 | W40 | 25 | 26 | 27 | 28 | 29 | 30 | W45 | 25 | 26 | 27 | 28 | 29 | 30 | ||
| Oct | Nov | Dec | ||||||||||||||||||||
| Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | Sun | Tue | Wed | Thu | Fri | Sat | |||||
| W46 | 01 | 02 | 03 | 04 | 05 | 06 | W51 | 01 | 02 | 03 | 04 | 05 | 06 | W56 | 01 | 02 | 03 | 04 | 05 | 06 | ||
| W47 | 07 | 08 | 09 | 10 | 11 | 12 | W52 | 07 | 08 | 09 | 10 | 11 | 12 | W57 | 07 | 08 | 09 | 10 | 11 | 12 | ||
| W48 | 13 | 14 | 15 | 16 | 17 | 18 | W53 | 13 | 14 | 15 | 16 | 17 | 18 | W58 | 13 | 14 | 15 | 16 | 17 | 18 | ||
| W49 | 19 | 20 | 21 | 22 | 23 | 24 | W54 | 19 | 20 | 21 | 22 | 23 | 24 | W59 | 19 | 20 | 21 | 22 | 23 | 24 | ||
| W50 | 25 | 26 | 27 | 28 | 29 | 30 | W55 | 25 | 26 | 27 | 28 | 29 | 30 | W60 | 25 | 26 | 27 | 28 | 29 | 30 |
| Saturnalia | ||||||
|---|---|---|---|---|---|---|
| Sun | Tue | Wed | Thu | Fri | Sat | |
| WX | 01 | 02 | 03 | 04 | 05 | (06) |
Overview
- Preserves the 12 month calendar.
- Each week is 6 days long.
- Every month has 5 weeks, and so 30 days.
- Every year and month starts on a Sunday, and every month ends on a Saturday.
- Every year ends with a 5-day week belonging to month (month “0”); this week is called “Saturnalia.” On leap years, this week has 6 days.
- Every ordinal day in every year falls on the same calendar date and same day of the week.
- There is an official, universal, date format: ISO-8601.
12 months
Preserving the 12 month calendar is critical. Calendars like the International Fixed Calendar and the Pax calendar add an extra month, giving the calendar 13 months.
12 is a really useful number: it’s divisible by 2, 3, and 4 – a fact used by both universities and corporations to have trimesters, semesters, and quarters. It’s also clearly divisible by 6, which we don’t use much in the calendar, but it’s there.
A 12-month calendar allows for keeping the 4 seasons in groups of 3 months each.
Saturnalia is able to re-use Gregorian month names, which roughly line up with the Gregorian calendar.
30-day month
Each month has the same number – 30 – days. Every month having the same number of days is a common feature of many calendar revision proposals; it does away with mnemonics like “30 days hath September…” and makes scheduling easier.
6-day weeks
Weeks lose a day, and there are more of them. Every week is 6 days long, with Monday being sacrificed, and the days are otherwise the same: Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday. The traditional “reserved” days in many religions are preserved. In addition, because of it’s unfortunate association with the end of the week-end, Monday has become possibly one of the least popular days in Western culture.
6 is a good number for dozenal, because it’s half twelve, and it has four divisors, the most of any number below 12.
What happens to the work week? Although this is outside the scope of this proposal, a recommendation is suggested below.
Saturnalia week
Because 12*30 is only 360, the extra 5 days are given to an extra week at the end of the year, arbitrarily named Saturnalia. During leap years, Saturnalia gains an extra, 6th day.
Saturnalia has no month, so the “month” value in representations is “0”. Neither does it have a week; it shows as week 0 as well:
Sat, December 30th, 2025 -> 2025-12-30, or 2025-W60-6
Sun, Saturnalia 1st, 2025 -> 2025-00-01, or 2025-W00-1
Leap days
Leap years follow the Gregorian calendar rules. The extra day is added at the end of Saturnalia.
Date format
While you will write dates any darned way you like, the only recognized format for Saturnalia dates is the date section of ISO-8601. Date+times follow ISO-8601, except the date is Saturnalia. The week/week+weekday format may be used, in which case there are between 1 and 60 weeks, and 1 and 6 days.
To distinguish between Saturnalia and Gregorion, when necessary the date may be prefixed by the horological symbol for Saturn, as in “♄2025-05-01”, or “♄2025-W25-1”. I’ll note here that the week is simple (although, maybe not trivial) to calculate; it’s (month-1)*5 + floor(day/6). For example, ♄2025-05-01 is week 25.
Benefits
Consistency
The year starts on the same week day: Sunday. Every month starts on the same week day, Sunday, and ends on the same day, Saturday. This consistency, again, makes scheduling and thinking about calendar time easier. The middle of the month falls exactly on midnight of the 15th, which is always a Wednesday, every month, every year. The first of the month is always a Sunday; the 30th of every month is a Saturday. The first of the year is always a Sunday. This is such a handy fact, it’s sometimes difficult to believe that it hasn’t been addressed before now.
Criticisms
Some songs will become irrelevant (e.g. Just Another Manic Monday)
Saturnalia does not try to retain alignment with the Gregorian calendar, and
except for January through the 30th, dates will rarely align. Weeks will never
rarely align, except in years where, in the Gregorian calendar, Jan 1 is a
Sunday. This is an enormous impediment to adoption.
In 2024:
- 93% (339 days) of the year, the months are the same (e.g., it’s Saturnalia August when it’s Gregorian August). This is because the Gregorian calendar averages 30.5 days per month.
- 24% (87) of the days have the name month-day number (Apr 03 Saturnalia is Apr 03 Gregorian)
- 14% (51) of the weekdays are the same (e.g. Sunday Saturnalia is Sunday Gregorian)
What is the work week in Saturnalia?
I suggest we use it to convert to a 4-day work week. Study and trial, over and over, show that in the modern world, shorter work weeks make for more productive and happy employees. In this scheme, the work week is Tuesday - Friday, with two rest days on Saturday and Sunday.
With a 4-day work week under the Saturnalia Calendar, and with the assumption that Saturnalia Week will be a holiday, here are 20 fewer working days in the year. Other holidays will either affect the total number of days or not, as in the current calendar, except that holidays will become more predictable as they’ll always fall on the same day in the week, every year.
Despite this, this still offers 32 more work days than if 4-day work weeks were adopted under the Gregorian calendar. This is because, in Saturnalia, weekends are not longer, as they would be under the Gregorian calendar. This means that employees both have more rest days more frequently, yet employers still retain most of the hours-per-year during which to conduct business.
Ignoring vacation and holidays:
| Calendar | Business days | Weekend days | # weeks | Business days |
|---|---|---|---|---|
| Gregorian | 5 | 2 | 52 | 260 |
| Gregorian | 4 | 3 | 52 | 208 |
| Saturnalia | 4 | 2 | 60 | 240 |
Studies show productivity declines with consecutive periods of work; past 8 hours, a knowledge worker’s productivity declines as they make poorer decisions more slowly. With this proposal, while there are only 20 fewer business days, shorter work weeks reduce employee stress and allow knowledge workers to maximize their productive period. The effectiveness of more frequent, short breaks is already demonstrated at smaller scale by Pomodo habits.
There is an additional argument to be made for maintaining momentum; the longer breaks in 3-day weekends as proposed by 4-day work week advocates in the Gregorian calendar allow for more opportunity to shed momentum.
Not all industries are knowledge industries, which gain most from the 4-day shift. In some industries, productivity is accurately measured in hours-on-the-job. While these industries are vanishing or being automated, they still exist. Saturnalia 4-day weeks preserve 12% more work days for businesses that benefit from maximizing working hours.
Naming
In ancient Rome, Saturnalia was a festival that started on December 17 and ran to December 19. The Saturnalia week would not align with the festival, which would roughly fall around Dec 21 Saturnalia, and the name is merely symbolic – there is no intended religious association.
Although it’s neither here nor there, on leap years, in the Saturnalia calendar the last day is Sat(urday), 06 Sat(urnalia).
Other calendars
I’ve said before that calendar reform is popular. If Saturnalia isn’t your thing, here are some other calendars which have the advantage over Saturnalia that they’re somewhat popular – not that they’ve been adopted necessarily, but they have advocates.
- https://www.hermetic.ch/cal_stud/palmen/lweek1.htm
- https://en.wikipedia.org/wiki/Pax_Calendar
- https://en.wikipedia.org/wiki/InternationalFixedCalendar
- https://en.wikipedia.org/wiki/Hanke–HenryPermanentCalendar