A nonary calendar.

Upon observing that nine cubed is off by one from the number of days in two years, a calendar system emerged.

There are 9 nonths in a biennium, with 9 neeks in a nonth, and 9 days in a neek. There is a biennial holiday between bienniums. Every other biennium holiday is two days.

The first day of the biennium corresponds with March 1st on the Gregorian calendar. The biennial holiday occurs on even number years and is equivalent to February 28th (or February 28th and 29th on Gregorian leap years).

The biennium is expressed in base 9 as well, so the current (at time of writing) biennium would be:

\(\lfloor2025 \div 2\rfloor = 1012 = 1344_9\)

I wrote this on 30₉th (27₁₀)th day of the 5th nonth, on the 3rd neekend.

Handy conversions:

Representing a nonary calendar on a page isn't too different from a 9 by 9 Sudoku grid, which can be used to represent the neeks in a biennium, or the days in a nonth. This also means scheduling exclusive recurring tasks maps to a Sudoku puzzle. For example:

We have 9 tasks to do this nonth. We must do each task once per neek, but never on the same neekday as another neek. We also can't do the task during the same third of the neek as the other neeks in our third of the nonth.

The closest existing calendars to this system that I'm aware of are the Mayan and French Revolutionary calendars, if you want comparisons, though neither were taken to the nines.