This is a calendar based on powers of three, starting with individual days, with units of three-day “half-weeks”; nine-day weeks like the medieval Welsh and Lithuanian calendars; 27-day months which are closer to the human menstrual cycle than Julian calendar months, although further from the synodic month; 81-day seasons; 243-day cycles; and 729-day biennials. This chart shows the Gregorian calendar months and days in a particular 729-day biennial beginning arbitrarily on February 17, 2015.

On this chart, every day is adjacent to the days before and after it.

Much of the visual design of this version of the calendar is due to Ganesha.

The biennials differ from pairs of mean tropical years by lacking about 1.484 days. The usual way to handle this to keep whatever calendar synchronized with the sun, so that planting dates keep happening on the same date instead of gradually rotating, is to add extra intercalary days every once in a while, usually in between years. If you simply alternated between one and two intercalary days after each biennial, you’d be as accurate as the Julian calendar; an occasional omission of the second intercalary day can adjust this scheme to arbitrarily good precision.

Once these intercalary days are added, or their loss is accepted, you can extend the process outward, with cycles of 6, 18, 54, 162, 486, 1458, 4374, and 13122 years. Each factor of three in timespan adds a factor of two in physical scale, so while this biennial fits comfortably on my screen, my lifespan would cover much of a wall in my room, while human history would cover a city block.

The empty space within the triangle of each week, month, season, cycle, and biennial provides space for planning for the future and reflection on the past; the visual resemblance between the different timescales invites us to consider each timespan as a microcosm of a larger timespan, or as an extended remix of a smaller one.

Meanwhile, at each scale, each period is divided into a beginning, a middle, and an end. The middle cycle of this biennial runs from October 18th, 2015, to June 16th, 2016; the end season of that cycle runs from March 28th to June 16th; the beginning month of that season runs from March 28th to April 23rd; the end week of that month runs from April 15th to April 23rd; and the middle half-week of that week runs from April 18th to April 20th. This context is particularly useful for providing meaning to shorter pieces of time from their larger context.

Finally, except for the corners, each day in this chart is adjacent not only to the days before and after it, but also a third day from further off, providing an opportunity to reflect on that third day. The middle days are the days that are adjacent to the furthest-off other days. For example, August 11th, 2015, being the middle day of a month, is adjacent to October 4th; but November 27th is the middle day of a whole cycle, and so is adjacent to May 7th, 2016.

Scaling down from the day, each day consists of three 8-hour phases; each phase consists of three 160-minute blocks; each block consists of three 3200-second (53⅓ minute) "hours".

This timekeeping system is very similar to Kalentris and Crissov’s Trical, but they do not use the Sierpiński triangle to surface the fractal nature of the human experience of time.

Kalentris uses the terms “tick”, “blink”, “moment”, “run”, “come”, “boil”, “break”, “tierce”, “hour”, “watch”, and “shift” for the time units smaller than a day, and “tierce”, “week”, “month”, “tertiade” or “tertial”, “year”, and “tricycle” for the larger units; Trical uses “cond”, “ment”, “tant”, “min” or “nute”, “dim”, “egg”, “tertian”, “tour”, “watch”, “shift” for the former, then “trip”, “tine”, “moon”, “sean”, “triad”, and “jear” for the latter.

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