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The octal, or 8-day, week is common enough in some shift patterns.

Calendrical dating definition

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The octal, or 8-day, week is common enough in some shift patterns.

Then of course there are all sorts of arbitrary cycles devised for specific purposes, often containing their own irregularities and occasional exceptions, that don't map clearly to any of these established cycles.

I'll only address the Gregorian and the ISO year in this answer, but I will also refer to a concept which I will call a "Roman year" - that is, a year that otherwise follows Gregorian logic but rolls over on 1-Mar instead of 1-Jan.

Where I have seen this approach used, I'm not sure that it has had any consistently recognised name.

It is also common for date cycles to proceed downwards to an anchor point rather than upwards from it - for example, the "second to last day of each month", or the "last day of the year".

The main cycles in common civic and business use are the day, week (7 days), fortnight (2 weeks), lunar (4 weeks), month, quarter (3 months), and year (12 months).

Finally, I'm going to employ the concept of what I call the "heptrig window", which is used implicitly for common kinds of calendrical presentation rather than explicitly for addressing dates.

Noting that naming things in programming is one of the hardest problems, I haven't been able to find a clear name for this concept so I have devised this one.

All database packages involve a set of standard date functions that extract various attributes from a date, such as the day of the month, but these are far from comprehensive.

So, with an answer to follow in a moment, the question I'm going to put is "how do we create a basic date table, and manipulate this into a simple calendar"?