I think a lot of misconceptions about calendars arise from the idea that a calendar measures time, like a clock or like a ruler measures distance.
All known calendars work by naming days (This is the definition in the Nupedia article). As such, a calendar can not measure time more accurately than 1 day. Furthermore, the duration of the day is known to vary in time owing to change in Earth's rotation rate, so is not a good standard in time measurement.
A [solar calendar]? may measure years, by virtue of the fact that its year runs close to the cycle of seasons, but more accurate measurement can be got from an ephemeris?.
The year even when measured in SI seconds, varies in duration and so can not be considered a unit of the same time that measured by SI seconds.
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How about calling it "observation based calendar" and get rid of the pragmatic terminology.
"A theoretical calendar is one that is based on a strict set of rules; an example is the Jewish calendar. Such a calendar is also referred to a rule-based or arithmetical calendar."
I thought a "theoretical calendar" was one proposed bu never used.
Let's just move away from those two term and go with Rule based and observation based.
-Paul Hill
The same applies to the addition of arithmetical and rule-based for theoretical calendars.