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There have been experiments where humans live underground, entirely cut
off from any kind of external time reference. What researchers learned is
that humans have a natural "internal clock" of 26 hours. After a few days
of adjustment, humans will sleep for about nine hours, be awake and active
for about 17 hours, and then sleep again. When there is a group, the
entire group quickly falls in to a common pattern of sleeping at the same
time, being awake and active at the same time, even being hungry at the
same time.

Applying this to a race that lives primarily underground: Perhaps your
orcs have a similar "common time" of a bit longer than an averge solar
day. This would be divided in to an "active period" and a "sleep period,"
based on the (presumably) instinctive agreement. Assuming enough
similarity to human biology, the active period would be twice as long as
the sleep period, so if "night" is measured as 10 intervals, "day" would
be 20 intervals. The length of those intervals is entirely arbitrary, so
pick something that make sense. Maybe a full night is "both hands worth of
fingers" intervals long, or maybe the orcs hold the number 11 to have
sacred meaning.

As for longer intervals, how about go with the amount of time it takes
from planting a staple crop to harvesting it? If the orcs had some kind of
agriculture, it seems logical that they would measure a period of days as
"one growing cycle" or "three growing cycles." This, in turn, can become
the basis of even longer periods. Perhaps biology or the orc culture
requires a field to be left fallow every "both hands" of cycles; you have
just defined a sabbatical. And the "both hands" must be observed by a
special ceremony or sacrifice: there you have a jubilee. And now, you say
that an orc child is considered an adult at two sabbaticals, or make a
proverb juxtaposing a long life and seeing two jubilees. What those time
periods actuall "mean" with regards to the position of the sun and moon is
entirely irrelevant.

Gregory Gadow