A Calendar for Zarmina's World

Though the sun may not move for the hypothetical denizens of Zarmina's World, they will not be without time-givers. If the revolution period in days of each of the planets in the habitable zone is as follows:

    c = 12.895
    g = 36.562
    d = 66.80

--then the apparent (synodic) period of c ("Metaluna") will be 19.92085985 and the period of d ("Usk") will be 80.77060652. Notice that the major cycle is almost exactly four times the duration of the minor cycle. I will call the long one a "yare" & the short one a "mynth". These periods will be known from antiquity, as both planets give visible disks (the inner one with phases) & significant illumination at the terminator anyway. Indeed, there is nothing else to count by.

For now i am naming the mynths Jabarch, Aprimune, Jugember, and Ocvecember.

After some 18 yares, the length of 72 (18 x 4) mynths will be short by a little over one mynth. Then it will be time to add an intercalary mynth ("fliedermynth") to make the cycles match up again. (This would happen once, maybe twice in a human-sized lifespan. So i call this period a "spaen".) When 57 spaens have passed, the small excess of 4161 (57 x 73) mynths over 1026 (57 x 18) yares will again nearly equal one mynth, and the usual intercalary mynth will have to be left out. This latter cycle (a "seecle") will be rather longer than an individual life, i think; & will mark the passage of cultural epochs & the lifespan of nations perhaps.

Further modifications will follow these lines, at yet greater intervals.

For smaller units, as i have adopted a number base of 9 (three hands of three fingers each), 1/9 of a mynth is about 52 hrs (a "dey"); 1/9 of a dey is about 5.8 hours (a "filge"); 1/9 of a filge is about 38.8 minutes (a "haor"). I don't know whether these creatures will sleep at all, or only at irregular intervals, but it will probably be useful to keep track of the 81 filges in a mynth, at any rate.

These numbers (in whatever base), seemingly given from heaven, will impress themselves on the mystically minded: the silver proportion 18:73 and the golden proportion 1026:4160...