First Mundane Reality: The Mean Solar Day
The first "mundane reality" in the derivation of Primel units is the mean solar day. It can be argued that the day is by far the most important unit of time impacting human life, literally on a daily basis. However, it is too large a period to act as a base unit of time for a metrology supporting everyday physics. Instead, Primel takes a pure dozenal fraction of the day, namely the hexcia·day (10−6z day), and uses that as its coherent base unit of time, the ⚀timel, also known colloquially as the ⚀vibe.
The idea of dividing the day in pure dozenal divisions has a long history in the Dozenal Society of America. Indeed, this was the first instinct of the founders since the very inception back in 1944d=1160z, and even earlier. In the article “The Do-Metric System”, in the June 1945d=1161z issue of The Duodecimal Bulletin, Vol 1, No 2 (available here), Ralph Beard documented the time system previously devised by George Terry and Rear-Admiral G. Elbrow:
| Dozenal Power | Dō·Metric Formal Derivation | Dō·Metric Formal Derivation | Dō·Metric Colloquial Name | Customary Equivalents (dozenal and decimal) | Primel Formal Derivation | Primel Formal Name | Primel Colloquial Name | |
|---|---|---|---|---|---|---|---|---|
0 | day | bimō·vic | day | = 20z hours = ᘔ00z minutes = 42,000z seconds | = 24d hours | day | ⚀hexqua·timel | day |
| -1 | edō·day | grōmō·vic | duor | = 2z hours = ᘔ0z minutes = 4,200z seconds | = 2d hours = 120d minutes = 7,200d seconds | uncia·day | ⚀pentqua·timel | ⚀dwell |
| -2 | egrō·day | dōmō·vic | temin | = 0.2z hours = ᘔz minutes = 420z seconds | = 0.16d hours = 10d minutes = 600d seconds | bicia·day | ⚀quadqua·timel | ⚀breather |
| -3 | emō·day | mō·vic | minette | = 0.ᘔz minute = 42z seconds | = 0.83d minute = 50d seconds | tricia·day | ⚀triqua·timel | ⚀trice |
| -4 | edōmō·day | grō·vic | grovic | = 4.2z seconds | = 4.16d seconds | quadcia·day | ⚀biqua·timel | ⚀lull |
| -5 | egrōmō·day | dō·vic | dovic | = 0.42z seconds | = 0.3472d seconds | pentcia·day | ⚀unqua·timel | ⚀twinkling |
| -6 | ebimō·day | vic | vic | = 0.042z seconds | = 0.02893518 seconds | hexcia·day | ⚀timel | ⚀vibe |
Tom Pendlebury's Tim-Grafut-Maz (TGM) metrology also derives its coherent time unit from the mean solar day, but not a pure dozenal division of it. Instead, it first takes a binary division, splitting the day into AM and PM semi·days, and then divides those dozenally, to use the semi·pentcia·day as its coherent timel, the Tim. This does make the conventional hour (or semi·uncia·day) a dozenal power of the Tim, but unfortunately the day itself is not. A nice property of Primel is that there is no awkward transition from measurements of shorter time periods less than a day, to measurements of longer time periods in multiples of days; it is simply a matter of adjusting the dozenal radix point. TGM loses this nice property by retaining this traditional binary division.
Since Primel, like TGM, is a coherent metrology, the choice for its coherent timel has a profound impact on the sizes of all the other coherent units in the metrology.
The ⚀timel is equivalent to 50/1728d=1/34.56d=0.042z of an SI second exactly. This assumes the definition of the SI second as exactly 1/86,400d=1/42,000z of the mean solar day of the epoch C.E. 1900d=1124z, which was calculated based on astronomical observations gathered between C.E. 1750d=101ᘔz and 1892d=1118z . Because the Earth's rotation is slowly decelerating, the actual mean solar day has lengthened to about 86,400.002d=42,000.003z SI seconds. However, Primel ignores this in order to keep its conversion to SI units simple.
Since C.E. 1967d=117Ɛz, the SI second has been precisely specified as 9,192,631,770d=1,946,716,076z periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133d=Ɛ1z atom. This makes the precise specification of the ⚀timel exactly 265,990,502.60416d=75,0Ɛ5,832.73z such caesium transition periods. (This makes the ⚀biqua·timel (or ⚀lull) the smallest power of the ⚀timel which is an whole number of such periods: 38,302,632,375d=7,50Ɛ,583,273z. This also happens to be the smallest power of the ⚀timel which can be comfortably counted aloud by most people.)