time of day
francis his ideal calendar and timekeeping systems would bring people closer to nature. using a sundial is one method, but it only works when the sun is shining. Using the sun as the focus of day time is very natural. People talk about morning and afternoon with the dividig line the moment when the sun is highest in the sky. This is averaged as 12.00 noon so people talk about the same thing, but nothing is keeping you from using your own personal time aligned with the sun.
The problem is how do you know the sun is highest in the sky, or if it's halfway? What if it's clouded? Software helps, as well as the periodic call for prayer in Islam on specific positions of the sun. Stellarium calculates the position of the sun across the sky in relation to the horizon and is a nice way to visualize the pathway during the day. There is other sun position software, command line or for android.
For short fixed time periods a sandtimer can be used as well. For a 20-25m sandtimer for timeboxed tasks or meditation. The longer the period the larger the sandtimer has to be, or you can keep the time with a pencil and a sandbox. In that case you must not forget to pay attention to time 'running out' otherwise you've lost keeping track of the time.. but tracking the time consciously is not really a natural way.
Another element is the way how to divide a day in the most natural way. There is no particular reason to divide the day, night or both in 24, 12 or 10. Base 6 is nice, so one can choose to divide the day in 6 parts and the night in 6 so the complete day would then consist of 12 'hours'.
A factor in deciding the size of the parts is your own food, prayer or sleep schedule. We usually sleep at night, but it's healthy to nap in the afternoon as well like in Singapore, China or Spain. Monasteries have specific prayer schedules.
weeks and collection of days
we have a collection of days called a week to give a certain structure to life and society just as the structure of the day is more or less given by the sun position. the collection is called a 7 day week, but it's divorced from the position of heavenly body, so it's not really natural even though it's approximately 1/4th of a lunar month (7.4 to be exact). So what would be the most natural collection of days? As base 6 (senary counting system) is nice one could opt for a 6 day week, but that is less natural. But one could divide the lunar cycle in 6 parts and coincidentally end up with 4.9 weekdays. But it seems the moon would perhaps be less easy to read the week from with a 6 'week' division then a 4 week division. The Sovjets appearently had a 5 day week calendar for a while. And there again is the psychological or environmental factor, would a 5 day week work 'better'? Did non-western cultures have non 7 day weeks? You could count it on one hand and one name the weekdays after the sun, moon, venus, mars and jupiter only - leaving mercury out - it's not really visible most of the time.
Perhaps the movement of venus can also be used in a collection of days, the mayans and olmeks used it for their calendaring as well.
months are by definition based on the lunar cycle, so we'll keep them, but not the western month.
the shortest day, solstice, the longest day, the vernal and autumnal equinoxes are natural markers - not six divisions but four, so perhaps it's natural to do that with the mooncycle as well.
the number 108
There is something special with the number 108, it's the number of beads in a buddhist mala and the number of times the diameter of the earth fits into the sun. So perhaps it can be factored in somewhere as well. And now we're talking special numbers or ratio's, perhaps the golden mean, tau (6,3) or square root 2 (1,4) can be put into the time system as well.