Dividing the Solar Year
A solar year is driven by one orbit of the Earth around the Sun. Because the Earth’s axis is tilted, at two points in the orbit the axis is oriented directly toward or away from the sun and these positions are called solstices. From the surface of the Earth the Sun seems to move from a maximum northern and southern position in the sky and on the horizon from one solstice to the next and back again over the course of a year.
Scientific measurements can determine the precise moments of solstices marked on opposite sides of a 360° circle of ecliptic longitude defined by the plane in which the Earth orbits the Sun. Exactly halfway between the solstices the axis of the Earth is exactly parallel to the sun and these positions are called equinoxes. Some cultures in the past divided the year into 8 parts and these divisions have come to be known as crossquarter days. If the degrees of ecliptic longitude were to be divided into 8 equal parts of 45° each, that might be one method to have an 8 part year, but the number of days between the divisions would not be even because the Earth's orbit around the Sun is not perfectly circular, but rather elliptical. This means that the Earth moves at varying speeds along its orbit, with the fastest speed occurring when it is closest to the Sun (perihelion) and the slowest speed occurring when it is farthest from the Sun (aphelion). As a result, the Earth travels through some parts of the ecliptic faster than others, which causes the number of days between exact 45° divisions to be uneven. Without modern concepts of celestial coordinate systems, it is more likely that people in the past would have divided the year by day intervals, ideally as evenly as possible. The solstices are still the most likely starting and 'halfway' points, but due to the elliptical orbit of the Earth, the solstices are not an even number of days apart. Also the number of days in a year can't be divided up completely evenly, and there is even a fractional day that must be adjusted for approximately every four years. By observation alone it is difficult to determine the exact day of solstices as the sun does not appear to change position for several days. By starting only with the intervals from one approximate solstice to the next, the day intervals can be divided up as evenly as possible into 8 parts of 45 or 46 days each. More of the 46 day intervals should go into the longer ‘half’ of the year to keep solar positions in the sky and on the horizon matching up as closely as possible as the sun will pass through all the same places twice on the way northward and southward between the solstice extremes. It should also be noted that the midpoints between solstices in days would not match the modern concept of astronomical equinoxes, again due to variations in Earth's orbital speed, and fluctuating orbital parameters change the intervals over time. See Images and Video Links Below for More Information: 
above: sample graph image from the spreadsheet
(see below) 
Click Here for CrossQuarter Dates
calculated for the next several years.
The link is to a spreadsheet that is view only on the web, but if you have a Google account you can click 'File' then 'Make a Copy' so that you can make edits to preference settings, UTC offset amounts, etc.
The dates are calculated using two different systems (and a third variation). One system is based on the modern celestial coordinate system of ecliptic longitude (this is the system that was used by the now defunct archaeoastronomy.com website) and the other set of dates is determined by more evenly dividing by time. There is also a fixed date calendar with repeating day count intervals (in a way much more like a calendar system would be put together) so that the dates of approximate solstices and 45 or 46 day intervals remain constant. Any of these systems can be subdivided further for a 16 part year.
calculated for the next several years.
The link is to a spreadsheet that is view only on the web, but if you have a Google account you can click 'File' then 'Make a Copy' so that you can make edits to preference settings, UTC offset amounts, etc.
The dates are calculated using two different systems (and a third variation). One system is based on the modern celestial coordinate system of ecliptic longitude (this is the system that was used by the now defunct archaeoastronomy.com website) and the other set of dates is determined by more evenly dividing by time. There is also a fixed date calendar with repeating day count intervals (in a way much more like a calendar system would be put together) so that the dates of approximate solstices and 45 or 46 day intervals remain constant. Any of these systems can be subdivided further for a 16 part year.
Below are 16 part fixedinterval calendars for MODERN use:
Below are approximate proxy dates for observing sunrises/sunsets at ancient sites that
match putative 16 part divisions of the year based on orbital configurations of the past:
match putative 16 part divisions of the year based on orbital configurations of the past:




