The Earth Epic Calendar has seven-day weeks because that is what just about the entire world uses.
People may opt to use the traditional names of the days of the week on the Earth Epic Calendar. I have also introduced names of the days of the week that are more secular. Few people know this, but the days Tuesday through Friday are named after Norse pagan gods, and Saturday is named after Saturn, a Greek pagan god. There is, of course, nothing wrong with that, but some people may prefer more secular or religion-neutral expressions of the days of the week. Therefore the Earth Epic Calendar offers this as an option.
The days are named as follows:
In most years, three out of the four Quarters have ninety-one days (this is two out of four Quarters during leap years). Because 91, unlike 30 or 31, is evenly divisible by seven, the first day of each Quarter will start on the same day of the week. Because Northlight for the next 5,000 years will have 92 instead of 91 days, Westlight 0 will fall one day of the week forward from Northlight 0. Day 0 of each Quarter will then fall on the same day of the until the next Westlight 0 unless the next year is a leap year. Since Eastlight currently has an extra day during leap years, the Northlight 0 following the leap day on the last day of Eastlight will fall also one weekday forward from previous Quarters. Then the next Quarter, Westlight 0 will fall one weekday forward from Northlight as usual, meaning that it will begintwo weekdays forward from the previous Westlight.
It will be up to future generations to decide whether to continue with a seven-day week. The seven-day week is not inherently critical to the structure of the Earth Epic Calendar. Such a system exists to accommodate conditions as they exist in the early 3rd millennium CE/mid- to late Millenium 11 EE.
Instead of seven day weeks, one option would be to divide the quarter into roughly nine units of ten days each. As such, it would not be necessary to even have named days of the week, as the last digit of the date would be sufficient to determine the day of the week. This was tried during the French Revolution, but was unpopular largely due to laborers only getting 1 1/2 days of rest out of 10. The current five day work week means that 28.5% of the week is set aside for rest (though, unfortunately, many workplaces require six and even seven days of work per week.) A strong argument could be made for having three or even four out of the ten days being set aside for rest and recreation. But this is for society to decide for itself in the future.