Google Gemini query: I’m finding this 7 day work week pretty arbitrary, and thinking of a calendar system that could make more sense. What about if there were 5 days in a week instead? Wouldn’t that work out to some 73.05 weeks in a year? I see that’s very close to 72, which can then easily be divided into 12 months, but I know it’s not an exact fit. Are you able to propose a new calendar system based on this 5 day week and 72 weeks in a year? I imagine some days might need to be added as exceptions to certain months so the number of days total out to 365.25.

Google Gemini response:

Yes, that's an excellent basis for a calendar. Your calculation is spot on: a 72-week year with 5-day weeks gives you a very tidy 360-day base (72 x 5 = 360). This regularity is the foundation of several proposed "perpetual" calendars. You're also correct that you'd need to add extra days to align with the approximate 365.25 day solar year. Here is a proposed calendar system based on your 72-week idea. Let's call it the "Harmonic-72 Calendar."

1. The Base Calendar (360 Days)

This is the core of the system, built on your suggestion:

• Week: 5 days. (We could name them A, B, C, D, E; or Sol, Luna, Mars, Merc, Jove; or simply 1, 2, 3, 4, 5).
• Months: 12 months.
• Weeks per Year: 72 weeks.

By dividing the 72 weeks evenly among the 12 months, we get a perfectly balanced structure. Since each week is 5 days long, this creates a "perpetual" calendar where every month is identical:

• Every month has exactly 30 days.
• Every month starts on Day 1 of the week.
• Every month ends on Day 5 of the week.
• A specific date (like the 18th) falls on the exact same day of the week every single month, forever.

2. Handling the Solar Year (The Missing 5.25 Days)

Your 360-day base is 5.25 days short of the solar year. We can fix this by adding "intercalary days" (or "extra days") that exist outside of the 12-month, 72-week structure. This preserves the perfect regularity of the main calendar.

The "Year-End" Period: After the last day of the 12th month (Month 12, Day 30), we insert a 5-day special period:

• These 5 days are not part of any week or month.
• They could be a global holiday, a time for festivals, or a period of reflection.
• This brings the total for a common year to 365 days.

The Leap Day: To account for the 0.25, we add one additional intercalary day every four years:

• This "Leap Day" would be added to the "Year-End" period, making it 6 days long.
• This brings the total for a leap year to 366 days.

Summary: The "Harmonic-72 Calendar"

Here is the final structure:

The great benefit is its perfect consistency. You would never again need to ask, "What day of the week is my birthday on this year?" It would always be the same.