It is important to remember that Quarterly is the first day of the calendar quarter, not "three months between elections". If someone is elected on Dec 15, the elections will run again on Jan 1.
Aren't there delays in cases where the elections happened too close to the planned elections? I may be making this up, but I thought I noticed that in monthly elections, if an unscheduled election happens near the end of the month, a new election does not take place. I assumed it was the same with quarterly elections. But yes indeed, theoretically, the quarterly elections are on set months, and not "three months between".
