Tetraëteris 

A tetraëteris is the Greek name for the period in 4 tropical years where the Moon phase occurs 2 weeks earlier, defined as 49 synodic months, 52.961595389901795 sidereal months, 53.174596199249 draconic months, 52.513969931831795 anomalistic months, and 1,446.998810185187 days.

Though if you intercalate it, you get 50 synodic months, 54.04244427541 sidereal months, 54.25979204005 draconic months, 53.58568360390999 anomalistic months, and 1,476.52939814815 days.

If you go halfway between 49 and 50 synodic months, you get 49 1/2 synodic months, which’s 53.5020198326559 sidereal months, 53.717194119649506 draconic months, 53.0498267678709 anomalistic months, and 1,461.7641041666686 days, which makes up half of an octaëteris, leading from a new/full moon to a full/new moon less than 1 day later.
Which’s just about 4 full synodic revolutions of Uranus, and leads from a new/full moon to a full/new moon within 15 days later.

The tetraëteris has been used for the Olympic games in that if the Olympic games of a games occurred 49 synodic months after the last events, then the next games would occur 50 synodic months later, then 49 more later, and then 50, vice versa, as 49 + 50 = 99 synodic months, making an octaëteris.

Ben: If we didn't have COVID-19, the Tokyo Summer Olympics would've occurred in 2020.
Gregory: Well yeah.
Ben: Because the French Summer Olympics is happening between July 26 and August 11 in 2024.
Gregory: Ikr?
Ben: Because the Greeks knew the Moon was useful for calculating the Olympics.
Gregory: How do you know that?
Ben: Because they used the tetraëteris and octaëteris calendars.
Gregory: Interesting.
Ben: Well the London Summer Olympics took place between July 27 and August 12th in 2012 and the Rio Summer Olympics took place between August 5 and 21 in 2016.
Gregory: Looks like modern adjustments for the Olympic calendars.
Ben: Yeah.

Tetraëteris by gregben October 2, 2023