I can date my first colour photos of the sky back to 1976, when my interest in capturing the Moon above a cityscape sprouted into a lifelong obsession. In retrospect, I am a bit surprised that it took almost a decade of living in Edmonton before I experienced the unexpected coincidence of a moonset and reflected sunrise pictured above. I was simply wanting the post-sunrise moonset so I could catch both the Moon and landscape properly exposed in a single shot (on slide film!).
Year after year I tried to repeat this wonderful observation (which included the ever uplifting dawn chorus from the birds at springtime). Despite improvements in planning tools, I was thwarted by bad luck with the timing of the weather or life. I quickly discovered that I had two chances per year, at the equinoxes. Even giving myself +/- a day on either side of full phase didn't help because its position on the ecliptic (and particularly declination) carried it 7 or 8 degrees to either side. The slowly shifting orbit modified its height above or below the ecliptic plays a minor role here. Clouds are a much greater nuisance, because to see both the setting Moon and rising Sun requires a block of clear skies across 10 degrees of longitude, the width of Alberta.
In the end, it took me 19 years, almost exactly to the day. When I saw the date of my first image I grinned: this is an anniversary of one Metonic cycle. My pattern-obsessed good friend Bruce McCurdy is a fan of the Metonic cycle, pointing it out now and then to myself and members of the Royal Astronomical Society of Canada and having written a piece about it in the Journal of the RASC, April 2001 and at other times for his "Orbital Oddities" column.
Our Observer's Handbook features a contribution by long term editor Roy Bishop on p125 of the 2019 edition, in the "Eclipses" section, where he writes "[it is] a cycle known to astronomers in ancient Babylon, and that was discovered independently around 430 BCE by Meton, a Greek astronomer."
It's a bit like watching the big and small hands of a clock overlap after some turns. Think of the big hand like the lunar month (29.5 days), and the small hand like a year. After 354 days, the Moon has cycled 12 times, but we're 11 days short of a year (12 for a leap year). Advance another year, we are 22 days short; another and it's 33 days, close to a lunar month, but not quite! It takes 19 years before the cycles line up perfectly (shifted by a day thanks to the leap year), a total of 6940 days.
You'll notice that the Moon is not quite in the same position in the images. This is mostly due to the oval shape of its orbit (that sets the speed), which has its own cycle. Buried in the details, one can find that a year is not 365 and 1/4 days, but 365.242189 equinox to equinox, while a lunar month is 29.530589.
I've been waiting a long time to catch the full Moon setting as the rising Sun reflects off buildings near the Alberta Legislature, so it is most fitting that I achieved this on a Metonic anniversary.