LuniSol - Moonth 5, Day 22
Metonic - Year 17, Lunation 203, Day 14
Dreamspell - Blue Magnetic Eagle (1 Men), Kin 235
Mayan Tzolk'in - 5 Manik (Yellow Rhythmic Star) - Kin 188
Mayan Ha'ab - 11 Uo
The Metonic cycle is the best thing since sliced bread! Ok, well, sorta. The Metonic cycle is equivalent to 235 synodic lunar months (e.g. new moon to new moon or full moon to full moon) or 19 tropical years (spring equinox to spring equinox). This means that on your [insert multiple of 19]th birthday, the sun and moon will be exactly where they were in the sky when you were born.
The universe is perfect in its own way but a lunar month does not go evenly into a solar year. All lunisolar calendars must be adjusted to keep in sync with the seasons. I've complained about our current Gregorian calendar previously: the months are arbitrary lengths and no longer coincide with any lunar cycle.
I'm going to attempt to use 3 different cycles.
The tropical lunar month and the tropical solar year
A tropical lunar month is about 28 days. The tropical solar year is 365.25 days. This gives us 13 months of 28 days + 1 extra day (2 extra days during leap year). The first extra day will be Yule Eve and the second one will be 2/29. Extra days do not belong to a month or week; they are a "day out of time."
This is comprised of 19 lunar years of unequal lengths. A lunar year varies from 354 to 384 days. A leap month is sometimes inserted to keep pace with the seasons. Chinese calendar is great example of this.
Mayan 13:20 count
I have 2 apps for this, Dreamspell & Tzolk'in. Dreamspell is a modern interpretation while Tzolk'in is the authentic count of the Mayan. It takes 52 tropical years for a Tzolk'in day (called kin) to fall on the same day in the Gregorian calendar.
The Dreamspell combines the Mayan 13:20 with the tropical lunar month & solar year. However I don't agree with the Dreamspell's yearly start date of 7/26, the heliacal rising of Sirius. I like the winter solstice better.
Whew! That's a lot! Following the lunar cycle is the easiest. I'm getting good at determining where the moon would be in the sky during the different phases. Full moon is better seen from my front porch whereas the waning crescent is viewable from my backyard.