Top 10 Metonic Intervals/Subcycles
The Metonic cycle is a cycle of approximately 19 tropical years where the Moon phase occurs around the same day of the Gregorian, Julian, and other common calendars.It consists of 235 synodic months (235 x the moon phases as seen from Earth repeat) or 12 periods of 12 synodic months + 7 periods of 13 synodic months.
Tropical years are the years that are referenced they're crucial for the phases since our Moon reflects sunlight.
The full cycle is made up of 19 intervals/subcycles, where the Moon phases occur at the nearest time in respect to the background sky and calendar dates.
The names for these intervals/sub-cycles aren’t publicly on the mainstream, but are Greek prefixes based on the number of years they approximate.
The period within 1 tropical year where the moon phases occur over 11 days earlier.
It consists of 12 synodic months and is more stable than an Earth year.
The period over 2 tropical years where the moon phases occur around 7 1/2 days later.
It consists of 25 synodic months, or 2 lunar years + 1 synodic month.
It also approximates 2 synodic periods of Uranus, allowing the moon phases to synchronize with Uranus.
Half of a diëteris equals a subcycle of opposing lunar phases taking place around 3 3/4 days later after 1 year, lasting 12 1/2 synodic months.
The period within 3 tropical years where the moon phases occur around 3 days earlier.
It consists of 37 synodic months, which intercalates an extra synodic month over 3 lunar years.
It's also nearly an integer number of weeks, meaning such phases occur toward the same day of the week, though overtime, the offset with the weeks is more noticeable.
It equals 1/2 hexaëterides, which's 74 synodic months (resulting in moon phases around 6 days earlier in 6 tropical years).
It also equals 1/3 of an enneaëteris, which's 111 synodic months (resulting in moon phases around 9 days earlier in 9 tropical years).
It equals 1/4 dodecaëterides, which's 148 synodic months (resulting in moon phases around 12 days earlier in 12 tropical years).
It also equals 1/8 of 3 octaëterides, making up 297 synodic months (resulting in moon phases occur around 4 1/2 days later in 24 tropical years as that's 1 Metonic cycle + a pentaëteris).
The period within 4 tropical years where the moon phases occur around 13 1/2 days earlier.
It consists of 49 synodic months, meaning the addition of a lunar fortnight (1/2 synodic months) creates a half-octaëteris.
This's why the tetraëteris was useful for scheduling the Ancient Olympics as the events were between 49 and 50 synodic months apart.
The period over 5 tropical years where the moon phases occur around 4 1/2 days later.
It corresponds to 62 synodic months, intercalating 2 synodic months over 5 lunar years, and equaling 1/2 decaëterides, which's 124 synodic months (resulting in moon phases around 9 days later in 10 tropical years).
The period within 6 tropical years where the moon phases occur around 6 days earlier.
It equals 1/2 dodecaëterides, which's 148 synodic months (resulting in moon phases around 12 days earlier in 12 tropical years).
It also equals 1/4 of 3 octaëterides (an icositetraëteris, where the moon phases occur around 4 1/2 days later in 24 tropical years).
The period over 7 tropical years where the moon phases occur around 12 days later.
Amazingly, if you subtract a lunar fortnight, you get a subcycle of 86 1/2 synodic months of opposing phases occurring around 2 1/4 days earlier, and if you double that, you get a tetradecaëteris, which's 173 synodic months and ends around 4 1/2 days earlier in the calendar with the same phases.
The period over 8 tropical years where the moon phases occur around 1 1/2 days later.
It consists of 99 synodic months or 8 1/4 lunar years.
Plus, it approximates 5 synodic and 13 sidereal periods of Venus, meaning the moon phases every subcycle closely synchronizes with Venus.
It's been used as the calendar for the Olympic games in Ancient times, as the games in 49 synodic months would lead to games in 50 synodic months, and then 49 and 50 again vice versa.
Though if you add 1 synodic month over this, you get an eclipse cycle of 100 synodic months, meaning in 8 years, eclipses happen over 1 month later.
The period within 9 tropical years where the moon phases occur around 9 days earlier.
It consists of 111 synodic months.
Interestingly, if you add half of a synodic month (such as a lunar fortnight), you get an eclipse cycle of a half-saros, half of a saros (which in turn is the most famous eclipse cycle), leading to opposing eclipses on the same orbital node over 5 1/2 days later.
The period over 10 tropical years where the moon phases occur around 9 days later.
It consists of 124 synodic months, though if you continue that or subtract 1 synodic month (creating 123 synodic months), you get a period at the right circumstances for eclipses, though even better if you remove a lunar fortnight (1/2 synodic months) leading to opposing eclipses over 5 1/2 days earlier.
It is the antidote of the enneaëteris.
The period within 11 tropical years where the moon phases occur around 1 1/2 days earlier.
It consists of 136 synodic months and is fairly close to 12 synodic periods of Jupiter, meaning the moon phases repeat near synchronization with Jupiter in 11 years.
Though if you subtract 1 synodic month, you get an eclipse cycle known as a tritos, which really comes in more proper synchronization with Jupiter.
In 11 years, eclipses happen over 1 month earlier.
It is the antidote of the octaëteris.
The period within 12 tropical years where the moon phases occur around 12 days earlier.
It consists of 148 synodic months as it's a tritëteris x 4.
It is the antidote of the heptaëteris.
The period over 13 tropical years where the moon phases occur around 6 days later.
It consists of 161 synodic months, adding a lunar leap year over a dodecaëteris and adding a decaëteris over a triëteris.
It is the antidote of the hexaëteris.
The period within 14 tropical years where the moon phases occur around 4 1/2 days earlier.
It consists of 173 synodic months and adds a triëteris over a hendecaëteris.
It is the antidote of the pentaëteris.
The period over 15 tropical years where the moon phases occur around 13 1/2 days later.
It consists of 186 synodic months and is the antidote of the tetraëteris.
The period over 16 tropical years where the moon phases occur around 3 days later.
It consists of 198 synodic months and is twice the equivalent to an octaëteris.
It is the antidote of the triëteris.
The period within 17 tropical years where the moon phases occur around 7 1/2 days earlier.
It consists of 210 synodic months is the antidote of the diëteris.
The period over 18 tropical years where the moon phases occur over 11 days later.
It consists of 223 synodic months and, in fact, is the same as a Saros cycle, which's the best known for eclipses.
Meaning every 18 years, eclipses occur over 11 days later, though there's an 8 hour forward shift, which's why it takes 3 x this period to get eclipses toward the same terrestrial longitude, forming an exeligmos (meaning revolution).
It is the antidote of the lunar year.
The full Metonic cycle.
Known by Meton of Athens since 432 B.C.E.
The period over 19 tropical years where the moon phases occur around the same day.
It consists of 235 synodic months and intercalates 7 synodic months over 19 lunar years.
Since it's 110 hollow months + 125 full months of the Moon, it yields a short eclipse series of up to 5 events, making up the Callippic period.