19 Tooth Lunar-driven Cycle

Dear Karl and Calendar People,

Here is the basic cycle my device attempts to use:

The basic unit of the system is the lunation, periodically calibrated
by observation of eclipses.
A subunit of a lunation is what I call a tooth, because my device uses
a gear for this purpose. The lunation is divided into 19 teeth.

The shortest useful lunisolar cycle consists of 18 Metonic cycles with
an adjustment. In this period of time there are:

80370 teeth
4230 lunations
342 1/235 years

The number of years is a fraction because the solar device is adjusted
by one tooth in this frequency. The cycle completes an integer number
of years in:
18886950 teeth
994050 lunations
80371 years

Note that due to the observational nature of the device, it is immune
from changes id delta-T and should be quite stable as long as the
moon's orbital period remains stable.

I need to revise my illustration that I posted previously. I will do
so when I have time.

Victor