The Moon is always full of surprises! I have been making simple observations of it for almost thirty years, and they have allowed me to get pretty accurate values of the synodic and sidereal months. These involved just naked-eye observations. More recently I have been using photographic methods, first to measure how the angular size of the moon varied and, in just the last year or so, how its angular distance above or below the ecliptic changed. From the first set of measurements I can find a value for the anomalistic month, and from the second I can find the draconic month. But these are works in progress. There are many small contributions to the Moon’s orbital motion that cause small variations in all of this periods, and the only way I have of sorting them out is to extend my measurements over as long a time as possible. Have patience!
This shows the new moon, photographed on August 4th, 2016. Just visible to the right of the Moon and slightly above is the planet Mercury.