The moon phases refer exclusively to the Synodic month, but the necessary time for a full moon revolution round the Earth is approximately 2 days small. How does this happen?

Earth moves: it revolves round the Sun. Therefore, the Earth has moved during the necessary time for the Moon to make a full circle round the Earth (cf. points E and E1 in figure). When the Moon has moved to point S, its projection on the sky is the same with the corresponding star on the projection point M. Despite its full revolution in the zodiac, the Moon has to move on the small arc S – M1 to synod with the Earth and the Sun (–> synodic month).
The necessary time interval for Moon to make a full revolution round the Earth and to have the same projection on sky, is called Sidereal month. Its duration is 27,32166 days.
If we study the complete motion of Moon and Earth round the Sun during a year, we will see that the Moon does not return to some constant point, but its motion is dragged by the Earth and looks like a “lace”.

By observing the motions in the figure from right to left,* we will see that Earth drags the Moon during the New Moon phase behind, according to the earthly orbit round the Sun. The Moon precedes the Earth from the Full Moon and afterwards and drags the Earth until the next New Moon. This change of positions, which looks like a counterweight motion, is essentially the Eternal Dance which balances life on Earth.
The Moon orbit plane diverges unto ± 5ο 8΄ from the plane which is formed by the Earth orbit round the Sun. By necessity, there are section points of the two planes. These points are called nodes. When the Moon crosses the horizon moving towards the northern hemisphere, the node is called ascending. On the contrary, when it crosses the horizon moving towards the northern hemisphere, the node is called descending. The duration between two crossings from the same node of the orbit, is called Draconic month or nodical month and is equal to 27,2122.
The Moon moves daily approximately 13ο towards East. The Sun moves daily towards East too, but only 1ο. Therefore, the phaenomenal delay of 12o makes the Moon to rise or set, in the mean, 51 minutes later from the previous day. This difference is not constant. The difference fluctuates in the geographical latitudes of the northern hemisphere between 25 and 75 minutes – according to year season.
The Moon retardation is most apparent during the Full Moon. The biggest retardation occurs during the nearest Full Mooon to the spring equinox (21 March); it can be as big as 1 hour and 20 minutes. On the contrary, the Moon retardation has its minimum during the Full Moon of the autumn equinox (23 September): only 13 minutes.
The height of Moon in the horizon is influenced by the year season. The Full Moon crosses low the horizon in the summer, when the Sun moves high in the sky. On the contrary, the Full Moon crosses near the zenith with bright light in the winter, when the Sun moves in the northern part of the ecliptic. Therefore, the Greek proverbs about the brightness of the January moon are scientifically justified: the January moon made the night almost day; the daughter sees the January moon and embroiders.

* The direction in the figures is the clockwise one as accepted internationally in the scientific books.