IWC Schaffhausen PORTUGIESER PERPETUAL CALENDAR Mode D'emploi page 26

These 29.530588402 days which elapse between one full moon and the
next are arrived at as follows:
Expressed in simple terms, a month is the duration of one orbit of the moon
around the earth. Depending on the point of reference from which we ob-
serve the orbit, the months can have different lengths. No other celestial
body has an orbit as complicated as that of the moon. One may well imagine
that a month is over once the moon has completed 360 degrees in its orbit
around the earth. It is then back at the same point in relation to the sky. This
month (known as the sidereal month) lasts for precisely 27 days, 7 hours,
43 minutes and 11.5 seconds. However, the earth has also continued on its
path around the sun. In order to occupy the same position in relation to the
sun, the moon must continue on its orbit a little beyond 360 degrees. There-
fore this month lasts longer, and we can only use this month for calculating
the length of the months and for the moon phase watch. It is known as the
synodic month. This period lasts for 29 days, 12 hours, 44 minutes and
2.9 seconds, or 29.530588402 days. If we now divide the length of the year
(365.2422 days) by this period, the rounded result is 12.368 orbits a year. The
aforementioned complicated orbit of the moon means that the calculated
(mean) lengths of the month in the case of the synodic month may deviate by
up to 6 hours.
All of this is taken into account in the complicated mechanism of the per-
petual calendar in your watch. It now shows you the correct moon phase
mechanically with a deviation of only one day in 577 years.