Was the Gregorian calendar based on the moon?

Although the Gregorian calendar has "months", it is not in any way governed by the phases of the moon. It is strictly a solar calendar, so its emphasis is to remain in sync with the solstices and equinoxes, the characteristics of the Earth's orbit of the sun. Only lunar calendars, like the Muslim calendar, and lunisolar calendars, like the Jewish calendar, are based on the phases of the moon, with each month beginning at the time of the new moon.