The original month of Ramadan/Tevet (December in the Gregorian Calendar) which was corrupted into "Saturnalia" and the "Feast of Fools" came to conclusion through the 8 day celebration of Kalenda (laylat ulQadr) described in the Talmud as the Fast of the Tenth Month established by Adam for the children of Noah, following the advent period of solemnity and fasting. The original Kalenda (Noachite New Year) celebration following immediately on from Saturnalia began with the vigil on the eve of Dec 25th (originally just after the winter solstice) and lasted until Jan 1st. The fact that it is still remembered today by high-church Christians is a still lasting testimony to the fact that Christianity's origins were once regarded as a legitimate Noachite extension of Judasim. The Christmas Proclamation of "Kalenda"  otherwise mentioned only in the Talmud and Mishna (Avodah Zara 8a), is announced at the conclusion of the prayer vigil held just before midnight mass at Christmas Eve. It may also be included in the Midnight mass itself immediately before the Gloria.
There are some similarities between the old Muhammedan Calendar and Umar's Hijri Calendar visible even today despite some position changes. For example the month names: Sivan/Ṣafar (Gemini), Elul/alŪlā (Virgo), Cheshvan/Shaʿbān, and Shevat/Shawwāl. Also, the major Hajj of the year is in the originally spring month of Dhū al-Ḥijja exactly like Passover in Aviv (spring). This is followed by the fasting of Iyyar/Muḥarram (Taurus) commemorating the deliverance from Egypt. Moreover, the 7th month is still sacred in both. Finally, Ramadan corresponds to the Gregorian Calendar's month of December of course.
It is therefore also known that Dhū al-Ḥijja corresponds to what is now March in the Gregorian Calendar, Muḥarram corresponds to April in the Gregorian Calendar, Ṣafar corresponds to May in the Gregorian Calendar, and the 7th month corresponds to September in the Gregorian Calendar.