R’ Safra [54b bottom]: When Rosh Chodesh (the first day of the month) falls out on Shabbos, we sing the songs of both Holy days, but we do Rosh Chodesh’s first. This is done to publicize the fact that this day was in fact the start of the new month [it even pushes aside the law of: Tadir V’she’ainu Tadir, Tadir Kodem (prioritizing whichever is more frequently observed)].
**We see such amazing HASHGACHA PRATIS (Divine Providence) again TODAY, as we specifically read Parshas Hachodesh (the special once a year reading about the New Month) exactly Today when we mentioned the Rosh Chodesh law in Today’s Daf Yomi.
T’s Lesson: Every month the moon waxes and wanes and we never for a moment doubt that it will go through its cycle again. We know Hashem sets this ‘routine.’ The moon represents the Jewish people. We have been persecuted, attacked, and beaten down throughout history, and sometimes to the point of near extinction (i.e. Purim, The Holocaust etc.) However, just as the moon is about to vanish it starts to grow larger and shine brighter. So too with the Jewish people. Hashem promises eternal protection and guidance no matter how difficult the times (after Purim we gained more power, prestige and victory, after the holocaust the state of Israel was born). Hashem will never let us completely go, even when we must (for some ultimately good reason) endure harsh times. This message needs to be brought to the forefront of our minds at every opportunity. Therefore, we set the song of the Rosh Chodesh to be sung before the song of the Shabbos (symbolizing true peace and harmony).