The day of 7 Adar is the day of Moshe Rabbenu’s death, and many have the custom to observe a fast on this day. Others have the custom of learning special material in the synagogue on the night of 7 Adar in commemoration of Moshe Rabbenu’s passing.
In truth, the precise date of Moshe’s passing is subject to debate. The Midrashic text Yalkut Shimoni (Yehoshua, chapter 5) cites the view of Rabbi Eliezer who held that Moshe passed away on 7 Shebat, and not 7 Adar. Of course, the accepted view is that he passed away on 7 Adar. However, even within the accepted position we find different views concerning Moshe’s death. Rabbi Yehoshua maintained that Moshe died on 7 Adar during an ordinary, twelve-month year, when there was only one Adar. Rabbi Elazar Ha’moda’i, by contrast, claimed that Moshe died during Adar Rishon of a leap year, when there were two months of Adar. The Gemara in Masechet Kiddushin (38a) comments that Moshe died thirty days before Beneh Yisrael began their preparations to cross the Jordan River, which occurred in Nissan. Clearly, then, according to the Gemara, Moshe died either on 7 Adar of a regular year, or on 7 Adar Sheni during a leap year.
This debate, of course, will affect the date of the observance of 7 Adar during a leap year. If Moshe died on 7 Adar of an ordinary year, or on 7 Adar Sheni of a leap year, then the observance should be held in Adar Sheni. According to Rabbi Elazar Ha’moda’i, however, Moshe died during Adar Rishon, in which case the observance should be held on 7 Adar Rishon.
Practically speaking, those who observe 7 Adar should, in a leap year, observe the occasion twice, both on 7 Adar Rishon and on 7 Adar Sheni, in order to satisfy all views.
Regarding the commemoration of a loved one’s Yahrtzeit, the Shulhan Aruch rules that if a parent passed away, Heaven forbid, in Adar, then in a leap year the Yahrtzeit is observed during Adar Sheni. If the parent passed away during Adar Rishon in a leap year, then in regular years the Yahrtzeit is observed on that date during the single month of Adar, and in leap years, the Yahrtzeit is observed during Adar Rishon. If the parent passed away during Adar Sheni of a leap year, then the Yahrtzeit is of course observed in a leap year during Adar Sheni.
Summary: There are those who observe a fast and conduct a special learning session on 7 Adar, the Yahrtzeit of Moshe Rabbenu. In a leap year, these customs should be observed both on 7 Adar Rishon and on 7 Adar Sheni. An ordinary Yahrtzeit for a loved one who passed away during Adar is observed in a leap year in Adar Sheni. Of course, if the loved passed away in a leap year in Adar Rishon or Adar Sheni, then the Yahrtzeit is observed during a leap year in that same month.
