The period of the counting of the Omer is exalted indeed and filled with sanctity, as the Ramban writes in his commentary on Parashat Emor that the days between the holidays of Pesach and Shavuot, i.e. the Omer counting period, retain the sanctity of Chol Ha’Moed and are not days of national tragedy and mourning like the Three Weeks between the Seventeenth of Tammuz and the Ninth of Av. Maran zt”l would mention this Ramban so that that people would not mistakenly think that these were ominous days for the Jewish nation.
Nevertheless, a terrible occurrence befell the Jewish nation during this time, as the Gemara (Yevamot 62b) recounts: “Rabbi Akiva had twelve thousand pairs of students and they all died between Pesach and Shavuot because they did not treat each other respectfully.” They all perished from Askara (an agonizing illness leading to acute respiratory failure). This means that Rabbi Akiva had a tremendous, flourishing empire of Torah which served to disseminate the Torah throughout the Jewish nation and would they remain alive, their Torah and that of their descendants and pupils would have served to illuminate the torch of Torah for generations on end. However, it was decreed in Heaven that they all die during this period.
The Responsa of the Geonim (the Sages of Israel of the generation immediately preceding that of the Rishonim) mention that because of this tragic event, the entire Jewish nation observes the custom of not getting married during this period of time as a sign of mourning. It is also customary not to wear new garments, take haircuts, or listen to music during this time.
Nevertheless, we do not observe these mourning customs throughout the entire duration of the Omer period; these customs are only observed until the 33rd or 34th day of the Omer, for the Sefer Ha’Manhig and other great Rishonim write that Rabbi Akiva’s students ceased dying on the 33rd day of the Omer. Indeed, the Rama (in his gloss on Chapter 493) rules that from the 33rd day of the Omer, it is permissible to hold weddings.
On the other hand, the Sephardic custom is to continue these mourning customs until the 34th day of the Omer and it is forbidden to get married on any of these days. The reason for this is based on what the Sefer Ha’Manhig has written in the name of Rabbeinu Zerachya Ha’Levi who had found in any old manuscript that had come from Spain that the students of Rabbi Akiva died from Pesach until “half of Shavuot.” This means that the thirty days preceding the holiday of Shavuot are divided in half, i.e. fifteen days before Shavuot, and on this day, Rabbi Akiva’s students ceased dying.
Other Rishonim concur and write that if we subtract fifteen days from the forty-nine days between Pesach and Shavuot, the product will be thirty-four. It is nevertheless permissible to get married immediately from the morning of the 34th day of the Omer, for the rule regarding the laws of mourning is that “a portion of the day is likened to the entire day.” Thus, since a portion of the 34th day of the Omer has already passed, one need not observe the mourning customs any longer.
It is permissible to hold an engagement party during the Omer counting period. If the actual Shidduch has been closed at the time of the celebration (as opposed to at an earlier time), there are those who rule leniently and allow for music at this party as well.