According to the Halacha we do not say Tachanunim for the first 13 days of the month of Sivan. The reason is that the days before Shavuot, since it was preparation for the holiday, so it was a holiday in itself. The Sheloshet Yime Hagbalah, the 3 days specifically before the Matan Torah, they prepared, so therefore we say Yehi Shem up to the Holiday. On the holiday itself of course, there is no Tachanunim. And then we have 7 days, according to the Gemara, if the person didn’t bring his Korban, he can make it up after the holiday. So technically, if the holiday was on the 6th of Sivan, we say Yehi Shem until the 12th. That would be 7 days. However, the Minhag in Hallab was to say Yehi Shem an extra day. Actually the 13th day of Sivan is a Machloket in itself amongst the Rabbis. Are you supposed to say Yehi Shem or not? Because the question is; ‘Is it 7 days from the 6th of Sivan or 7 days from the 7th of Sivan?’ Of course we have 2 days Yom Tov, so the 13th already is in question. But the Minhag in Hallab anyway is to say Yehi Shem on the 13th of Sivan.
The basis for this custom, of the added day of Yehi Shem is because there was a miracle that took place in Hallab. There are different versions of a story. What happened? They call it the Miracle of Nusan. Nusan was a Christian boy that was taken, and a libel was then placed against the Jewish people claiming that we took him. And then he was found alive. There was a Machloket; if he was found in Nissan or Sivan. But the extra day that we say Yehi Shem, was to commemorate that miracle that we were saved from a blood libel.
