Happy new year to the Daat Emet staff!
I wanted to clarify the source of the law for the 100 shofar blasts sounded in the synagogue on Rosh Hashanah.
Rosh Hashanah is another example of how the Oral Torah is a different edition of the law than is the Written Torah. The sages of the Mishnah and the Talmud turned the seventh month (Tishrei) into the first (the new year). The “sacred occasion commemorated with loud blasts” (Leviticus 23:24) they turned into a day of judgment on which people stand in fear before a judge who threatens that three books stand open before Him, and he will determine who shall live and who shall die. (That’s how the religious people amuse themselves with a play, as though they were really standing before a supreme judge and begging for his mercy.) To show you how seriously Jews take this play they’ve directed for themselves we will cite verses in which they explain why so many shofar blasts are sounded, though it is not mandated by the Scriptures.
[In the Scriptures it is written “commemorated with loud blasts”] but we do not know how these loud blasts ought to sound. Targum Onkeles translates it as a cry, so it should sound like a man crying and weeping, but we still do not know if this is like a man moaning from his heart, like a sick man who makes short sounds one after the other, or as a man wailing who makes periodic short cries, or if it is both together — moaning and wailing. Due to doubt we use all the possibilities mentioned (Tur Orach Chaim 590).
See how far people’s obsession for precision in minor details and neglect for the main point goes — in fear and awe they precisely sound blasts yet treat lightly the rights of man (the secular and the gentile).
As to your question of how the 100 blasts were arrived at:
Thirty blasts are sounded due to doubt [I will not detail the calculations, but from Chazal’s exegesis and doubts it is decided that 30 blasts must be sounded]. These thirty blasts are sounded three times over the course of the prayers, and at the end another ten are added to make up the hundred (which is a more recent custom). Why? Because this is what the Shlah wrote!!! (Mishneh Berura 596:2). Thus “commemorated with blasts” became one hundred blasts.
If you want to know how Chazal arrived at Tishrei as the start of the new year, see our words on the portion of Behar.
Wishing you a good new year,