What is the significance of the notes played on the Shofar? And why does the rabbi sometimes add additional notes which are not in the laypersons prayerbook?
The Torah itself mentions the Tekiah- the simple call of the Shofar, and the Teruah- the ululating sound. There are two opinions as to what kind of sound the Torah’s Teruah is- three longer wails (Shvarim) or more staccato cries (what the siddur calls Teruah). This is because both sounds are crying sounds made at different times in a person’s cry. Our Shofar blowing on Rosh HaShana includes, therefore, all three sounds. Although the Torah gives no reason for the Mitzva, the Rambam tells us that the sound of the shofar awakens us to repentance- teshuva. HaRav Kook explains that the simple Tekiah at the beginning and end of each series of blowing, punctuated by the ululating cries, parallels the basic sanctity of a Jewish life that is expressed through the ups and down of actions and character until, at the end, the full measure of that sanctity is revealed. There should be no difference between your Machzor and that of your rabbi. He may instruct the person blowing the shofar to blow some notes again when he feels they were not done right the first time.