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Machzor is a cycle, deriving from the root chazar, to return. New olim to Israel who studied at the same ulpan might ask each other which machzor (year group) they were in to see if they were there at the same time.
The most well-known machzor is the prayer book for the High Holy Days. In fact, all prayer books for specific festivals are called machzorim, for they contain the prayers that we say cyclically around the year.
The Bodleian and British Libraries each own a manuscript of the early 12th-century Machzor Vitry, named after the small French town in which its author, Rabbi Simcha ben Shmuel, lived. Machzor Vitry includes all the prayers for the year as well as customs and laws - mostly according to Rashi's rulings. Machzor Vitry is the basis for Ashkenazi traditions and differences between them and the Sephardic tradition.
The machzor accompanies us throughout the High Holy-Days, traditionally the most spiritually intense times of the Jewish year. One of the great yeshivah heads of the 20th century, Rabbi Yitzchak Hutner, challengingly remarked: "A Rosh Hashanah and Yom Kippur machzor without tear stains is like a Pesach haggadah with no wine marks - you can tell that it hasn't really been used."