Rashi on Numbers 8:11/רש"י על במדבר ח׳:י״א

1והניף אהרן את הלוים תנופה AND AARON SHALL MAKE A WAVING WITH THE LEVITES — just as the guilt offering of the leper (to whom the Levites are compared in some respect; cf. Rashi on v. 7) required waving whilst alive. — Three times is the command of waving the Levites mentioned in this section (vv. 11, 13, 15): the first refers to the sons of Kohath; therefore (because it is they who are referred to) Scripture adds with regard to them, “that they may execute the service of the Lord” — for it was upon them (the sons of Kohath) that the service of the most holy objects: the Ark, the table, etc., devolved. The second refers to the sons of Gershon, and therefore Scripture adds with regard to them, “a waving for the Lord”, for upon them devolved the service of the holy (though not the most holy) objects: the hangings and the catches which were visible in the Holy of Holies. The third refers to the sons of Merari.