“Concerning the divisions of the porters: Of the Korhites was Meshelemiah the son of Kore, of the sons of Asaph. Meshelemiah: or, Shelemiah, ver.14. Asaph: or, Abiasaph Chap.9.19.& 6.37.”
Or, courses, or turns. This Asaph was not the notable musician, but another of that name called also Ebiasaph, 1 Chron. 6:23 , 37 and 9:19 and also Jasaph.