Albert Barnes Commentary 1 Chronicles 9:34

"These were heads of fathers` [houses] of the Levites, throughout their generations, chief men: these dwelt at Jerusalem." — 1 Chronicles 9:34 (ASV)

Chief throughout their generations - The superintendents were the genealogical heads of the different Levitical divisions, and each exercised special authority over those of his own family line. This hereditary principle prevailed not only in the high priesthood but also in the priestly offices of the second rank.