Charles Ellicott Commentary 1 Chronicles 6:39-43

"And his brother Asaph, who stood on his right hand, even Asaph the son of Berechiah, the son of Shimea, the son of Michael, the son of Baaseiah, the son of Malchijah, the son of Ethni, the son of Zerah, the son of Adaiah, the son of Ethan, the son of Zimmah, the son of Shimei, the son of Jahath, the son of Gershom, the son of Levi." — 1 Chronicles 6:39-43 (ASV)

The pedigree of Asaph the Gershonite is traced back through thirteen names to Levi. That of Heman names twenty ancestors for the same period of time. This is one more illustration of the common usage of omitting names in these genealogies.