Charles Ellicott Commentary 1 Chronicles 25:6

"All these were under the hands of their father for song in the house of Jehovah, with cymbals, psalteries, and harps, for the service of the house of God; Asaph, Jeduthun, and Heman being under the order of the king." — 1 Chronicles 25:6 (ASV)

All these were under the hands of their father ... and harps. — More accurately, All these were under the direction of their conductor in the music in the house of Jehovah, with cymbals, harps, and lutes (see notes on 1 Chronicles 25:2–3).

According to the king’s order to Asaph, Jeduthun, and Heman. — More accurately, under the directions of the king (and), Asaph, Heman, and Jeduthun. The meaning is that the arrangement of the duties of the minstrels was accomplished by David with the assistance of the three chief musicians, just as, in the classification of the priests, the king had been helped by the chief priests Zadok and Ahimelech (1 Chronicles 24:3).

All these. — That is, the twenty-four leading minstrels, enumerated in 1 Chronicles 25:2–4. Each performed under the supervision of his own “father,” i.e., director.