Harps on the Sheminith - "Sheminith" properly means "the eighth," and has been compared with the modern musical term "octave." Further, "Sheminith" and "Alamoth" are regarded as contrasted, and the harps of Mattithiah and his companions are supposed to have been pitched an octave below the psalteries of Zechariah and his brethren.

The word translated "to excel," is taken as meaning "to lead," and Mattithiah, etc., as leaders of the singers.

On the Sheminith - According to the Targum, this signifies an instrument that sounded an octave, or, according to others, an instrument with eight strings. The Syriac and Arabic have it, instruments to sing with daily, at the third, sixth, and ninth hour; the Vulgate, an octave, for a song of victory: some think the eighth band of the musicians is intended, who had the strongest and most sonorous voices; and that it is in this sense that shelomith and lenatstseach should be understood.

And Mattithiah, and Elipheleh, and Mikneiah, and Obededom, and Jeiel, and Azaziah,.... These six were appointed to sound:

with harps on the Sheminith to excel; which Sheminith some take to be an harp with eight strings, or the beginning of a song, or a musical tone, the bass; see the title of Psalm 6:1.

And Mattithiah, and Elipheleh, and Mikneiah, and Obededom, and Jeiel, and Azaziah, with harps on the {k} Sheminith to excel.

(k) Which was the eighth tune, over which he that was most excellent had charge.

15:21 To excel - Which word may be added to note the excellency of that instrument, or part of musick; or that there was a greater extension or elevation of the voice than in the former. This way of praising God by musical instruments, had not hitherto been in use. But David instituted it by divine direction, and added it to the other ordinances of that dispensation.

on the...: or, on the eighth to oversee

15:1-24 Wise and good men may be guilty of oversights, which they will correct, as soon as they are aware of them. David does not try to justify what had been done amiss, nor to lay the blame on others; but he owns himself guilty, with others, of not seeking God in due order