Albert Barnes Commentary 1 Chronicles 25

The captains of the host — Rather, “the princes” of 1 Chronicles 23:2 and 1 Chronicles 24:6.

Under the hands of Asaph... — That is, “under the direction of Asaph,” who himself “prophesied,” or performed the sacred services, “under the direction of the king.”

To lift up the horn: Some interpret this phrase literally, suggesting that Heman and his sons played the horn during musical services. However, there is no other evidence that the horn was used in this way.

A more probable explanation is that the phrase belongs to the next clause. There, it would follow the word “God,” meaning that God, in order to “lift up the horn” of Heman (that is, to increase his dignity), gave him fourteen sons and three daughters.

With their brethren - that is, "with others of the tribe of Levi." Each son of Asaph, Jeduthun, and Heman was at the head of a band of twelve skilled musicians, consisting partly of his own sons and partly of Levites from other families (1 Chronicles 25:9–31). The 24 band leaders, together with their bands, formed a body of 288 persons (24 x 12 = 288).

In addition to these, we also read of over 3,700 singers. They were probably divided, like the trained musicians, into 24 courses, which would have contained about 155 members each (1 Chronicles 23:5).

As well the small as the great - Compare 1 Chronicles 24:31. The lot was not applied indiscriminately to all 24 courses, but was only used to determine which course of Asaph, which of Jeduthun, and which of Heman should be taken on each occasion. Asaph was given precedence over his brothers, and his four courses were assigned the first place and then each alternate place. Jeduthun took rank next and received alternate places, first with Asaph and then with Heman, until his courses were exhausted. After this, all the later places necessarily fell to Heman, whose courses continue without interruption from the 15th.