Jamieson, Fausset and Brown on 1 Chronicles 25:2

2. according to the order of the king--Hebrew, "by the hands of the king," that is, "according to the king's order," under the personal superintendence of Asaph and his colleagues.

which prophesied--that is, in this connection, played with instruments. This metaphorical application of the term "prophecy" most probably originated in the practice of the prophets, who endeavored to rouse their prophetic spirit by the animating influence of music (see on 2Ki 3:15). It is said that Asaph did this "according to David's order," because by royal appointment he officiated in the tabernacle on Zion (1Ch 16:37-41), while other leaders of the sacred music were stationed at Gibeon.