Albert Barnes Commentary Psalms 81:1

"Sing aloud unto God our strength: Make a joyful noise unto the God of Jacob." — Psalms 81:1 (ASV)

Sing aloud unto God our strength - The strength and support of the nation; He from whom the nation has derived all its power. The word rendered "sing aloud" means to rejoice, and then, to make or cause to rejoice. It would be appropriate for a high festal occasion, where music constituted an important part of the public service. And it would be a proper word to employ in reference to any of the great feasts of the Hebrews.

Make a joyful noise - A noise indicating joy, as distinguished from a noise of mourning or lamentation.

Unto the God of Jacob - Not here particularly the God of the patriarch himself, but of the people who bore his name—his descendants.